Human-like Control of Dynamically Walking Bipedal Robots
Human-like Control of Dynamically Walking Bipedal Robots
Human-like Control of Dynamically Walking Bipedal Robots
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<strong>Human</strong>-<strong>like</strong> <strong>Control</strong> <strong>of</strong><br />
<strong>Dynamically</strong> <strong>Walking</strong> <strong>Bipedal</strong> <strong>Robots</strong><br />
Tobias Luksch<br />
Vom Fachbereich Informatik der<br />
Technischen Universität Kaiserslautern<br />
zur Verleihung des akademischen Grades<br />
Doktor der Ingenieurwissenschaften (Dr.-Ing.)<br />
genehmigte Dissertation.
Zur Begutachtung eingereicht am: 26. Oktober 2009<br />
Datum der wissens. Aussprache: 18. Mai 2010<br />
Vorsitzender: Pr<strong>of</strong>. Dr. rer. nat. Rolf Wiehagen<br />
Erster Berichterstatter: Pr<strong>of</strong>. Dr. rer. nat. Karsten Berns<br />
Zweiter Berichterstatter: Pr<strong>of</strong>. Dr.-Ing. Rüdiger Dillmann<br />
Dekan: Pr<strong>of</strong>. Dr. rer. nat. Karsten Berns<br />
Zeichen der TU im Bibiliotheksverkehr: D 386
Acknowledgments<br />
It would have been a tremendous task indeed to write a doctoral thesis without the help<br />
and support <strong>of</strong> many people around me, to only some <strong>of</strong> whom it is possible to give<br />
particular mention here.<br />
In the first place, I wish to express my gratitude to my supervisor Pr<strong>of</strong>. Dr. Karsten Berns,<br />
who made it possible for me to continue my interests in the control <strong>of</strong> walking machines.<br />
He granted all the freedom and support one could wish for with regard to deciding on and<br />
to following the own research directions. During many sessions at late evening hours, he<br />
spared his time for scientific discussions, with topics ranging from specific problems to<br />
future visions. Special thanks go to my second referee Pr<strong>of</strong>. Dr. Rüdiger Dillmann, who<br />
was willing to take the job <strong>of</strong> reading and judging yet another doctoral thesis despite his<br />
tight schedule.<br />
Furthermore, I would <strong>like</strong> to thank several students who helped me in developing and<br />
implementing some ideas <strong>of</strong> this work: the mechanical design <strong>of</strong> the single leg prototype<br />
was done by Florian Flörchinger, Matthias Roth, and Jan Schumann. Zornitza Chiderova,<br />
Dominik Lamp, and Boris Gilsdorf did the first evaluations on various aspects <strong>of</strong> the<br />
simulation <strong>of</strong> bipedal walking. In particular, I am very grateful to Max Steiner, who<br />
did substantial work on the stable standing control and on preliminary integration <strong>of</strong><br />
machine learning methods. In this context, I wish to thank Pr<strong>of</strong>. Dr. Katja Mombaur and<br />
Gerrit Schultz, then her diploma student, for their cooperation in the bmbf project on<br />
optimization-based generation <strong>of</strong> natural fast and stable motion patterns <strong>of</strong> bio-inspired<br />
walking machines, the results <strong>of</strong> which were included in the prototype development.<br />
My infinite gratitude must be expressed to all the colleagues at the Robotics Research Lab:<br />
Christopher Armbrust, Sebastian Blank, Tim Braun, Tobias Föhst, Carsten Hillenbrand,<br />
Jochen Hirth, Yasir Niaz Khan, Lisa Kiekbusch, Jan Koch, Syed Atif Mehdi, Martin<br />
Proetzsch, MaxReichardt, AlexanderRenner, DanielSchmidtandDanielSchmidt, Norbert<br />
Schmitz, Helge Schäfer, Thomas Wahl, Jens Wettach, and Gregor Zolynski. They created a<br />
truly inspiring environment and enjoyable atmosphere to work at. Regarding the realization<br />
<strong>of</strong> this thesis, special thanks go to Martin for valuable discussions on even the most obscure<br />
facets <strong>of</strong> behavior-based control. To Thomas, for solely taking on the research on bipedal<br />
walking and for his help with the prototype. To Jens and to Tim for their great work on the<br />
simulation environment. And to Carsten, for his priceless help in all questions concerning<br />
electronics and mechanics, and many fruitful and enjoyable discussions regarding all aspects<br />
<strong>of</strong> robot design and development.<br />
I also wish to thank Rita Broschart for her support concerning all kinds <strong>of</strong> administrative<br />
endeavor. Further thanks go to Lothar Gauss; since his joining the group, producing parts<br />
in the workshop became a much easier and less time-consuming task.
ii<br />
Finally, I thank my parents for their support, especially my father for taking up the tedious<br />
task <strong>of</strong> pro<strong>of</strong>-reading this whole thesis and supplying me with countless corrections and<br />
suggestions regarding my flawed technical writing. Last but not least, my thanks and love<br />
go to my wife Birgit. Only her encouragement, understanding, and insistence enabled me<br />
to finish this thesis.
Abstract<br />
Despite several decades <strong>of</strong> research, locomotion <strong>of</strong> bipedal robots is still far from achieving<br />
the graceful motions and the dexterity observed in human walking. Most <strong>of</strong> today’s bipeds<br />
are controlled by analytical approaches based on multibody dynamics, pre-calculated<br />
joint trajectories, and Zero-Moment Point considerations to ensure stability. However,<br />
beside their considerable achievements these methods show several drawbacks <strong>like</strong> strong<br />
model dependency, high energetic and computational costs, and vulnerability to unknown<br />
disturbances. In contrast to this, human locomotion is elegant, highly robust, fast, and<br />
energy efficient. These facts gave rise to the main hypothesis <strong>of</strong> this thesis, namely that a<br />
control system based on insights into human motion control can yield human-<strong>like</strong> walking<br />
capabilities in two-legged robots.<br />
This thesis thus presents a control methodology for bipeds relying heavily on the transfer<br />
<strong>of</strong> concepts found in the locomotion control <strong>of</strong> humans. Based on a thorough review on<br />
biomechanics and neuroscience literature, a control approach is derived that can achieve<br />
dynamic, efficient, and robust walking <strong>of</strong> three-dimensional and fully articulated bipeds.<br />
Being located above the neural level, the control system is structured as a hierarchical<br />
network <strong>of</strong> local feed-forward and feedback units, without using a complete dynamic model<br />
or pre-calculated joint trajectories. Sensor event-based spinal pattern generators coordinate<br />
the stimulation and synchronization <strong>of</strong> control units and the compliance <strong>of</strong> passive joints.<br />
By applying local torque commands instead <strong>of</strong> joint angle control, passive dynamics and<br />
self-stabilizing effects <strong>of</strong> elasticities can be exploited. Postural control is achieved by the<br />
phase-dependent activity <strong>of</strong> several reflexes <strong>of</strong> various complexity.<br />
The suggested approach is tested in a full-featured dynamics simulation framework on an<br />
anthropomorphic biped with 21 degrees <strong>of</strong> freedom and human-<strong>like</strong> morphology, weight,<br />
and actuation. The control system can achieve three-dimensional dynamic walking <strong>of</strong><br />
variable velocity as well as balanced standing. It is able to cope with the high complexity<br />
and the mechanical elasticities <strong>of</strong> the modeled biped. The emerging, naturally looking<br />
walking gait shows remarkable similarities to human walking. Simultaneous control <strong>of</strong><br />
only a subset <strong>of</strong> joints is sufficient to direct the passive dynamics <strong>of</strong> the robot towards a<br />
walking gait. The achieved walking velocity <strong>of</strong> up to 5 km/h can compete with even the<br />
most advanced <strong>of</strong> today’s bipeds. At the same time, energy efficiency is much better than<br />
in joint angle controlled robots. The control system shows considerable robustness against<br />
unknown and unexpected disturbance <strong>like</strong> steps, slopes, or external forces.
Contents<br />
1 Introduction 1<br />
1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3<br />
1.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5<br />
2 Technical <strong>Control</strong> Methods for <strong>Bipedal</strong> <strong>Robots</strong> 7<br />
2.1 Challenges in <strong>Bipedal</strong> <strong>Walking</strong> . . . . . . . . . . . . . . . . . . . . . . . . . 7<br />
2.1.1 <strong>Dynamically</strong> vs. Statically Stable <strong>Walking</strong> . . . . . . . . . . . . . . 7<br />
2.2 Common Methods in <strong>Control</strong>ling Bipeds . . . . . . . . . . . . . . . . . . . 10<br />
2.2.1 Zero-Moment Point . . . . . . . . . . . . . . . . . . . . . . . . . . . 10<br />
2.2.2 Virtual Model <strong>Control</strong> . . . . . . . . . . . . . . . . . . . . . . . . . 12<br />
2.3 Examples for Technically <strong>Control</strong>led Bipeds . . . . . . . . . . . . . . . . . 13<br />
2.4 Assessment <strong>of</strong> Technical <strong>Control</strong> Approaches . . . . . . . . . . . . . . . . . 20<br />
3 <strong>Human</strong> Locomotion <strong>Control</strong> 23<br />
3.1 Structural Organization <strong>of</strong> Motion <strong>Control</strong> . . . . . . . . . . . . . . . . . . 23<br />
3.1.1 Functional Morphology . . . . . . . . . . . . . . . . . . . . . . . . . 23<br />
3.1.2 Neurological Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . 26<br />
3.1.3 Sensorimotor Interaction . . . . . . . . . . . . . . . . . . . . . . . . 30<br />
3.1.4 Hierarchical Layout <strong>of</strong> Motion <strong>Control</strong> . . . . . . . . . . . . . . . . 32<br />
3.2 Normal <strong>Walking</strong> in <strong>Human</strong>s . . . . . . . . . . . . . . . . . . . . . . . . . . 36<br />
3.2.1 Biomechanical Gait Analysis . . . . . . . . . . . . . . . . . . . . . . 36<br />
3.2.2 Phases <strong>of</strong> <strong>Walking</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . 47<br />
3.2.3 Reflex Function during <strong>Walking</strong> . . . . . . . . . . . . . . . . . . . . 48<br />
3.2.4 Postural <strong>Control</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50<br />
3.3 Key Aspects <strong>of</strong> Biological <strong>Walking</strong> <strong>Control</strong> . . . . . . . . . . . . . . . . . . 53<br />
3.4 Biologically Inspired <strong>Control</strong> <strong>of</strong> <strong>Bipedal</strong> <strong>Robots</strong> . . . . . . . . . . . . . . . 55<br />
3.4.1 Exploitation <strong>of</strong> Inherent Dynamics and Elasticities . . . . . . . . . 55<br />
3.4.2 Neuro-, Reflex-, and Oscillator-based <strong>Control</strong> . . . . . . . . . . . . 60<br />
4 A Biologically Supported Concept for <strong>Control</strong>ling Bipeds 67<br />
4.1 Passive <strong>Control</strong> Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67<br />
4.2 <strong>Control</strong> Unit Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69<br />
4.2.1 Locomotion Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 69<br />
4.2.2 Spinal Pattern Generators . . . . . . . . . . . . . . . . . . . . . . . 70<br />
4.2.3 Motion Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70<br />
4.2.4 Motor Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70<br />
4.2.5 Local Reflexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71<br />
4.2.6 Postural Reflexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71<br />
4.3 Hierarchical Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
vi Contents<br />
5 <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped 75<br />
5.1 System Premises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75<br />
5.1.1 Kinematic Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75<br />
5.1.2 Assumed Actuation and Sensor System . . . . . . . . . . . . . . . . 77<br />
5.1.3 The Behavior-based <strong>Control</strong> Architecture iB2C . . . . . . . . . . . 77<br />
5.2 Guidelines for Designing <strong>Control</strong> Units . . . . . . . . . . . . . . . . . . . . 81<br />
5.2.1 Feed-Forward <strong>Control</strong> Units . . . . . . . . . . . . . . . . . . . . . . 81<br />
5.2.2 Feedback <strong>Control</strong> Units . . . . . . . . . . . . . . . . . . . . . . . . 82<br />
5.2.3 Guidelines for Implementing iB2C Features . . . . . . . . . . . . . . 83<br />
5.3 Stable Standing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83<br />
5.3.1 Balanced Standing <strong>Control</strong> in <strong>Human</strong>s . . . . . . . . . . . . . . . . 83<br />
5.3.2 Stabilized Standing <strong>Control</strong> . . . . . . . . . . . . . . . . . . . . . . 85<br />
5.3.3 Stable Standing State Machine . . . . . . . . . . . . . . . . . . . . 85<br />
5.3.4 Ground Adaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . 86<br />
5.3.5 Posture Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . 88<br />
5.3.6 Posture Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 88<br />
5.3.7 Relaxed Stance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89<br />
5.4 Dynamic <strong>Walking</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90<br />
5.4.1 Interrelation between Locomotion Modes . . . . . . . . . . . . . . . 90<br />
5.4.2 <strong>Walking</strong> Initiation . . . . . . . . . . . . . . . . . . . . . . . . . . . 91<br />
5.4.3 Spinal Pattern Generator for <strong>Walking</strong> . . . . . . . . . . . . . . . . . 95<br />
5.4.4 <strong>Walking</strong> Phase 1: Weight Acceptance . . . . . . . . . . . . . . . . . 97<br />
5.4.5 <strong>Walking</strong> Phase 2: Propulsion . . . . . . . . . . . . . . . . . . . . . 99<br />
5.4.6 <strong>Walking</strong> Phase 3: Stabilization . . . . . . . . . . . . . . . . . . . . 101<br />
5.4.7 <strong>Walking</strong> Phase 4: Leg Swing . . . . . . . . . . . . . . . . . . . . . . 102<br />
5.4.8 <strong>Walking</strong> Phase 5: Heel Strike . . . . . . . . . . . . . . . . . . . . . 104<br />
5.4.9 Posture <strong>Control</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105<br />
6 Implementation <strong>of</strong> <strong>Bipedal</strong> <strong>Walking</strong> <strong>Control</strong> 113<br />
6.1 Simulation Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113<br />
6.1.1 Embedding the Physics Engine . . . . . . . . . . . . . . . . . . . . 113<br />
6.1.2 Actuators and Joint <strong>Control</strong> . . . . . . . . . . . . . . . . . . . . . . 115<br />
6.1.3 Simulation <strong>of</strong> Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . 118<br />
6.1.4 Model <strong>of</strong> Simulated Biped . . . . . . . . . . . . . . . . . . . . . . . 119<br />
6.2 Notes on the Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 121<br />
6.2.1 Group Layout and Phase Representatives . . . . . . . . . . . . . . . 121<br />
6.2.2 Application <strong>of</strong> iB2C Features . . . . . . . . . . . . . . . . . . . . . 122<br />
7 Balanced Standing Experiments 125<br />
7.1 Adaptation to the Ground Geometry . . . . . . . . . . . . . . . . . . . . . 125<br />
7.2 External Forces and Platform Movements . . . . . . . . . . . . . . . . . . . 126<br />
7.3 Posture Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Contents vii<br />
8 Dynamic <strong>Walking</strong> Experiments 137<br />
8.1 Normal <strong>Walking</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137<br />
8.1.1 Locomotion Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . 137<br />
8.1.2 Switching <strong>Walking</strong> Phases . . . . . . . . . . . . . . . . . . . . . . . 139<br />
8.1.3 Behavioral Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . 142<br />
8.1.4 Kinematic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 148<br />
8.1.5 Kinetic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158<br />
8.2 <strong>Walking</strong> under Disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . 168<br />
8.2.1 Sloped Terrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169<br />
8.2.2 <strong>Walking</strong> over Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . 174<br />
8.2.3 Constant External Forces . . . . . . . . . . . . . . . . . . . . . . . 175<br />
9 Conclusion and Outlook 177<br />
9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178<br />
9.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182<br />
A Biomechanical and Anatomical Terms 185<br />
B Dynamics Simulation Framework 191<br />
B.1 MCA2 and SimVis3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191<br />
B.2 Embedding <strong>of</strong> the Physics Engine . . . . . . . . . . . . . . . . . . . . . . . 193<br />
B.3 Interface to <strong>Control</strong> System and Simulation . . . . . . . . . . . . . . . . . 195<br />
B.4 Simulation Scenario for Biped Experiments . . . . . . . . . . . . . . . . . . 198<br />
Bibliography 203
viii Contents
1. Introduction<br />
Since many centuries, man is dreaming <strong>of</strong> creating an artificial servant as assistant in<br />
daily life or as laborer for exhausting work. Before the advent <strong>of</strong> industrial robotics,<br />
these moving machines built <strong>of</strong> inanimate matter have been imagined as <strong>like</strong>nesses <strong>of</strong><br />
man, working in humanly environment. The golem described in the Jewish folklore can<br />
be seen as an early example, a figure <strong>of</strong> human shape being formed from clay. The tale<br />
<strong>of</strong> Rabbi Judah Loew ben Bezalel tells <strong>of</strong> his creation <strong>of</strong> a golem to defend the Jewish<br />
ghetto <strong>of</strong> the 16th century Prague against anti-Semitic attacks. Figure 1.1 shows Paul<br />
Wegener’s interpretation <strong>of</strong> a golem in his silent movie series from 1920. The character<br />
<strong>of</strong> the golem inspired many writers, <strong>like</strong> Johann Wolfgang von Goethe in his poem“The<br />
Sorcerer’s Apprentice”, Mary Shelley and her novel“Frankenstein”, or the Czech writer<br />
Karel ˘ Capek. His science fiction play“R.U.R.”(Rossum’s Universal <strong>Robots</strong>) from 1921<br />
introduced clone-<strong>like</strong> artificial creatures working for and then rebelling against their human<br />
creators. These androids are called <strong>Robots</strong> based on the Czech work robota meaning labor,<br />
thus making the term known and popular.<br />
While the golems, ˘ Capek’s robots, or Frankenstein’s creature are made <strong>of</strong> animated clay<br />
or human tissue, the idea <strong>of</strong> an artificial laborer also infected inventors and engineers. As<br />
early as 1886 Zadock Dederick built and was granted a patent for his Steam Man, a 250kg<br />
heavy machine powered by a steam engine and pulling a rockaway carriage (Figure 1.1).<br />
In 1893, George Moore adopted the idea and built a similar mechanical man, supported<br />
by a horizontal bar and able to walk in circles. At the New York World’s Fair in 1939, the<br />
robot Elektro was exhibited (Figure 1.1). Build by J.M. Barnett <strong>of</strong> the Pittsburgh-based<br />
Westinghouse Electric Corporation as an elaborate marketing tool, the 120kg machine <strong>of</strong><br />
about 2.1m in height could move its mouth, fingers, and limbs. Triggered by simple voice<br />
commands, it would replay recorded speech samples, walk, or smoke cigarettes. Similar<br />
projects <strong>of</strong> that time include the radio controlled robot George by Pilot Officer Sale (1950),<br />
Garco by Harvey Chapman (1953), Gygan by Piero Fiorito (1957), or MM47 by Claus<br />
Scholz (1961).<br />
The walking mechanisms <strong>of</strong> the machines mentioned above were <strong>of</strong> rather primitive form,<br />
the leg movement mostly induced by a single rotating motor and straight-line linkages. To<br />
enable more robust locomotion on uneven ground, more sophisticated constructions became
2 1. Introduction<br />
Figure 1.1: The Golem in Paul Wegener’s silent movies (1920), Steam Man created by Zadock<br />
Dederick (1886), Elektro built by the Pittsburgh-based Westinghouse Electric Corporation (1938),<br />
WL-1 (1967) and WABOT-1 (1973), developed by Ichiro Kato, Waseda University.<br />
necessary. The development <strong>of</strong> walking machines aroused the interest <strong>of</strong> the scientific<br />
community. Ichiro Kato <strong>of</strong> the Waseda University in Japan started his pioneer work on<br />
bipedal robots in 1966. His first robot WL-1 from 1967 is shown in Figure 1.1, WL-3<br />
developed in 1969 could already perform preliminary static walking as well as standing<br />
and sitting motions [Lim 06]. In 1973, Kato’s group built the robot WABOT-1, which is<br />
commonly accepted as the first fully articulated anthropomorphic biped [Kato 73].<br />
With the emergence <strong>of</strong> complex machines <strong>like</strong> those developed by Kato and others, and<br />
the availability <strong>of</strong> microprocessors, it soon became apparent that not only the mechanical<br />
design but also the control <strong>of</strong> bipedal robots poses challenging problems. While Rabbi<br />
Loew could simply write the instructions for his golem on a piece <strong>of</strong> paper and place it<br />
in the golem’s mouth, controlling two-legged locomotion turned out to be much more<br />
difficult. The high center <strong>of</strong> mass, the small support area spanned by only two feet,<br />
and an essentially dynamic gait make preserving balance and stability a tough job. As<br />
robotics scientists mainly emerged from mechanical engineering, the mathematical tools<br />
and concepts <strong>of</strong> this research field where applied to find fitting control strategies, the<br />
most prominent one being Vukobratović’s Zero-Moment Point concept. It found its first<br />
application in 1984 on Kato’s robot WL-10RD and will be described in detail later in<br />
this thesis. Since then, the majority <strong>of</strong> research projects on bipedal robots complied with<br />
these ideas and methods. Mainly located in Japan and other Asian countries, these efforts<br />
yielded impressive machines <strong>like</strong> Honda’s Asimo or Kaist’s Hubo.<br />
But in spite <strong>of</strong> over four decades <strong>of</strong> research, the problem <strong>of</strong> mechanical bipedal locomotion<br />
is still far from being solved. Compared to the elegant and efficient walking motions <strong>of</strong><br />
humans, even the most sophisticated bipedal robots appear clumsy and slow. One possible<br />
way <strong>of</strong> improving the performance <strong>of</strong> two-legged walking machines could be the transfer <strong>of</strong><br />
ideas from biology, not only in respect to the mechanical setup, but also to the control<br />
concepts.<br />
The knowledge necessary for this approach can be found in research on biomechanics<br />
and neurosciences. As with the urge for an artificial servant, man’s aspiration to know<br />
the working <strong>of</strong> his own body has a history <strong>of</strong> many centuries. Aristotle (384–322 BC) is<br />
commonly seen as founder <strong>of</strong> kinesiology, the science <strong>of</strong> movement <strong>of</strong> the body. In his book
1.1. Objectives 3<br />
“De Motu Animalium”he was the first to treat the action <strong>of</strong> muscles and their geometrical<br />
relationship to extremities, and to analyze walking as cyclic motion. The studies <strong>of</strong><br />
Archimedes (287–212 BC) on gravity and leverage laid the foundation to mechanical<br />
analysis <strong>of</strong> motion. The Roman physician Galen (AD 131–201) introduced the principle<br />
<strong>of</strong> antagonistic muscle work or the distinction between muscle and sensory nerves in his<br />
treatise“De Motu Musculorum”, considered to be the first textbook on biomechanics.<br />
It was up to Leonardo da Vinci (1452–1519) to further the field <strong>of</strong> kinesiology during the<br />
Renaissance after many centuries <strong>of</strong> stagnation. The artist and scientist had an interest in<br />
the structure <strong>of</strong> the human body and tried to identify muscles, nerves, and the mechanics<br />
<strong>of</strong> the body during various motions. In 1543, the Flemish physician Andreas Vesalius<br />
published his text“On the Structure <strong>of</strong> the <strong>Human</strong> Body”, correcting some <strong>of</strong> the error<br />
made by Galen. In the late 16th and the following century, important contributions can<br />
be attributed to Galileo Galilee, Marcello Malpighi, and especially to Giovanni Alfonso<br />
Borelli. He was the first to understand that the forces produced by muscles have to be<br />
larger than those acting against the skeletal motion, as the levers <strong>of</strong> the musculoskeletal<br />
system magnify motion rather than force. This was even before Isaac Newton (1642–1727)<br />
wrote his famous work“Principia Mathematica Philosophiae Naturalis”containing the<br />
three laws <strong>of</strong> rest and movement, being essential for the analysis <strong>of</strong> body dynamics. In<br />
the 18th century, electricity replaced the notion <strong>of</strong>“animal spirits”as origin <strong>of</strong> muscle<br />
activation. Luigi Galvani (1737–1798) first stated the presents <strong>of</strong> electrical potentials in<br />
muscles and nerves. In 1748 David Hartley established the term reflex as an automatic<br />
response to a stimulus.<br />
The 19th century saw the beginning <strong>of</strong> modern gait analysis. The Weber brothers<br />
published their book “Die Mechanik der Menschlichen Gehwerkzeuge”, describing the<br />
natural frequency <strong>of</strong> a pendulum-<strong>like</strong> leg swing and establishing the mechanism <strong>of</strong> muscular<br />
action on a scientific basis. The arise <strong>of</strong> photographic techniques applied by Eadweard<br />
Muybridge or Jules Marey allowed more detailed analysis <strong>of</strong> motion. Christian Wilhelm<br />
Braune and Otto Fischer experimentally determined the body’s center <strong>of</strong> gravity. Adolf<br />
Eugen Fick (1829–1901) introduced the terms isometric and isotonic during his analysis <strong>of</strong><br />
the mechanics <strong>of</strong> muscular movement and energetics. Sherrington’s work“The Integrative<br />
Action <strong>of</strong> the Nervous System”is published in 1906. Sixteen years later, Archibald V.<br />
Hill (1886–1977) receives the Nobel Prize for his studies on the oxygen consumption<br />
during muscle work. In the middle <strong>of</strong> the 20th century, analyzing dynamic motions and<br />
scrutinizing the“why”<strong>of</strong> human movement began to dominate research on biomechanics<br />
and neurosciences. This objective has not changed up to now, and still human motion<br />
control is far from being completely understood. Nevertheless, recent results in these fields<br />
encourage the transfer <strong>of</strong> biological concepts to the design and control <strong>of</strong> technical systems.<br />
Combined with the advances made in the development and control <strong>of</strong> complex robotic<br />
systems, this strategy acted as motivation for the work at hand.<br />
1.1 Objectives<br />
The goal <strong>of</strong> this thesis is the derivation <strong>of</strong> a control methodology for dynamical locomotion<br />
<strong>of</strong> bipedal robots based on concepts found in human motion control.<br />
This goal is based on the hypothesis that a control system similar to the human one will<br />
enable a robot to perform locomotion in a <strong>like</strong>wise fashion. Obviously, neither all aspects
4 1. Introduction<br />
<strong>of</strong> human motion control nor all capabilities <strong>of</strong> human locomotion can be expected to be<br />
considered or included. A reasonable subset needs to be regarded that is tailored to be<br />
applicable to bipedal robots with today’s technical means, but still is as general as possible<br />
to allow a broad range <strong>of</strong> motions and skills. Balanced standing and three-dimensional<br />
dynamic walking <strong>of</strong> a fully articulated anthropomorphic biped shall be the target forms <strong>of</strong><br />
locomotion for this work. This allows to analyze the control performance during both more<br />
static and dynamic motions <strong>of</strong> a complex robotic system. Further modes <strong>of</strong> movement <strong>like</strong><br />
running or jumping should potentially be viable.<br />
While the results <strong>of</strong> a single thesis surely cannot fully compete with the abilities <strong>of</strong> machines<br />
developed over decades, it at least should be shown that some <strong>of</strong> their drawbacks can be<br />
overcome. As in the natural example, a walking style <strong>of</strong> less clumsiness, higher speed, or<br />
better efficiency should be expected. In case a comparison to human walking should result<br />
in substantial similarities, e.g. regarding joint angle trajectories, even a step towards the<br />
confirmation <strong>of</strong> biomechanical or neuroscientific hypotheses could be ventured.<br />
To design a biologically inspired control concept in correspondence to the goal just<br />
formulated several issues have to be addressed. The following topics are regarded as being<br />
crucial and thus will be approached in detail within this thesis:<br />
Analysis <strong>of</strong> Recent Results from Biomechanics and Neuroscience<br />
As mentioned on the previous pages, biomechanics and neuroscience have a long lasting<br />
history. Accordingly the state-<strong>of</strong>-the-art on these topics is extensive and still growing.<br />
Nevertheless it needs to be examined to identify the key aspects <strong>of</strong> human motion control<br />
that have the potential to be transferred to a robotic control system. Fortunately, some<br />
researchers <strong>of</strong> these disciplines have already <strong>of</strong>fered some advice for the robotics community<br />
that can serve as starting point for the analysis.<br />
Dependence <strong>of</strong> Mechanics and <strong>Control</strong> in <strong>Human</strong> Motion Generation<br />
It can be assumed that during the course <strong>of</strong> evolution, the human morphology has been<br />
optimized towards bipedalism. Research on functional morphology can help to identify<br />
the properties <strong>of</strong> the musculoskeletal system essential for locomotion. While this work’s<br />
objectives cannot include the development <strong>of</strong> mechanical solutions, still properties <strong>like</strong><br />
muscle characteristics, mass distribution, or limb geometry need to be analyzed as control<br />
aspects are depending on them. Especially potential exploitation <strong>of</strong> passive dynamics<br />
should be considered.<br />
Granularity and Classes <strong>of</strong> Suitable <strong>Control</strong> Units<br />
The selected biological key aspects have to be transferred to a technically feasible control<br />
approach. As this thesis follows the concept <strong>of</strong> behavior-based robot control, a suitable<br />
fusion <strong>of</strong> conceptual ideas needs to be found. This implies that the granularity <strong>of</strong> control<br />
units should be above the level <strong>of</strong> biological neurons. A set <strong>of</strong> classes <strong>of</strong> such control units<br />
should be derived from the functional units found in natural motion control, including<br />
feedback as well as feed-forward mechanisms. To arrange such control units and to manage<br />
their communication, a structural layout needs to be defined serving as a design guideline.
1.2. Structure 5<br />
Implementation <strong>of</strong> Dynamic <strong>Walking</strong> within the <strong>Control</strong> Concept<br />
Having determined relevant classes and a control structure, the control units necessary<br />
to synthesize dynamic walking need to be designed. Functional units identified in the<br />
analysis <strong>of</strong> human walking have to be mapped to the suggested control concept. Solutions<br />
for the implementation <strong>of</strong> the derived control units must be developed. As a bipedal robot<br />
will never be an exact copy <strong>of</strong> the human morphology, adaptation <strong>of</strong> these units as well as<br />
the design <strong>of</strong> new units will be necessary.<br />
Test Environment for Validation<br />
Lacking an actual robot featuring the properties relevant for human-<strong>like</strong> dynamic walking,<br />
a suitable model needs to be developed within a simulation environment. The simulation<br />
has to reflect physical effects <strong>like</strong> gravity, mass distribution, or collision, otherwise dynamic<br />
locomotion and exploitation <strong>of</strong> passive dynamics could not be observed.<br />
Naturally, there already has been and still is research on the transfer <strong>of</strong> control aspects from<br />
biology to walking machines, as will be presented in Chapters 3. Hence this thesis aims at<br />
differing from previous work regarding the extend <strong>of</strong> including biological analysis and the<br />
resulting applicable control aspects, the manner in which these aspects are transformed<br />
into a robot control system, and the complexity <strong>of</strong> the considered robotic target platform.<br />
Only a small minority <strong>of</strong> the research projects on biologically motivated robot control has<br />
been applied to the dynamic walking <strong>of</strong> a fully articulated biped. Finally, as this work<br />
introduces behavior-based control concepts to bipedal robot control, it can be examined if<br />
this harmonizes with the biologically motivated approach or can bring additional benefits<br />
compared to other control methods.<br />
1.2 Structure<br />
This thesis is structured as follows:<br />
Chapter 2 begins by defining the main challenges <strong>of</strong> dynamic bipedal walking that have to<br />
be handled by the control system. Then common control methods <strong>like</strong> the Zero-Moment<br />
Point approach are introduced. These methods are based on techniques from mechanical<br />
engineering or industrial robotics, e.g. multibody dynamics, and will be called technical<br />
control methods in contract to biologically inspired ones for the remainder <strong>of</strong> this work.<br />
The state-<strong>of</strong>-the-art <strong>of</strong> these approaches is reviewed and their advantages and drawbacks<br />
are assessed.<br />
In order to develop a human-<strong>like</strong> biped control system, Chapter 3 introduces basic and<br />
advanced aspects <strong>of</strong> human locomotion control, both regarding its structural organization<br />
and its functional analysis. Based on these results from biomechanical and neuroscientific<br />
research, key aspects <strong>of</strong> biological walking control and implications for robotics are derived.<br />
The chapter concludes with an evaluation <strong>of</strong> literature on biologically inspired control <strong>of</strong><br />
two-legged robot locomotion.<br />
In Chapter 4, the insights just gained are used to design a control concept for dynamic<br />
bipedal locomotion. It is discussed how passive dynamics can be exploited and in what<br />
way they influence the control system. Classes <strong>of</strong> control units are suggested based on<br />
active feed-forward and feedback mechanisms observed in human walking. These control
6 1. Introduction<br />
units are arranged in a hierarchical layout similar to the structure that is assumed to exist<br />
in biological locomotion control.<br />
Chapter 5 describes the design and implementation <strong>of</strong> stable standing and dynamic<br />
walking control applying the suggested methodology. First, requirements regarding the<br />
mechatronics and the control system <strong>of</strong> the target platform are given. Then it is discussed<br />
how suitable control units can be found, e.g. by consulting gait analysis research. Next,<br />
the control units and the resulting network for balanced standing on uneven surfaces and<br />
under external disturbances as well as for dynamic walking are introduced.<br />
The simulation environment and the model <strong>of</strong> the bipedal robot used for the experiments<br />
are presented in Chapter 6. Additionally, it contains notes on particularities <strong>of</strong> the<br />
implementation regarding the behavior-based architecture and the control framework.<br />
The experiments on stable standing are described in Chapter 7. It is shown how the robot<br />
adapts to the ground geometry and how it reacts to external disturbances. Furthermore,<br />
the results <strong>of</strong> the posture optimization method are presented.<br />
Finally, Chapter 8 analyzes the performance <strong>of</strong> the suggested control system during<br />
dynamic walking. Behavioral activity as well as kinematic and kinetic progresses are<br />
discussed. The resulting motions are compared to data from human gait analysis. The<br />
robustness <strong>of</strong> the control system is evaluated by applying different disturbances during<br />
walking.<br />
The thesis is concluded in Chapter 9. The main aspects and contributions <strong>of</strong> the suggested<br />
control methodology are summarized and an outlook on possible future research is given.<br />
A short glossary on biomechanical terms, some anatomical guidance, and details on the<br />
implementation <strong>of</strong> the simulation framework are given in the appendices.
2. Technical <strong>Control</strong> Methods for<br />
<strong>Bipedal</strong> <strong>Robots</strong><br />
Looking at control methods for two-legged robots two fundamentally different approaches<br />
can be observed: the technical and the biological approach. In this thesis technical control<br />
approaches are understood as the class <strong>of</strong> methods mainly based on insights from industrial<br />
robotics and mechanical engineering. They draw on sound mathematical concepts <strong>like</strong><br />
multibody dynamics, linear and nonlinear control theory, or established joint constructions<br />
and materials from industrial robots. Biologically inspired approaches try to transfer<br />
results from human motion analysis, biomechanics, or neuroscientific research to technical<br />
system. While not totally dismissing approved mathematical and engineer’s resources,<br />
they focus more on new materials and actuation systems, intelligent mechanics, and, most<br />
notably, on adopting control concepts found in nature.<br />
This chapter will review the technical control approaches as they are most commonly used<br />
for bipeds. Then it will be argued that it is well worth looking at how nature is creating<br />
and controlling bipedal locomotion, as done in the subsequent chapter. But to start with,<br />
the main challenges in controlling two-legged locomotion will be introduced. These apply<br />
to the technical as well as the biological control methods.<br />
2.1 Challenges in <strong>Bipedal</strong> <strong>Walking</strong><br />
The task <strong>of</strong> getting a bipedal robot to walk can be divided into several separate problems.<br />
For each <strong>of</strong> these challenges a solution must be found to achieve stable, cyclic locomotion.<br />
This section will shortly introduce this set <strong>of</strong> problems to enhance the understanding on<br />
the subject matter <strong>of</strong> this thesis. However, first there must be distinguished between two<br />
fundamentally different ways <strong>of</strong> walking.<br />
2.1.1 <strong>Dynamically</strong> vs. Statically Stable <strong>Walking</strong><br />
<strong>Walking</strong> can be performed in two entirely different ways: statically or dynamically stable.<br />
This holds true not only for two-legged walking, but also for other multipeds <strong>like</strong> four-legged
8 2. Technical <strong>Control</strong> Methods for <strong>Bipedal</strong> <strong>Robots</strong><br />
support<br />
CoM<br />
support<br />
Figure 2.1: Statically stable walking keeps the projection <strong>of</strong> the center <strong>of</strong> mass inside the<br />
support area, dynamic walking allows for temporarily instability.<br />
mammals. In statically stable walking it is possible to freeze the motion at any time<br />
without risking instability. This can only be achieved by always keeping the projection <strong>of</strong><br />
the center <strong>of</strong> mass within the support area <strong>of</strong> the feet with ground contact. For bipedal<br />
walking this creates the necessity to first fully move the weight <strong>of</strong> the body over the foot<br />
<strong>of</strong> the next stance leg before the swing foot can leave the ground. As a result statically<br />
stable walking, while guaranteeing stability, is comparatively slow and tedious, consumes<br />
more energy, and limits the possible step length.<br />
In contrast, dynamically stable walking, or dynamic walking in short, does not pose<br />
limitations that hard on the trajectory <strong>of</strong> the center <strong>of</strong> mass. Rather, it must be ensured<br />
thatinstabilityremainstemporarily. Toputitsimply, dynamicwalkingmeanstoconstantly<br />
fall, but to bring forward the swing leg in time to prevent tilting over. This far more<br />
efficient kind <strong>of</strong> walking allows for higher velocity by larger step size, shorter double<br />
support phase, and less time consuming adjustment <strong>of</strong> weight distribution. Figure 2.1<br />
illustrates the difference by showing projection <strong>of</strong> the center <strong>of</strong> mass during a statically<br />
and dynamically stable step.<br />
Nearly all walking found in two- or four-legged vertebrates is dynamic. If at all, statically<br />
stable walking can be observed in very slow or cautious locomotion, or in case highly<br />
deliberate foot placement is necessary. In bipedal robots, both ways <strong>of</strong> walking can and<br />
have been realized with dynamic walking being the considerably more challenging control<br />
problem. Possible approaches to achieve this behavior will be discussed later in this chapter<br />
and at the end <strong>of</strong> the next one.<br />
As this thesis focuses on dynamic walking, from now on this way <strong>of</strong> locomotion is implied,<br />
and the distinction is explicitly made when talking about the statically stable case. The<br />
challenges <strong>of</strong> walking described in the following also deal with dynamic locomotion, even if<br />
several <strong>of</strong> these problems must also be tackled for the statically stable alternative.<br />
Transition between Stance and Swing<br />
<strong>Walking</strong> is a process <strong>of</strong> discrete phases and transitions: each leg switches its role from<br />
stance to swing, and the biped alternates between single and double support. The challenge<br />
here is to find the proper point in time when to switch from double to single support and<br />
CoM
2.1. Challenges in <strong>Bipedal</strong> <strong>Walking</strong> 9<br />
Figure 2.2: A typical step during normal dynamic walking <strong>of</strong> a human subject from one heel<br />
strike to the next.<br />
back again. If the rear leg is lifted too early, energy to transfer the body over the stance<br />
leg might be insufficient. Lifted too late, the time to swing the leg forward to support<br />
the body will be too short. Also, the objectives <strong>of</strong> the control units involved may change<br />
depending on the walking phase. Switching from one phase to the next can be triggered by<br />
sensory events or after a certain amount <strong>of</strong> time. Figure 2.2 illustrates the phases during<br />
normal dynamic walking by showing a typical step <strong>of</strong> a human subject from one heel strike<br />
to the next. The swing phase lasts for about one third <strong>of</strong> the whole stride’s time. The key<br />
events normally referenced in bipedal robotics as well as in biomechanical gait analysis are<br />
foot strike, midsupport, toe-<strong>of</strong>f, forward swing, and deceleration.<br />
Support <strong>of</strong> the Trunk<br />
During its stance phase, a leg must support the weight <strong>of</strong> the upper body. The trunk<br />
height is a result <strong>of</strong> the stance leg’s length, which can be kept straight or act as virtual<br />
spring. If the leg is kept stiff, more potential energy must be used to lift the upper body<br />
as it moves forward <strong>like</strong> an inverted pendulum, but the torque in the knee can remain low.<br />
In case the knee is bended, the leg length must be synchronized with the translation <strong>of</strong><br />
the trunk.<br />
Leg Swing<br />
The forward swing <strong>of</strong> the leg has to meet two conditions: the foot must clear the ground,<br />
and the leg must arrive in front <strong>of</strong> the body in time to act as next swing leg. Ground<br />
clearance can be achieved through shortening the leg by bending the knee, and by keeping<br />
the foot oriented level to the ground. Uneven terrain can make this task even more difficult.<br />
The swing duration can be shortened by accelerating in the hip joint, but the maximum<br />
hip torque confines the minimal duration and as such the maximum walking velocity given<br />
a maximum step length.<br />
<strong>Control</strong> <strong>of</strong> Forward Velocity<br />
The appropriate forward velocity <strong>of</strong> the upper body is crucial for stable dynamic walking.<br />
As the system acts <strong>like</strong> an inverted pendulum while traversing over the stance leg, enough<br />
kinetic energy must be present to be transferred to potential energy <strong>of</strong> the upper body.<br />
In contrast, if the velocity is too high, the time for the swing leg to travel before the<br />
body might be too short and the biped tumbles. During walking, energy is consumed by<br />
damping and by foot impact. Measuring or estimating the proper forward velocity is not<br />
easily achieved.
10 2. Technical <strong>Control</strong> Methods for <strong>Bipedal</strong> <strong>Robots</strong><br />
The forward velocity can be influenced by many factors: the further back the center <strong>of</strong><br />
pressure is located in the stance foot during single support, the faster is the resulting<br />
forward movement. Bending the trunk forward accelerates the biped, leaning backwards<br />
slows it down. During double support, the center <strong>of</strong> mass can be transferred forward<br />
or backwards within certain limitations. A push-<strong>of</strong>f motion using the ankle <strong>of</strong> the rear<br />
leg before lifting it inserts energy into the system, too. Finally, the timing <strong>of</strong> the phase<br />
transition events as well as the variation <strong>of</strong> the step length change the amount <strong>of</strong> time the<br />
body mass is in front <strong>of</strong> and behind the stance leg, and thus is accelerating or decelerating<br />
the robot.<br />
Stability <strong>of</strong> the Trunk in the Sagittal Plane<br />
Keeping the upper body erect or purposefully leaning it forward or backwards as just<br />
mentioned is a further objective during walking. Trunk pitch is disturbed by inertia during<br />
foot impact as well as by gravity as its center <strong>of</strong> mass lies above the hip joint. It is further<br />
influenced by hip torques generated during leg swing.<br />
Lateral Stability<br />
While the challenges mentioned so far also hold true for planar walking, i.e. walking<br />
confined to the sagittal plane, lateral movement is only introduced in three-dimensional<br />
locomotion. Foot impact can heavily disturb lateral stability. Keeping the biped from<br />
falling to one side can be reached by leaning the upper body sidewards, by applying<br />
torque in the ankle joints, or by shifting the foot position <strong>of</strong> the swing leg to the left or<br />
right. While the first two methods only allow marginal influence, the last one can even<br />
compensate strong sidewards motions, however it must potentially act over several strides.<br />
Introducing feedback control for both lateral and anterior/posterior stability requires an<br />
estimation <strong>of</strong> the upper body’s orientation. Given an unknown ground orientation, this<br />
cannot be calculated by kinematics. Sensor systems <strong>like</strong> inertial measurement units or<br />
vision systems gauging the horizon can provide the necessary information.<br />
2.2 Common Methods in <strong>Control</strong>ling Bipeds<br />
Nature was not the first choice when biped engineers first looked for inspiration on how<br />
to control two-legged walking machines. Rather, established methods from electrical and<br />
mechanical engineering <strong>like</strong> multibody dynamics or classical control theory served as basis<br />
for the development <strong>of</strong> control systems. This section will review the most prominent and<br />
more recent developments <strong>of</strong> biped research to illustrate the technical control approach.<br />
Most <strong>of</strong> the control systems for walking bipedal robots are based on Vukobratović’s Zero-<br />
Moment Point (zmp) approach [Vukobratovic 72, Vukobratovic 04] or the derived Center<br />
<strong>of</strong> Pressure (cop) approach [Sardain 04]. Regarding the prominent role <strong>of</strong> the zmp, the<br />
next section will give a short overview on its ideas.<br />
2.2.1 Zero-Moment Point<br />
The zmp describes a criterion for dynamic balance first formulated by Miomir Vukobratović<br />
in 1968. It is defined as that point on the ground at which the net moment <strong>of</strong> the inertial<br />
forces and the gravity forces has no component along the horizontal axes.
2.2. Common Methods in <strong>Control</strong>ling Bipeds 11<br />
Figure 2.3: Visualization <strong>of</strong> the Zero-Moment Point. From [Vukobratovic 04], p160.<br />
Let us consider a biped robot in single support phase. The influence <strong>of</strong> the dynamics <strong>of</strong> the<br />
segments above the ankle is represented by the force FA and the moment MA (Figure 2.3b).<br />
The ground reaction in point P consists <strong>of</strong> the force R = (RX,RY,RZ) and the moment<br />
M = (MX,MY,MZ). The friction <strong>of</strong> the non-sliding foot on the ground compensates the<br />
horizontal components <strong>of</strong> FA and the vertical part <strong>of</strong> MA (Figure 2.3c) and can therefore<br />
be represented by (RX,RY,MZ). RZ represents the ground reaction that balances vertical<br />
forces. The remaining horizontal components <strong>of</strong> active moments can only be compensated<br />
by shifting the position P <strong>of</strong> the reaction force R within the support polygon (Figure 2.3d).<br />
If the support polygon <strong>of</strong> the foot is not large enough for an appropriate position <strong>of</strong> R, the<br />
force acts at the edge <strong>of</strong> foot and a uncompensated component <strong>of</strong> the reaction moment<br />
remains. This results in a rotation about the foot edge and the robot stumbles. Therefore<br />
the condition for the robot to be in dynamic equilibrium can be given for the point P on<br />
the foot sole where the ground reaction force is acting:<br />
MX = 0 and MY = 0 (2.1)<br />
The point P is then called the Zero-Moment Point. The static equilibrium equations for<br />
the supporting foot can be given as<br />
R+FA +msg = 0, (2.2)<br />
−→<br />
OP ×R+ −→<br />
OG×msg +MA +MZ + −→<br />
OA×FA = 0, (2.3)<br />
where O is the origin <strong>of</strong> the coordinate system, P the ground reaction force acting point,<br />
G the foot’s center <strong>of</strong> mass, A the ankle joint, and ms the foot mass.<br />
Projecting Equation 2.3 onto the horizontal plane gives<br />
( −→<br />
OP ×R) H<br />
+ −→<br />
OG×msg +M H A +MZ +( −→<br />
OA×FA) H<br />
= 0 (2.4)<br />
which is the basis for computing the ground reaction force acting point P. To ensure<br />
dynamic equilibrium, the point P must be within the support polygon. If the computed
12 2. Technical <strong>Control</strong> Methods for <strong>Bipedal</strong> <strong>Robots</strong><br />
Figure 2.4: The ground reaction force acting point P must be within the support polygon.<br />
From [Vukobratovic 04], p164.<br />
point is outside the support polygon (called fictitious, fzmp then), the zmp does not exist<br />
as Equation 2.1 is not met and the ground reaction force acting point P is actually on<br />
edge <strong>of</strong> support polygon. This results in a rotation around the foot edge and the loss <strong>of</strong><br />
balance (Figure 2.4).<br />
The zmp can be used for the task <strong>of</strong> <strong>of</strong>fline gait synthesis or as a key indicator for online<br />
gait control. It can be measured approximately by force sensors in the foot sole <strong>of</strong> the robot.<br />
An extension to the zmp and cop can be found in the foot-rotation-indicator [Goswami 99].<br />
It is identical to the cop when located within the foot’s support area, but when outside<br />
it gives information about the degree and direction <strong>of</strong> postural instability. Most <strong>of</strong> the<br />
bipeds presented in the following are using zmp calculation as part <strong>of</strong> their control system.<br />
2.2.2 Virtual Model <strong>Control</strong><br />
Another methodology for the control <strong>of</strong> bipedal robots is the Virtual Model <strong>Control</strong><br />
developed by Jerry Pratt [Pratt 95b, Pratt 01]. The goal <strong>of</strong> this approach is to keep the<br />
control algorithms easy to understand and intuitive.<br />
The idea <strong>of</strong> Virtual Model <strong>Control</strong> is to apply forces to the robot via virtual components<br />
that are attached within the robot or between the robot and the environment. The<br />
resulting actual joint torques and forces create the same effect that the force <strong>of</strong> the virtual<br />
component would create. These components, which have to create a force based on their<br />
state, might include springs, dampers, masses, potential field, or others. The placement <strong>of</strong><br />
the components remains with the designer and requires physical intuition. No complete<br />
dynamic model <strong>of</strong> the robot is required. The equation describing the static dynamics for a<br />
serial link chain is given as<br />
τ = J T F (2.5)<br />
where τ are the joint torques, J is the Jacobian relating the two attached frames <strong>of</strong> the<br />
virtual components, and F is the force produced by it.<br />
<strong>Robots</strong> controlled by Virtual Model <strong>Control</strong> include a simulated six legged walking<br />
machine [Torres 96]. The 18 degree <strong>of</strong> freedom robot can walk in any direction, turn, and<br />
balance an inverted pendulum on its back. The bipedal robot Spring Turkey (Figure 2.5a)<br />
can walk in the sagittal plane [Pratt 97]. Each leg has an active degree <strong>of</strong> freedom in its<br />
knee and hip, but not feet or ankle. The robot is supported and balanced by a virtual<br />
“granny walker”composed <strong>of</strong> two springs and dampers (Figure 2.5b). <strong>Control</strong> <strong>of</strong> forward<br />
speed during double support is realized by a virtual“dog-track bunny”connected to the
2.3. Examples for Technically <strong>Control</strong>led Bipeds 13<br />
(a) (b)<br />
Figure 2.5: (a) The bipedal robot Spring Turkey. (b) Virtual components are attached to the<br />
robot. From [Pratt 97], p197.<br />
robot by a damper. The coordination <strong>of</strong> the legs is realized by a virtual“reciprocating gait<br />
orthosis”. A state machine selects the components during the different phases <strong>of</strong> walking.<br />
Spring Turkey can walk in a not so robust manner at a speed <strong>of</strong> up to 0.5m. The robot s<br />
Spring Flamingo is also partly controlled by using the Virtual Model <strong>Control</strong> and discussed<br />
in Section 3.4.1.<br />
2.3 Examples for Technically <strong>Control</strong>led Bipeds<br />
Since four decades, reseach institutes throughout the world have been developing bipedal<br />
robots. Despite their anthropomorphic appearance, most <strong>of</strong> the efforts follow a more industrial<br />
approach in the design and control <strong>of</strong> their machines and apply the aforementioned<br />
zmp calculation for generating joint trajectories. The most prominent representatives <strong>of</strong><br />
this kind <strong>of</strong> robots are described in the following section, two <strong>of</strong> them in more detail.<br />
The H7 Robot by the JSK Laboratory<br />
The Jouhou System Kougaku (jsk) Laboratory <strong>of</strong> the University <strong>of</strong> Tokyo has a long<br />
tradition <strong>of</strong> building humanoid robots, some <strong>of</strong> which are shown in Figure 2.7. The aim<br />
<strong>of</strong> its work is to develop an experimental research platform for walking, autonomous<br />
behavior and human interaction. The design <strong>of</strong> their latest robot H7 focused on additional<br />
degrees <strong>of</strong> freedom (resulting in 30), extra joint torques, high computing power, real-time<br />
support, power autonomy, dynamic walking trajectory generation, full body motions,<br />
and three-dimensional vision support. Being 1.5m tall and weighting 57kg, the robot<br />
features 7 degrees <strong>of</strong> freedom per leg including an active toe joint. A real-time capable<br />
on-board computer, four lead-acid batteries, wireless lan, two ieee1394 high resolution<br />
cameras, 6-axis forces sensors and an inertial measurement unit complete the robot’s<br />
equipment [Kuffner 01, Chestnutt 03, Nishiwaki 06].<br />
The online walking control system <strong>of</strong> H7 allows to generate walking trajectories satisfying<br />
a given robot translation and rotation as well as an arbitrary upper body posture. It<br />
is composed <strong>of</strong> several hierarchical layers as shown in Figure 2.6. Each layer represents<br />
a different control cycle and passes its processed results to the next, lower layer which<br />
usually runs at a higher frequency.<br />
The gait decision layer chooses the gait and calculates the footstep locations. The algorithm<br />
proposed by the authors determines the next swing leg’s foot point relative to the foot
14 2. Technical <strong>Control</strong> Methods for <strong>Bipedal</strong> <strong>Robots</strong><br />
Figure 2.6: Hierarchical layers <strong>of</strong> the dynamic walking control system <strong>of</strong> the robot H7.<br />
From [Nishiwaki 06], p83.<br />
<strong>of</strong> the supporting leg. Given a desired torso motion per step <strong>of</strong> (x,y,θ) with x being the<br />
forward, y the sideward and θ the rotational <strong>of</strong>fset, the next foot point is set at (x,2y±w,θ)<br />
from the support foot, with w being the normal foot distance. Furthermore, geometrical<br />
collision conditions are considered.<br />
Generating dynamically stable walking trajectories in the next layer is based on Zero-<br />
Moment Point considerations. Rather than analytically deriving the zmp trajectory from<br />
the robots motion, the authors suggest a method with the walking trajectories following a<br />
given zmp trajectory by horizontally shifting the torso. The starting point is an initial<br />
robot trajectory<br />
A(t) = (...,xi(t),yi(t),zi(t),θi(t),...). (2.6)<br />
describing the position and orientation for each <strong>of</strong> the robot’s segments. Given the gravity<br />
g and the position (xi,yi,zi), the mass mi, the inertia tensor Ii, and the angular velocity<br />
ωi <strong>of</strong> each robot link i, the x component (y similar) <strong>of</strong> the zmp P = (xp,yp,0) T can be<br />
calculated as �<br />
mizi¨xi −<br />
xp =<br />
� {mi(¨zi +g)xi +(0,1,0) T Ii, ˙ωi}<br />
− � (2.7)<br />
m1(¨zi +g)<br />
resulting in a zmp trajectory PA(t) = (xpa(t),ypa(t),0) T for the robot trajectory A(t). A<br />
(t),0) can be followed by finding horizontal and<br />
desired zmp trajectory P∗ A (t) = (x∗pa (t),y∗ pa<br />
vertical shifts x ′ i(t) and y ′ i(t) for each link <strong>of</strong> the robot. For this, the following equation<br />
must hold true, where xe p = x∗ p −xpa,x e i = x ′ i −xi<br />
x e p =<br />
� mizi¨x e i − � mi(¨zi +g)x e i<br />
− � m1(¨zi +g)<br />
. (2.8)<br />
If a uniform horizontal body shift is assumed, i.e. the whole upper body moves consistently<br />
(x e i = x e ), equation 2.8 can be transformed to<br />
x e p =<br />
� mizi<br />
− � m1(¨zi +g) +xe . (2.9)
2.3. Examples for Technically <strong>Control</strong>led Bipeds 15<br />
Figure 2.7: <strong>Human</strong>oids developed by the jsk Lab <strong>of</strong> the University <strong>of</strong> Tokyo: H5, H6, and H7.<br />
After discretizing time and assuming certain boundary conditions, xe (i) can be obtained<br />
from equation 2.9 in trinomial form, resulting in a robot trajectory following the desired<br />
zmp trajectory P∗ A (t). This method requires that mass, inertia and pose are known for all<br />
robot links.<br />
A walking trajectory is then calculated online for each footstep, but already for three<br />
steps in advance. Although normally only the first <strong>of</strong> these steps is used, the next two<br />
pre-calculated steps would bring the robot to a stop, thus improving the systems safety.<br />
Furthermore it is checked for each generated trajectory whether it remains within joint<br />
angle and velocity limits, and whether it is free <strong>of</strong> self-collision.<br />
Inthelastlayerbeforethemotorservolayer, thegeneratedwalkingtrajectoriesaremodified<br />
based on sensor feedback. This step aims at compensating disturbances, modelling errors or<br />
changes in the environment. Three controllers are used to achieve this: the horizontal torso<br />
position is shifted according to the difference between the desired and the measured zmp;<br />
the roll deflection <strong>of</strong> the upper body is compensated based on the inertial measurements;<br />
and the servo gain is lowered before foot contact to lower the impact <strong>of</strong> ground reaction<br />
forces.<br />
Higher levels <strong>of</strong> H7’s control system deal with foot point planing in environments containing<br />
obstacles, with object manipulation, or with full-body motion planing. Furthermore,<br />
autonomous behavior is improved using the visual system by object tracking or 3D<br />
reconstruction <strong>of</strong> the environment.<br />
The <strong>Human</strong>oid Robotics Project (HRP) by AIST<br />
The National Institute <strong>of</strong> Advanced Industrial Science and Technology (aist) in Tsukuba,<br />
Japan and Kawada Industries are developing the HRP robots since 1998 supported by<br />
the <strong>Human</strong>oid Robotics Project <strong>of</strong> the Ministry <strong>of</strong> Economy, Trade and Industry (meti).<br />
Figure 2.8 shows the latest models <strong>of</strong> this research project. The robot HRP-2 features 35<br />
degrees <strong>of</strong> freedom and is able to walk, lay down and stand up again [Kaneko 04]. Again,<br />
the locomotion control system is based on zmp calculation [Kaneko 02b, Kajita 03].<br />
The approach used a simplified dynamic model <strong>of</strong> the robot to enable online reference zmp<br />
trajectory calculation. Assuming an inverted pendulum constrained to a horizontal plane
16 2. Technical <strong>Control</strong> Methods for <strong>Bipedal</strong> <strong>Robots</strong><br />
Figure 2.8: The HRP robot series developed by the National Institute <strong>of</strong> Advanced Industrial<br />
Science and Technology in Tsukuba and Kawada Industries: HRP-2LR, HRP-2P, HRP-2,<br />
HRP-3P, and HRP-3<br />
<strong>of</strong> height zc as replacement model <strong>of</strong> the robot moving in the x/y-plane, the dynamics <strong>of</strong><br />
the system can be described as (similar in y-direction)<br />
¨x = g<br />
zc<br />
+ 1<br />
τy, (2.10)<br />
mzc<br />
where g denotes gravity, x the position <strong>of</strong> the body, m its mass, and τy the torque about<br />
the y-axis. This linear dynamics is called the Three-Dimensional Linear Inverted Pendulum<br />
Mode (3d-lipm). From this relation the position <strong>of</strong> the zmp can be calculated as<br />
px = − τy<br />
. (2.11)<br />
mg<br />
When substituted in equation 2.10 and rewritten as needed for the control <strong>of</strong> the zmp<br />
position , it results in<br />
px = x− zc<br />
¨x.<br />
g<br />
(2.12)<br />
Assuming the robot’s center <strong>of</strong> mass (CoM) position is given as (x,y) in the equations<br />
above, the resulting zmp can easily be calculated. But generating a walking pattern is the<br />
inverse problem: given a reference zmp trajectory, the movement <strong>of</strong> the center <strong>of</strong> mass is to<br />
be found. The authors propose to formulate the zmp control as a servo problem. Defining<br />
the time derivative ux <strong>of</strong> the horizontal acceleration ¨x as output <strong>of</strong> a servo controller<br />
working on the zmp error pref −p and as input <strong>of</strong> a reformulation <strong>of</strong> equation 2.12, the<br />
system shown in Figure 2.9 can calculate the CoM trajectory.<br />
But in this way the CoM is only moved as soon as the zmp reference value is shifted, but it<br />
should start moving before this to achieve the desired zmp. Thus a control concept known<br />
as“previewcontrol”isused, previouslydescribedbyKatayamaetal.in1985[Katayama 85].<br />
By first discretizing equation 2.12, an optimal preview servo controller is designed resulting<br />
inacontrollaw foru(k) containing anerrortermbasedonthezmp error, a state termbased<br />
on the CoM position, and a preview term based on the future zmp reference trajectory.<br />
Using a preview length <strong>of</strong> 1.6s, good matching <strong>of</strong> the zmp trajectory can be achieved.<br />
If the multibody model <strong>of</strong> HRP-2P is used instead <strong>of</strong> the simplified one, tracking errors <strong>of</strong><br />
the reference zmp can be observed. In order to compensate this, the authors suggest using
2.3. Examples for Technically <strong>Control</strong>led Bipeds 17<br />
Figure 2.9: Generating a CoM trajectory by tracking the zmp. From [Kajita 03], p1622.<br />
a second preview control using the tracking error from the multibody model as input. In<br />
doing so, the maximum zmp error can be reduced sufficiently. Using walking patterns<br />
generated by this approach, spiral stair climbing <strong>of</strong> the simulated HRP-2P could be shown.<br />
Several further improvements to this walking algorithm have been proposed. By adding<br />
an additional zmp control based on sensor feedback and virtual time shift <strong>of</strong> the reference<br />
zmp trajectory, walking on uneven terrain can be achieved with the simulated HRP-<br />
2 [Kajita 06]. Further enhancements to the gait can be reached by adding a passive toe<br />
joint [Sellaouti 06]. Higher walking speed and longer steps are made possible by adding an<br />
under-actuated phase during the single support phase before heel strike and by adapting<br />
the reference zmp trajectory accordingly. Recently, additional skills <strong>like</strong> sitting on a chair<br />
or opening and passing through a door have been shown [Arisumi 09, Escande 09].<br />
Besides the fully articulated HRP robots, advanced leg modules without an upper body<br />
have been developed to investigate more sophisticated ways <strong>of</strong> locomotion. Using these<br />
robot (HRP-2L, HRP-2LR and HRP-2LT) running-<strong>like</strong> motion could be achieved using<br />
inverted pendulum based control trajectories [Kaneko 02a, Nagasaki 03, Kajita 05]. The<br />
elasticity necessary for running is simulated by an active control <strong>of</strong> the dc motors instead<br />
<strong>of</strong> exploiting passive, mechanical elasticity. Adding a toe spring increases running speed up<br />
to 3 km/h in simulation [Kajita 07]. Currently, a dust and water pro<strong>of</strong> version <strong>of</strong> the HRP<br />
robot series is being developed [Akachi 05, Kaneko 08]. It can keep a balanced posture<br />
while handling tools <strong>like</strong> an electric screwdriver.<br />
Further Technically <strong>Control</strong>led Bipeds<br />
TheWasedaUniversityisdevelopingbipedalrobotssince1966. Themostrecentinstallment<br />
<strong>of</strong> their research is the Wabian-2R robot (WAseda BIped humANoid) featuring a total<br />
<strong>of</strong> 41 degrees <strong>of</strong> freedom [Ogura 06a]. Based on Zero-Moment Point calculations, a more<br />
human-<strong>like</strong> walking with stretched knees and toe-<strong>of</strong>f motion could be achieved [Ogura 06b].<br />
The pattern generation approach generates trajectories for the feet using inverse kinematics<br />
and Newton-Euler dynamics calculation. The knee trajectory is predetermined using cubic<br />
splines rather then exploiting the natural dynamics <strong>of</strong> the system. Compensatory motions<br />
in the waist maintain the robot’s balance according to the zmp trajectory. An iterative,<br />
genetic algorithm optimizes the calculated trajectories in order to minimize waist rolling,<br />
hip joint pitching, and ankle pitching.<br />
In 1984 the company Honda began to work on humanoid robots. The P2 robot was<br />
introduced in 1996 and can statically walk in any direction as well as climb stairs. Its six<br />
degree <strong>of</strong> freedom legs feature damping to reduce the impact on the joints while walking.<br />
The control system uses a detailed model <strong>of</strong> the robot and its foreknown environment
18 2. Technical <strong>Control</strong> Methods for <strong>Bipedal</strong> <strong>Robots</strong><br />
Figure 2.10: Further technically controlled humanoids: Asimo, KHR-3 (HUBO), Johnnie, and<br />
Wabian-2.<br />
and calculates stable trajectories with the help <strong>of</strong> the zmp method [Hirai 98]. The newest<br />
Honda robot called Asimo is equipped with 28 degrees <strong>of</strong> freedom at the height <strong>of</strong> a<br />
child [Sakagami 02]. While recent research focuses on its cognition skills and interaction<br />
with humans [Mutlu 06], the robot possesses an elaborate locomotion system. As the<br />
zmp-based walking approach is already working rather solid, further work is done on e.g.<br />
footstep planing [Chestnutt 05]. With a specialized model <strong>of</strong> Asimo, running motions <strong>of</strong><br />
up to 10 km/h can be achieved [Takenaka 09b].<br />
TherobotJohnnie hasbeendevelopedattheUniversity<strong>of</strong>Munichstartinginthelate1990s<br />
with the aim to achieve jogging motions [Gienger 00, Lohmeier 04]. It is equipped with 17<br />
joints and a sophisticated sensor setup. Using acceleration and gyroscopic sensors, the<br />
attitude <strong>of</strong> the trunk is calculated including acceleration compensation to balance the robot<br />
throughout the walking cycle. Cartesian trajectories for the center <strong>of</strong> gravity, the rotation<br />
<strong>of</strong> the upper body, and the foot pose are derived as fifth-order polynomials from reduced<br />
dynamic models and zmp positions. The computed torque method used for the modeling<br />
allows to consider the entire system dynamics for the control <strong>of</strong> the robot [Löffler 03].<br />
This model-based control poses high demands on the computational performance, the<br />
communication bandwidth, and the frequency <strong>of</strong> the sensor data. Therefore, the intended<br />
running motion could not be achieved. This goal is hoped to be reached with the successor<br />
Lola by reducing the weight, introducing new sensor systems, and revising the control<br />
concept [Lohmeier 06, Buschmann 09].<br />
Further robots <strong>of</strong> similar design and control approach are the KHR-2 and KHR-3 (aka.<br />
HUBO) by Kaist in Korea [Kim 05, Park 05], BHR-2 <strong>of</strong> the Beijing University <strong>of</strong> Science<br />
and Engineering [Peng 06], the Toyota Partner <strong>Robots</strong> [Soya 06], or the robot developed<br />
by the French inria project bip [Bourgeot 02].<br />
Beside the Zero-Moment Point method there exist other technical control systems using<br />
trajectories calculated on the basis <strong>of</strong> a dynamic model. One example <strong>of</strong> this approach can<br />
be found in the control <strong>of</strong> the robot Rabbit developed as joint project under the French<br />
Institute for Research in Computer Science and <strong>Control</strong> (inria). The project aims at the<br />
investigation <strong>of</strong> different control concepts <strong>of</strong> walking and running, stability <strong>of</strong> posture or<br />
robustness against external forces [Sabourin 05, Morris 06].
Robot Group DoF per Leg Height Weight Literature<br />
Wabian-2R Uni. Waseda, Japan 41 6+1p 1.5 65 [Ogura 06a]<br />
H6 Uni. Tokyo, Japan 35 7 1.3 55 [Kuffner 01]<br />
H7 Uni. Tokyo, Japan 30 7 1.5 57 [Chestnutt 03, Nishiwaki 06]<br />
P2 Honda, Japan 30 6 1.8 210 [Hirai 98]<br />
P3 Honda, Japan 30 6 1.6 118 [Hirai 99]<br />
Asimo Honda, Japan 26 6 1.2 52 [Sakagami 02]<br />
Asimo (research) Honda, Japan 34 6 1.3 54 [Chestnutt 05, Bolder 07, Takenaka 09b]<br />
HRP-2 AIST, Japan 30 6 1.5 58 [Kaneko 04, Arisumi 09, Escande 09]<br />
HRP-2L AIST, Japan 12 6 1.4 58 [Kaneko 02a, Nagasaki 03]<br />
HRP-3 AIST, Japan 42 6 1.6 68 [Akachi 05, Kaneko 08]<br />
SDR-4X (QRIO) Sony, Japan 38 6 0.6 6.5 [Fujita 03]<br />
Partner <strong>Robots</strong> Toyota, Japan 31 6 1.4 40 [Soya 06]<br />
KHR-2 Kaist, Korea 41 6 1.2 56 [Kim 05]<br />
KHR-3 (HUBO) Kaist, Korea 41 6 1.3 55 [Park 05]<br />
BHR-2 Uni. Beijing, China 32 6 1.6 63 [Peng 06]<br />
THBIP-I Uni. Beijing, China 32 6 1.7 130 [Zhao 02]<br />
Johnnie TU Munich, Germany 17 6 1.8 49 [Gienger 00, Löffler 03]<br />
Lola TU Munich, Germany 22 7 1.8 55 [Lohmeier 06, Buschmann 09]<br />
BARt-UH Uni. Hanover, Germany 13 3 1.3 25 [Albert 01]<br />
Lisa Uni. Hanover, Germany 12 6 1.3 38 [H<strong>of</strong>schulte 04]<br />
BIP INRIA, France 15 6 1.8 105 [Bourgeot 02]<br />
Rabbit INRIA, France 4 2 1.4 36 [Sabourin 05, Morris 06]<br />
Rh-1 Uni. Madrid, Spain 21 6 1.4 40 [Arbulu 07]<br />
Spring Turkey MIT, USA 4 2 0.6 10 [Pratt 97]<br />
Table 2.1: Recent examples for bipeds following the technical control approach (height in [m], weight in [kg]).<br />
2.3. Examples for Technically <strong>Control</strong>led Bipeds 19
20 2. Technical <strong>Control</strong> Methods for <strong>Bipedal</strong> <strong>Robots</strong><br />
Table 2.1 summarizes recent developments <strong>of</strong> bipedal walking machines following technical<br />
control approaches <strong>like</strong> the Zero-Moment Point method. The state-<strong>of</strong>-the-art on biped<br />
control concepts being inspired more by biological ideas are covert at the end <strong>of</strong> the next<br />
chapter in section 3.4.<br />
2.4 Assessment <strong>of</strong> Technical <strong>Control</strong> Approaches<br />
Technical control approaches as those mentioned above rely on concepts developed for<br />
industrial robotics and sound mathematical calculations <strong>like</strong> the zmp stability concept<br />
and joint angle control. While these methods have been shown to work for a multitude <strong>of</strong><br />
applications, never-the-less several shortcomings can be observed. The following section<br />
will discuss the advantages (Plus) and drawbacks (Minus) <strong>of</strong> this class <strong>of</strong> control systems<br />
and machines.<br />
Plus: Analytical Approach based on Multibody Dynamics<br />
Technical control approaches describe the process to be controlled as a dynamical system<br />
in an analytical way. The complexity varies from simplified inverted pendulum models to<br />
full multibody dynamics models <strong>of</strong> the robot and its environment. Physical laws build<br />
the foundation <strong>of</strong> control algorithms that are analytically deduced from these models.<br />
Assuming a correct and exhaustive model, the algorithms can derive a stable solution<br />
within the considered situation.<br />
Plus: Mathematically Sound<br />
The calculations needed for these approaches rely on mathematical and mechanical tools<br />
and strategies that have shown their soundness and correctness over the last decades or<br />
centuries. Even methods developed explicitly for biped walking <strong>like</strong> the Zero-Moment Point<br />
calculation are already applied for more that 30 years [Vukobratovic 04]. Considering this<br />
fact and the analytical nature <strong>of</strong> the concepts, the confidence in their feasibility is well<br />
justifiable.<br />
Plus: Exact and Purposeful Motions<br />
As exact joint trajectories are generated and – at least considering the used models –<br />
stability is ensured, highly purposeful motions <strong>of</strong> the controlled robots are possible. This<br />
allows to implement skills going beyond mere walking. Climbing stairs, crouching while<br />
walking, or performing martial arts exercises are just a few examples <strong>of</strong> what has been<br />
shown with state-<strong>of</strong>-the-art humanoids.<br />
Plus: Tried and Tested Mechanics<br />
In nearly all cases, the robots described above can be designed based on approved industrial<br />
mechanics as their control methods do not create novel requirements for e.g. the actuation<br />
system. The use <strong>of</strong> high-end dc motors or gear boxes <strong>like</strong> harmonic drives allows precise<br />
movements. This, in fact, is a mandatory requirement <strong>of</strong> technically controlled machines,<br />
as tracking errors <strong>of</strong> the given joint trajectories would introduce a discrepancy from the<br />
model that could endanger stability. High frequency and high gain controllers as used in<br />
industrial robotics are necessary to guarantee exact reproductions <strong>of</strong> trajectories.
2.4. Assessment <strong>of</strong> Technical <strong>Control</strong> Approaches 21<br />
Minus: Slow and Unnatural Looking Motions<br />
But despite the advantages just mentioned and the long lasting history <strong>of</strong> technically<br />
controlled bipeds, the resulting motions are still far behind those observed in humans or<br />
othertwo-leggedanimals. <strong>Walking</strong>and, whereevenpossible, runningspeediscomparatively<br />
low and motions do not look naturally. One reason for this can be found in the fact<br />
that those machines only do morphological and kinematic imitation <strong>of</strong> human walking.<br />
However, the dimensions and trajectories do not fit to the masses and actuation concepts<br />
<strong>of</strong> technical robots. The walking motions <strong>of</strong> the robot H7 has been compared to that<br />
<strong>of</strong> human subjects regarding CoM trajectory, joint angles, torques and ground reaction<br />
force [Kagami 03]. In nearly all cases the values differ substantially, with humans showing<br />
the more sophisticated and effective trajectories.<br />
Minus: High Energy Costs<br />
Locomotion <strong>of</strong> technically controlled bipeds has been shown to be very energy consuming.<br />
Several facts can be hold responsible for that: the necessity for high precision joint control<br />
as well as the heavy mechanics require high powered actuators. Following joint trajectories<br />
that do not match the actual movement <strong>of</strong> the robot’s segments oppose inertia and produce<br />
high peak torques. No energy is stored in elastic elements. The trajectories are optimized<br />
for stability resulting in unfavorable movements regarding efficiency. For instance the<br />
knee joint is bent much more than in human walking where an efficient semi-flat gait with<br />
lower impact forces and less head movement can be observed. It can be estimated that<br />
technically controlled robots <strong>like</strong> Asimo use at least 10 times the energy (normalized by<br />
weight and height) <strong>of</strong> a typical human during walking [Collins 05]. Similar results can be<br />
seen when comparing the simulated running motion <strong>of</strong> HRP-1 in simulation to human<br />
running [Kajita 02]. Peak torques <strong>of</strong> nearly 2000Nm and actuator power <strong>of</strong> up to 8500W<br />
are required for tracking the pre-calculated trajectory.<br />
Minus: High Computational Demands<br />
Computing joint trajectories based on a detailed dynamic model and stability constrains<br />
<strong>like</strong> zmp is computational expensive. As a consequence, many systems pre-calculate<br />
trajectories <strong>of</strong>fline, resulting in an inflexible control. On-line pattern generation <strong>like</strong> the<br />
one utilized in H7 take up to 5.2 seconds for calculating a three-step trajectory and<br />
still must be modified based on sensor feedback due to lacking accuracy <strong>of</strong> the dynamic<br />
multibody model [Nishiwaki 06]. Also the communication bandwidth can prove as bottle<br />
neck, as these control systems need high frequency sensor information for updating their<br />
models and equally fast control flow for precise position control <strong>of</strong> joint trajectories. This<br />
is the reason for changing the communication bus on LOLA from the slower canbus <strong>of</strong> its<br />
predecessor Johnnie to a sercos-based system [Lohmeier 06].<br />
Minus: Dependent on Dynamic Model<br />
Being based on dynamic models <strong>of</strong> the robot and the environment, technical control<br />
approaches consequently depend on the model’s correctness and level <strong>of</strong> detail. If not<br />
compensated, discrepancies from the model can lead to instability. Errors can occur by<br />
model inaccuracy concerning e.g. mass distribution, slip, gear backlash, or foot impact on<br />
uneven terrain. External forces and disturbances will lead to derivation, too.
22 2. Technical <strong>Control</strong> Methods for <strong>Bipedal</strong> <strong>Robots</strong><br />
Minus: No Exploitation <strong>of</strong> Natural Dynamics<br />
Exploiting the passive dynamics <strong>of</strong> the robot can help in creating natural motions, in<br />
saving energy, and in simplifying control. Technically controlled bipeds normally do<br />
not and cannot exploit the natural dynamics <strong>of</strong> the system as the joints are forced into<br />
fixed trajectories. Furthermore retarding gears will prohibit the natural motions to take<br />
place and make it difficult to store energy in parallel springs or to use the self-stabilizing<br />
properties <strong>of</strong> elastic actuators. It has been shown that walking can be achieved by purely<br />
relying on passive dynamics even without any actuation given cleverly designed mechanics,<br />
proper weight distribution and a small energy feed [McGeer 90]. Details on this principle<br />
<strong>of</strong> passive walking can be found in section 3.4.1.<br />
Minus: Difficult to Add Adaptability<br />
It can turn out to be difficult to add adaptability and to enhance the robustness <strong>of</strong> the<br />
control system in technically controlled bipeds. Very small disturbances can still be<br />
managed if safety stability margins are kept high enough. Otherwise feedback must be<br />
introduced, e.g. by comparing the measured zmp to the reference zmp and then adapting<br />
the model or the trajectories as for example done in the control <strong>of</strong> Rabbit [Wieber 06].<br />
More significant errors can prove to be hard to compensate in these monolithic systems.<br />
The models cannot reflect reality, and due to this fact, stiff mechanics, position based<br />
joint control, or even fully pre-calculated trajectories, adaptation to unknown terrain or<br />
external forces proves to be a tough problem.<br />
Beyond any doubt technical control approaches for bipeds have shown their feasibility and<br />
yielded impressive skills and machines. However, looking at the drawbacks just mentioned<br />
and comparing the results to what nature is capable, the following questions arise: How is<br />
nature managing to do so much better, are there fundamental differences in the control<br />
concepts, and can nature’s solutions be transferred to technical implementations? The<br />
next section is trying to answer these questions by sketching out how human motion<br />
control works, looking in particular at the processes during normal walking. Then selected<br />
literature on biologically motivated robotic approaches is reviewed.
3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Despite many decades <strong>of</strong> research on two-legged walking machines, the performance <strong>of</strong> the<br />
developed robots is still far behind human capabilities. So it is not surprising that in recent<br />
years robotics researchers tried to find help in the results <strong>of</strong> biomechanics, neurosciences,<br />
human movement analysis, and other biological fields. Therefore, this chapter first presents<br />
selected work related to these topics serving as introduction to the research on human<br />
locomotion control. This will allow to better compare the technical approaches with the<br />
natural one and to show the differences that motivated this work. Finally, literature on<br />
biologically inspired biped control in robotics is reviewed.<br />
Throughout this chapter, terminology <strong>of</strong> anatomy, neuroscience, and biomechanics will<br />
appear. Thetermsoutsidecommonparlanceareexplainedatfirstappearance. Additionally,<br />
the reader may refer to Appendix A including several tableaux illustrating anatomical<br />
planes, directions and joint rotations, a figure <strong>of</strong> the human skeleton marking the locations<br />
<strong>of</strong> major bones, and a diagram and a list <strong>of</strong> skeletal muscles indicating their location,<br />
function, and common abbreviation.<br />
3.1 Structural Organization <strong>of</strong> Motion <strong>Control</strong><br />
When examining human locomotion control, two different aspects can be distinguished: the<br />
structure <strong>of</strong> the control and the actual functional units that are responsible for generating<br />
locomotion within this structure. This section introduces the structural organization <strong>of</strong><br />
motion control, whereas the next section will discuss how dynamic walking is produced.<br />
In the following, structural organization is to be understood as the architecture underlying<br />
the control <strong>of</strong> locomotion. Topics to be discussed include the role <strong>of</strong> the morphology<br />
and the muscle, communication and processing by the nerve pathways and neural cells,<br />
principles <strong>of</strong> perception and creation <strong>of</strong> action, the layout <strong>of</strong> groups <strong>of</strong> nerve cells, or the<br />
integration <strong>of</strong> feedback control.<br />
3.1.1 Functional Morphology<br />
It is <strong>of</strong>ten claimed that human morphology has evolved to be optimal regarding bipedal<br />
locomotion. This introduces the question if bipedalism emerged mainly because <strong>of</strong> ad-
24 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.1: Possible modes <strong>of</strong> locomotion from which bipedalism may have originated.<br />
From [Richmond 02], p72.<br />
vantages gained by two-legged walking. It could also be presumed that other benefits <strong>of</strong><br />
standing on two legs have been more prominent, thus guiding the optimization process in<br />
other directions.<br />
About a dozen hypotheses for the evolution <strong>of</strong> bipedality have been stated over the last<br />
century. Most <strong>of</strong> them are based on the assumed behavior <strong>of</strong> the earliest known hominids<br />
(primates that use a habitual upright bipedal gait) <strong>of</strong> about six million years ago. These<br />
hypotheses differ in which advantage <strong>of</strong> bipedalism is supposed to be decisive. Examples<br />
include greater viewing distance, higher efficiency than ape quadrupedalism, reducing<br />
skin exposure to lower heat stress, tools usage, or arm carrying. K. D. Hunt analyzes<br />
chimpanzee bipedal behavior and the anatomy <strong>of</strong> the Australopithecus africanus, and<br />
argues for a synthesis <strong>of</strong> two scenarios [Hunt 94]. A combination <strong>of</strong> the terrestrial and<br />
arboreal bipedal postural feeding hypotheses could explain the poor bipedal mechanics<br />
and the arboreal competence <strong>of</strong> early hominids. Other reasons stated might have well<br />
played a role in refining the locomotor bipedalism in Homo erectus.<br />
Richmond et al. review literature on possible modes <strong>of</strong> locomotion from which bipedalism<br />
could have originated [Richmond 02]. They evaluate these modes in the light <strong>of</strong> current<br />
evidence from comparative primate anatomy, biomechanics, and fossil hominid anatomy.<br />
Possible candidates are arboreal or terrestrial quadruped ancestors, gibbon-<strong>like</strong> brachiating<br />
ancestors, climbing ancestors, or knuckle-walking ancestors (Figure 3.1). It is stated that<br />
human evolved most <strong>like</strong>ly from an ancestor adapted to knuckle-walking and climbing and<br />
thus reject all hypotheses that are purely based on arboreal ancestors.<br />
Wang et al. argue that the development <strong>of</strong> erect walking and longer legs compared to<br />
the trunk length might partly be motivated by load-carrying. In the period <strong>of</strong> the first<br />
hominids with modern body proportions at around 1.8–1.5 Million years ago, the use <strong>of</strong>
3.1. Structural Organization <strong>of</strong> Motion <strong>Control</strong> 25<br />
stone tools and raw material transport increases. Computer simulations <strong>of</strong> loaded and<br />
unloaded walking show that indeed carrying loads is more effective in erect posture and<br />
thus could be the reason for today’s human proportions beside the advantage <strong>of</strong> persevering<br />
walking.<br />
Early bipedal walking seems to have been much more compliant than walking found in<br />
modern humans. D. Schmitt suggests that the compliant gait found in early hominids<br />
and most <strong>of</strong> today’s apes can be explained by their smaller bodies and poorly stabilized<br />
hindlimbs [Schmitt 03]. These modes <strong>of</strong> locomotion allow to achieve fast walking speeds<br />
with long strides <strong>of</strong> low frequency, low vertical peak forces, and good impact shock damping,<br />
but create significant energy costs. The increase <strong>of</strong> energy efficiency by using a stiff-legged,<br />
inverted pendulum-<strong>like</strong> gait did only take place more recently in early members <strong>of</strong> the<br />
genus Homo with their robust skeleton and joints.<br />
Research<strong>of</strong>Massaadetal.isgoingalongsimilarlines[Massaad 07]. Inwalkingexperiments<br />
with several subjects it is shown that humans are perfectly able to walk more flatly or<br />
bouncy, but still normal gait amounted to a semi-flat form in the course <strong>of</strong> evolution. While<br />
flat walking reduces the mechanical work on the center <strong>of</strong> mass, bouncy walking decreases<br />
the energy the muscles have to supply be relying on pendulum-<strong>like</strong> passive dynamics.<br />
Furthermore muscles seem to work in unfavorable conditions during flat walking. Thus the<br />
semi-flat walking gait <strong>of</strong> modern humans may well present an optimal solution in balancing<br />
efficiency against muscle work.<br />
The geometrical layout <strong>of</strong> the human leg in particular has been examined on its adequacy<br />
for walking and running. As just mentioned, walking with a fully straight leg is not the best<br />
solution, andcomplianceisidentifiedasanecessaryfeature, too. Seyfarthetal.investigated<br />
the stability <strong>of</strong> elastic, three-segment legs [Seyfarth 01]. They demonstrated that instability<br />
in form <strong>of</strong> counter-rotation <strong>of</strong> joints can be reduced in several ways: nonlinear springs,<br />
asymmetric segment lengths, biarticular structures, mechanical constraints <strong>like</strong> heels, or a<br />
bow-<strong>like</strong> mode <strong>of</strong> movement. Except for the last strategy, all <strong>of</strong> these can be found in the<br />
human leg, thus gaining internal self-stabilizing properties. More details on the dynamics<br />
and self-stabilization <strong>of</strong> tri-segmented elastic limbs in mammals are reviewed and discussed<br />
by Fischer and Blickhan [Fischer 06].<br />
The fact that appropriately designed mechanics can significantly reduce the control effort<br />
is discussed by Blickhan et al. [Blickhan 07]. Modelling the quasi-elastic leg operation<br />
as spring-mass model, it is demonstrated that such an“intelligent mechanics”can show<br />
attractive behavior and passively compensate external disturbances without sensing them.<br />
This holds true for running (Figure 3.2) as well as for walking. This passive control only<br />
works if the actuator features muscle-<strong>like</strong> properties such as inherent compliance, adjustable<br />
joint stiffness, and shock absorption, but also damping. Furthermore, for the system to fall<br />
back in an attractive cycle, the touchdown angle <strong>of</strong> the swing leg must be properly chosen,<br />
whereas leg retraction before touchdown can extend the range <strong>of</strong> acceptable angles.<br />
Besides the self-stabilizing properties <strong>of</strong> the elasticity <strong>of</strong> the muscle-tendon system, locomotion<br />
and other movements can also benefit from elastic energy storage. Witte et al.<br />
show that in fact energy is stored in the human locomotor apparatus [Witte 97]. The<br />
amount <strong>of</strong> energy accumulated as recorded in their experiments is considerable and should<br />
not be neglected in the consideration <strong>of</strong> human functional morphology and its role during<br />
locomotion.
26 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.2: Elastic operation <strong>of</strong> the leg can passively stabilize running in the presence <strong>of</strong><br />
external disturbances without changing the angle <strong>of</strong> attack or the stiffness. From [Blickhan 07],<br />
p211.<br />
Günther et al. examine leg geometry and joint axis alignment with respect to the minimization<br />
<strong>of</strong> the sum <strong>of</strong> joint torques as optimization criterion [Günther 04]. By including<br />
sensible geometrical and biomechanical constraints, the extended human leg configuration<br />
indeed proves to be an optimal solution with its short foot and unequal ankle and knee<br />
angles.<br />
In due consideration <strong>of</strong> what was said in the previous paragraphs, Witte et al. suggest to<br />
base the design (and control) <strong>of</strong> bipedal robots on human functional morphology, thereby<br />
moving from purely anthropomorphic to “anthrop<strong>of</strong>unctional” robots [Witte 04]. It is<br />
shown that human gait is energetically close to optimal by using resonance mechanisms:<br />
the arms and the swing leg move <strong>like</strong> an suspended pendulum, the stance leg <strong>like</strong> an<br />
inverted pendulum, and the trunk involves torsional springs. In addition, the proportions<br />
and the mass distribution in the trunk and in the swinging extremities compensate for<br />
undesirable torques [Witte 91]. Witte and his colleagues conclude that bipedal locomotion<br />
relies on the coordinated interaction <strong>of</strong> masses, gravity, elasticity, and muscle work, thus<br />
going beyond pure rigid body dynamics. They also point out that, with humans being<br />
vertebrates, the central role <strong>of</strong> the trunk and spinal cord as origin or at least initiator <strong>of</strong><br />
movement should not be neglected.<br />
Implications for Robotics:<br />
The human locomotion apparatus is highly optimized for efficient bipedal<br />
locomotion. To facilitate walking and to reduce the control effort, robot<br />
design should be based on functional morphology and its motions<br />
should exploit the inherent dynamics <strong>of</strong> the system. Key aspects<br />
are a semi-flat walking gait, proper mass distribution and geometry <strong>of</strong><br />
trunk and extremities, and low-resistant elastic actuators.<br />
3.1.2 Neurological Basics<br />
After the discussion <strong>of</strong> passive control through intelligent mechanics in the previous section,<br />
in the following the active control system <strong>of</strong> human motion control is considered. Unless
3.1. Structural Organization <strong>of</strong> Motion <strong>Control</strong> 27<br />
(a) (b)<br />
Figure 3.3: (a) The central nervous system consists <strong>of</strong> the brain and the spinal cord. (b) The<br />
peripheral nervous system <strong>of</strong> the lower extremities. From [Hamill 03], p102.<br />
noted otherwise, the information in this section is taken from the biomechanics book by<br />
Hamill and Knutzen [Hamill 03].<br />
Coordination and monitoring <strong>of</strong> human movements is an extensive task considering the<br />
number <strong>of</strong> muscles and sensory receptors involved. The nervous system is responsible for<br />
this job by conveying and processing the sensor information and generating an appropriate<br />
stimulation <strong>of</strong> muscle fibers.<br />
The nervous system is composed <strong>of</strong> two parts, the central nervous system and the peripheral<br />
nervous system. The central nervous system consists <strong>of</strong> the brain and the spinal cord,<br />
and can be seen as central processing unit initiating all movement. The remaining nerves<br />
outside the brain and spinal cord make up the peripheral nervous system. It connects the<br />
inner organs and muscles with the spinal cord via the spinal nerves that exit the spinal<br />
cord on the anterior, or ventral, side <strong>of</strong> the vertebral column. The nerves emerging from<br />
the sensory receptors enter the spinal cord on the posterior, or dorsal, side. By this means,<br />
31 pairs <strong>of</strong> spinal nerves enter and exit the spinal cord. For instance, the lower extremities<br />
are connected via the five parts <strong>of</strong> the lumbar and the five parts <strong>of</strong> the sacral region at the<br />
lower end <strong>of</strong> the spine. Figure 3.3 illustrates the central nervous system (a) and the lower<br />
part <strong>of</strong> the peripheral nervous system (b).<br />
The base unit <strong>of</strong> the nerve system is the neuron. Motor neurons, being connected to and<br />
stimulating muscle fibers, consist <strong>of</strong> the cell body, dentrites, and the axon (Figure 3.4).<br />
The cell body, or soma, usually resides within the gray matter <strong>of</strong> the spinal cord or in a<br />
ganglia, a group <strong>of</strong> neurons outside the cord, that can span up to three levels <strong>of</strong> the spinal<br />
cord. Information from other neurons is passed to the neuron via bundles <strong>of</strong> dendrites.
28 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.4: The cell body, dentrites and axon <strong>of</strong> a motor neuron. The axon connects to other<br />
neurons or to motor fibers. From [Hamill 03], p105.<br />
This allows cross-talk <strong>of</strong> neurons from all over the spinal cord and other ganglia. The<br />
axon, a large nerve fiber covered with an insulated shell, forms the output <strong>of</strong> a neuron. It<br />
connects to other neurons or to muscle fibers, where it fans out to form motor endplates<br />
and embeds into fissures near the center <strong>of</strong> the fibers. One single motor neuron connects to<br />
up to 2000 fibers as in the gluteus maximus, or only to 5 or 6 fibers as in the eye muscles.<br />
If sufficiently activated, the motor neuron innervates all its muscle fibers by chemical<br />
transmission and causes them to contract within a few milliseconds. Depending on the<br />
type <strong>of</strong> the motor unit (corresponding to the existing types <strong>of</strong> muscle fibers), this reaction<br />
will elapse slower or faster. The slow-twitch oxidative Type I units have reaction times<br />
greater than 70ms and transport impulses at approximately 80 m/s. Fast-twitch oxidative<br />
Type IIa motor units contract after about 30-50ms. The fast-twitch glycolytic Type IIb<br />
units are even faster with impulse transmission at more than 100 m/s resulting in reaction<br />
times <strong>of</strong> about 30-40ms. Still, viewed from the perspective <strong>of</strong> control theory, these delays<br />
would make feedback control difficult. Type IIb units develop high tension, but fatigue<br />
more quickly than Type IIa or Type I units. Muscles differ in their number <strong>of</strong> associated<br />
motor neurons and the ratio <strong>of</strong> Type I, IIa, and IIb units depending on the nature <strong>of</strong> their<br />
task, e.g. slow, precise movements, or repetitive high forces.<br />
The actual impulse traverses the nerve in form <strong>of</strong> an action potential. The electric potential<br />
<strong>of</strong> the membrane changes from its neutral state at about -70mV by rapid depolarization,<br />
repolarization and hyperpolarization as the impulse travels along the nerve fiber. When<br />
the impulse reaches the muscle fiber at the motor endplates, it generates cross-bridging<br />
and thus shortening within the muscle sarcomere (excitation-contraction coupling). A<br />
single action potential develops a single twitch respond <strong>of</strong> the muscle. But if the impulses
3.1. Structural Organization <strong>of</strong> Motion <strong>Control</strong> 29<br />
Figure 3.5: Interneurons can excite or inhibit other neurons. The Renshaw cell is considered to<br />
play an important role in muscle coordination. From [Hamill 03], p108.<br />
follow continuously and in short progression, the twitches will sum up and form a constant<br />
muscle tension, a tetanus. The tension will decline as the impulses thin down. A muscle<br />
will create the more force the more <strong>of</strong> its motor neurons are firing, i.e. the more neurons<br />
are recruited, and the higher the rate at which they are sending impulses.<br />
Besides being innervated, the action potential in a motor unit can also be inhibited by<br />
connected neurons and interneurons within the spinal cord. Interneurons can be excitatory<br />
or inhibitory, and are interconnecting branches. One type <strong>of</strong> interneuron is the Renshaw cell<br />
which is considered responsible for organizing coordinated muscular responses. Figure 3.5<br />
illustrates a possible inhibition <strong>of</strong> a motor neuron via a Renshaw interneuron.<br />
While the motor neurons are the means by which the central nervous system controls<br />
muscle action, the sensory neurons provide the necessary feedback on the state <strong>of</strong> the<br />
musculoskeletal system, the skin, and other sensory organs <strong>of</strong> the body. After processing<br />
this information, the central nervous system will initiate appropriate reactions.<br />
The so called proprioceptors supply information on the state <strong>of</strong> the musculoskeletal system.<br />
These include the main sensory receptors <strong>of</strong> the muscles, the muscle spindles, and the<br />
Golgi tendon organ. Muscle spindles and their corresponding neurons measure the stretch<br />
<strong>of</strong> a muscle. The spindles are located parallel to the muscle fibers within the belly <strong>of</strong> the<br />
muscle and are enclosed in a capsule, forming a spindle shape, hence the name. Each<br />
capsule contains up to 12 nuclear bags and nuclear chain fibers that are innervated by the<br />
so called gamma motor neurons. The gamma motor neurons are located at ventral exits<br />
<strong>of</strong> the spinal cord close to the alpha motor neurons that stimulate the muscle fibers (see<br />
above). The fibers again are connected to Type I or Type II sensory neurons that send<br />
information to the dorsal horn <strong>of</strong> the spinal cord where their cell body is located. Type I<br />
sensory neurons are more sensitive to muscle stretch whereas Type II sensory neurons only<br />
react when the stretch surpasses a certain threshold. The sensory neurons will fire at a<br />
higher rate if the muscle is elongated more rapidly. If the muscle remains in the stationary<br />
stretched state, Type I neurons will fire at a low, constant rate.<br />
In contrast to the muscle spindle, the Golgi tendon organ measures force or tension in<br />
the muscle. The Golgi tendon organ lies between the muscle fibers and the tendon that<br />
connects to the bone, but in parallel to the tension generated in the passive elements<br />
during stretch. The sensory neuron connected to the Golgi tendon organ create a response<br />
that is proportional to the load <strong>of</strong> the muscle and to the rate <strong>of</strong> change <strong>of</strong> the load.
30 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Besides the two receptors just mentioned, there exist additional proprioceptors. A number<br />
<strong>of</strong> sensory receptors lie in proximity <strong>of</strong> the joints: the pacinian corpuscle responds to<br />
pressure, the Ruffini endings measure joint position and velocity, and free nerve endings<br />
create a pain sensation. The skin reacts to pressure, vibration, heat, cold, and damage.<br />
The vestibular system located in the inner ear is responsible for the sense <strong>of</strong> balance and<br />
spatial orientation. The cupula which lies within the ampulla arising in the semicircular<br />
canal <strong>of</strong> the vestibular organ, contains hair bundles and acts upon angular acceleration.<br />
The utricle and saccule in the vestibular sac again possess hair cells and are sensitive to<br />
linear acceleration, including gravity. The vision system also contributes to the sense <strong>of</strong><br />
balance by estimating the horizon and the optical flow. Contradiction <strong>of</strong> these two sources<br />
<strong>of</strong> information can cause nausea, e.g. when traveling in a swaying ship without the eyes<br />
perceiving this movement.<br />
Implications for Robotics:<br />
Biological control is organized as a network <strong>of</strong> basic units (neurons) and<br />
communication channels (nerve fibers). While the system is concentrated<br />
at the brain and spinal cord, it is still highly distributed and spatially<br />
related, e.g.motorneuronsforthefeetarelocatesatthelowerend<strong>of</strong>the<br />
spinal cord. The basic processing units can be gradually stimulated<br />
or inhibited. A distributed sensor system provides feedback on joint<br />
position, velocity, and torque, as well as a sense <strong>of</strong> balance. Motor control<br />
allows precise position control, adjustable elasticity, or pure torque<br />
control. Compared to technical systems, processing and communication<br />
in biological systems is relatively slow.<br />
3.1.3 Sensorimotor Interaction<br />
After having discussed how sensory information is transferred to the spinal cord and how<br />
motor action can be initiated from there, the question remains on how sensor input is<br />
processed to create an appropriate reaction. This section will introduce the foundation <strong>of</strong><br />
sensorimotor interaction in form <strong>of</strong> reflexes.<br />
The term reflex as“an automatic or involuntary response to a stimulus” 1 was first used in<br />
1748 by David Hartley. Its common scientific usage was established in Sherrington’s study<br />
<strong>of</strong> the nervous system from 1906 [Sherrington 06]. But while the concept <strong>of</strong> reflexes being<br />
a stereotyped response to nervous stimuli has persisted for long despite contradictionary<br />
evidence, nowadays it is agreed upon being false. Rather, reflex actions have been shown<br />
to be heavily affected by modulation and to exist in a wide range <strong>of</strong> complexity. Motor<br />
actions that conform the most with the former notion <strong>of</strong> a reflex are those“mediated by<br />
relatively straightforward circuitry in the spinal cord”[Nicholls 92]. But despite being<br />
in the focus <strong>of</strong> research for centuries, the function <strong>of</strong> reflexes especially during human<br />
locomotion is only slowly becoming clearer [Zehr 99].<br />
The most basic form <strong>of</strong> reflex arcs are monosynaptic reflexes. Sensory information is<br />
entering the spinal cord at the same level as the motor stimulation is leaving it [Hamill 03].<br />
On example for such a reflex is the stretch or myotatic reflex that creates a short muscle<br />
1 New Webster’s Dictionary and Thesaurus <strong>of</strong> the English Language
3.1. Structural Organization <strong>of</strong> Motion <strong>Control</strong> 31<br />
Figure 3.6: The flexor reflex as an example for a monosynaptic reflex arc. It causes quick<br />
withdrawal from a pain source. From [Hamill 03], p111.<br />
contraction after a rapid stretch. As the stretch is imposed on the muscle, the Type I<br />
sensory neurons <strong>of</strong> the muscle spindles are activated and stimulate interneurons in the<br />
spinal cord. If the activation is high enough, the interneurons will excite the motor neurons<br />
<strong>of</strong> the muscle just stretched and initiate its contractions. At the same time, additional<br />
connections to inhibitory interneurons will cause a reciprocal inhibition, or relaxation, <strong>of</strong><br />
the antagonistic muscle. Similarly, the Golgi tendon organs are responsible for the inverse<br />
stretch reflex. In case <strong>of</strong> a high velocity stretch, the reflex creates a relaxation <strong>of</strong> the<br />
muscle by reducing the alpha motor neuron output, thus relieving the strain <strong>of</strong> the muscle.<br />
Another example for monosynaptic reflexes is the flexor reflex (Figure 3.6). It triggers a<br />
rapid withdrawal movement due to a sensory information indicating pain.<br />
Reflexes processing information from different levels <strong>of</strong> the spinal cord and affecting muscles<br />
further apart are termed propriospinal. The crossed extensor reflex is an example for this<br />
group <strong>of</strong> reflexes. Similar to the flexor reflex, it reacts to pain stimulus, but it also initiates<br />
an extention <strong>of</strong> the limb opposite to the pained one. Another example for propriospinal<br />
reflexes is the tonic neck reflex. Here, a rotation <strong>of</strong> the head to one side is causing an<br />
extension <strong>of</strong> the arm on the same side and a flexion <strong>of</strong> the arm on the contralateral side.<br />
If the motor response results from information transmitted to and processed by the<br />
brain, a reflex is called supraspinal. Most postural reflexes belong to this group, e.g. the<br />
labyrinthine righting reflex. Incorporating upper levels <strong>of</strong> the nervous system and many<br />
levels <strong>of</strong> the spinal cord, it stimulates the neck and limb muscles to maintain or move to<br />
an upright position.<br />
However, reflexes do not always react to sensory stimulus in the same, recurring way. While<br />
monosynaptic reflexes show little variation, more complex reflexes seem to be modulated.<br />
Zehr et al. examined the function <strong>of</strong> sural nerve reflexes during human walking [Zehr 98].<br />
They show that the muscular response initiated by the reflexes depends on the part <strong>of</strong><br />
the step cycle in which the nerve was stimulated as well as on the intensity <strong>of</strong> stimulation.<br />
These cutaneous reflexes mainly seem to serve for postural stabilization during walking,<br />
e.g. lifting the leg during the first part <strong>of</strong> the swing phase by ankle dorsiflexion and knee<br />
flexion in case the foot collides with an obstacle.
32 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Zehr and Stein also review research on the modulation <strong>of</strong> reflex responses during static<br />
tasks and locomotion [Zehr 99]. They show the existence <strong>of</strong> task-, phase- and intensity<br />
dependency. A simple modulation <strong>of</strong> the soleus H-reflex 2 depending on the subjects<br />
postural orientation can be observed. While keeping a constant peripheral stimulation, the<br />
amount <strong>of</strong> reflex inhibition changes [Rossi 88]. Similar modulation effects can be shown<br />
on the tonic motor output by cutaneous nerve stimulation while sitting or standing.<br />
Rossignol et al. review literature on the dynamic sensorimotor interactions in the spinal<br />
cord and at supraspinal levels [Rossignol 06]. It is postulated that locomotion emerges<br />
as a combination <strong>of</strong> central, feed-forward programs and feedback mechanisms. The<br />
central program originates in some kind <strong>of</strong> spinal circuitry, a central pattern generator<br />
that is genetically prescribed and generates basic motion patterns to trigger, stop, or<br />
steer locomotion. Feedback provoked by sensory afferents from spinal to supraspinal<br />
levels modulates the locomotor pattern. This interaction is a phase-dependent, corrective<br />
response not only due to heavy perturbations, but also present during normal, stable<br />
locomotion. Sensorimotor interaction can interfere with the descending pathways at various<br />
levels <strong>of</strong> the nervous system and results in a continuous adjustment <strong>of</strong> the overall emergent<br />
locomotion behavior.<br />
Implications for Robotics:<br />
Reflexes provide the basic method for feedback control in nature.<br />
They work independently, locally, and in parallel. Reflexes can occur<br />
in different degrees <strong>of</strong> complexity in terms <strong>of</strong> the number <strong>of</strong> sensory<br />
receptors and muscles that are involved and <strong>of</strong> the level <strong>of</strong> the central<br />
nervous system they are located on. Reflexes can be modulated by<br />
the intensity <strong>of</strong> the stimulus, by the current phase <strong>of</strong> motion, or by the<br />
current task in general (walking vs. sitting). Combined with central,<br />
feed-forward programs stable locomotion can be achieved.<br />
3.1.4 Hierarchical Layout <strong>of</strong> Motion <strong>Control</strong><br />
To produce a limb motion during grasping or locomotion, a multitude <strong>of</strong> muscles have to<br />
work together in a coordinated manner. For each <strong>of</strong> these muscles, again multiple muscle<br />
neurons have to be stimulated with suitable intensity. It does not seem <strong>like</strong>ly that for each<br />
motion, either voluntary or instinctive, this vast number for neurons is directly controlled<br />
by a region in the brain. Rather, one might suggest that motion control takes place on<br />
successive levels.<br />
Neuroscientific research results seem to support the assumption that neural motor control<br />
is <strong>of</strong> a hierarchical layout. Bizzi et al. found a spatial connection between the stimulation <strong>of</strong><br />
regions in the spinal cord <strong>of</strong> frogs and the kinematic reaction <strong>of</strong> its legs [Bizzi 91, Lemay 01].<br />
Exciting these interneurons at increasing strength produces similarly increasing force<br />
measured at the ankle <strong>of</strong> the frog’s limb. Co-stimulation <strong>of</strong> different regions in the spinal<br />
cord results in a vectorial sum <strong>of</strong> the corresponding ankle forces. This suggests the existence<br />
<strong>of</strong> movement primitives creating activities <strong>of</strong> whole groups <strong>of</strong> muscles. A limited number<br />
<strong>of</strong> these simple units can generate a rich variety <strong>of</strong> movements.<br />
2 H<strong>of</strong>fmann reflex: reaction <strong>of</strong> muscles after electrical stimulation <strong>of</strong> sensory fibers in their innervating<br />
nerves
3.1. Structural Organization <strong>of</strong> Motion <strong>Control</strong> 33<br />
Figure 3.7: Decomposition <strong>of</strong> 32 emg waveforms during walking resulting in five basic temporal<br />
components. Different statistical methods produce similar components. From [Ivanenko 06],<br />
p340.<br />
In order to analyze to what extent muscle activity is generated by centrally organized<br />
movement primitives (or muscle synergies), electromyographic 3 (emg) signals <strong>of</strong> intact<br />
and deafferented (limited sensor feedback) frogs during swimming and jumping are compared<br />
[Cheung 05]. Synergies can be found by a modified formulation <strong>of</strong> the non-negative<br />
matrix factorization algorithm. Most synergies are not specific to one but are shared<br />
by both data sets, thus suggesting a central origin and organization. However, with the<br />
reduced sensor feedback, the synergies are altered in amplitude and timing, indicating that<br />
some modification by feedback is taking place. It is further speculated that each shared<br />
synergy corresponds to a basic biomechanical function.<br />
Later results on the combination <strong>of</strong> such muscle synergies for movement show that the<br />
same synergies are even used for different modes <strong>of</strong> locomotion [Bizzi 07]. Each synergy<br />
can be seen as function unit in the spinal cord producing a specific pattern <strong>of</strong> muscle<br />
activation. By generating a more sophisticated motion as combination <strong>of</strong> these simpler<br />
modules, the complexity <strong>of</strong> locomotion control is reduced.<br />
Analysis <strong>of</strong> human locomotion control leads to similar findings. Earlier work by Patla,<br />
Vaughan, et al. examining emg patterns <strong>of</strong> the lower limbs during walking using patterns<br />
3 More information on electromyography will be given in Section 3.2.1
34 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.8: Mapping muscle activation during normal walking to the position <strong>of</strong> the corresponding<br />
motor neurons in the spinal cord. From [Ivanenko 06], p341.<br />
recognition algorithms already suggest variant and invariant features among these signals<br />
[Patla 85, Vaughan 92, Olree 95]. Ivanenko et al. include a larger set <strong>of</strong> muscles in<br />
their analysis [Ivanenko 04]. They use statistical methods <strong>like</strong> factor analysis or pca for<br />
the decomposition <strong>of</strong> 32 emg waveforms recorded during normal walking (Figure 3.7).<br />
Five basic temporal components can be identified whose weighted sum explains about<br />
90% <strong>of</strong> the total emg waveforms. This holds true even for different walking velocities<br />
and for various degrees <strong>of</strong> body weight support. Ivanenko and colleagues also apply their<br />
methods to data sets <strong>of</strong> other groups, e.g. Winter’s or Vaughan’s data, and produce similar<br />
results [Ivanenko 06]. Moreover, the identified components seem to be timed to kinematic<br />
or kinetic events.<br />
Mapping the emg activity <strong>of</strong> muscles back to the location <strong>of</strong> their corresponding motor<br />
neurons in the spinal cord also yields interesting results [Ivanenko 06]. Figure 3.8 shows<br />
such a spatiotemporal mapping <strong>of</strong> normal walking activity. These maps show common<br />
features over different walking speeds, e.g. bursts <strong>of</strong> activity at different locations that are<br />
temporally aligned. This could be seen as evidence that coordinated activity origins from<br />
a central pattern.
3.1. Structural Organization <strong>of</strong> Motion <strong>Control</strong> 35<br />
(a) (b)<br />
Figure 3.9: Hypothetical scheme <strong>of</strong> muscle activation. (a) An activation component creates<br />
a muscle synergy influenced by central control and feedback. (b) Activation components<br />
are triggered by central spinal pattern generator and/or higher levels <strong>of</strong> the nervous system.<br />
From [Ivanenko 06], p347.<br />
The concept <strong>of</strong> central motor patterns can also be tested by disturbing basic locomotion<br />
with voluntary movements. For example, when stepping over an obstacle during walking,<br />
an additional activation component can be identified alongside the five basic components<br />
<strong>of</strong> walking. When performing the same voluntary task while standing, in this case lifting<br />
one leg, again characteristic activation patterns are found. These can be superimposed on<br />
the walking components and timed with the corresponding kinematic events, resulting in<br />
overall activation similar to the one observed in the combined movement.<br />
This allows the assumption that motor patterns are not only used for one specific movement<br />
but can be called on for different tasks. Further evidence for this can be found when<br />
comparing the temporal components during walking and running [Cappellini 06]. The<br />
same five components can account for both modes <strong>of</strong> locomotion with only a phase shift<br />
<strong>of</strong> one <strong>of</strong> the components. Thus, despite their diverse biomechanical demands, walking<br />
and running mainly differ in the timing <strong>of</strong> motor programs.<br />
Considering the results discussed in the previous paragraphs, Ivanenko et al. suggest a<br />
hypothetical scheme <strong>of</strong> muscle activation as shown in Figure 3.9. Components or motor<br />
patterns create muscle activation via a weighting network <strong>of</strong> distributed interneurons<br />
connected to muscle neurons. Feedback and central control can alter the weights. Central<br />
control and/or rhythmic pattern generation in the spinal cord create a spatial and temporal<br />
sequence <strong>of</strong> activation and superposition <strong>of</strong> voluntary motor programs. Again, sensory<br />
feedback and downstream commands may modulate this process.<br />
In his review on central control <strong>of</strong> muscle activity during human walking, Nielsen states<br />
that neural control is located on many levels <strong>of</strong> the nervous system [Nielsen 03]. In the<br />
human more than in the animal kingdom, the supraspinal level gets involved, as becomes<br />
visible in positron emission tomography (pet) <strong>of</strong> the motor cortex. There even is evidence<br />
<strong>of</strong> a direct monosynaptic pathway having developed from the motor cortex to spinal motor<br />
neurons. But still the spinal circuitry is capable <strong>of</strong> generating basic rhythmic locomotion<br />
activity patterns.
36 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.10: Photographs taken by Eadweard Muybridge in the late 19th century for analyzing<br />
human locomotion.<br />
Implications for Robotics:<br />
Motion control in humans is <strong>of</strong> hierarchical layout. Motor programs<br />
provide an interlayer to create coordinated synergies <strong>of</strong> movement.<br />
Activation <strong>of</strong> these patterns can create locomotion if they are timed to<br />
correspond to kinematic or kinetic events. Feedback should be<br />
integrated to modulate the patterns according to outside influence and<br />
internal state.<br />
This section has discussed the structural organization and principles deployed in human<br />
motioncontrol. Thefollowingsectionwillspecificallycoverhumanwalkinganddemonstrate<br />
how the mechanisms above are employed during this form <strong>of</strong> locomotion.<br />
3.2 Normal <strong>Walking</strong> in <strong>Human</strong>s<br />
The study <strong>of</strong> human locomotion has a long history. Already in the 19th century series<br />
<strong>of</strong> photographs were taken to better understand the motions <strong>of</strong> animals and man. With<br />
the help <strong>of</strong> chief engineer for the Southern Pacific Railroad, John D. Isaacs, Eadweard<br />
Muybridge (1830–1904) developed a method for capturing a sequence <strong>of</strong> pictures using<br />
multiplecameras. Thatwayhetookthousands<strong>of</strong>images<strong>of</strong>animalsandhumansperforming<br />
various task (Figure 3.10).<br />
3.2.1 Biomechanical Gait Analysis<br />
Although Muybridge’s scientific interest in the topic <strong>of</strong> motion analysis is arguable, his<br />
contribution can still be seen as an important step during the development <strong>of</strong> the research
3.2. Normal <strong>Walking</strong> in <strong>Human</strong>s 37<br />
Figure 3.11: A typical setup for biomechanical gait analysis featuring kinematic tracking using<br />
markers, emg measurement, and force plates for capturing ground reaction forces (Source: bts<br />
Bioengineering, Italy).<br />
field called kinesiology, or in modern and more general terms, biomechanics. Today’s<br />
methods for analyzing human gait have advanced significantly, including high-speed<br />
cameras, or X-ray systems. Figure 3.11 shows a typical setup for capturing gait data<br />
with multiple sensor systems. The topics <strong>of</strong> biomechanical research can be divided in<br />
the examination <strong>of</strong> functional anatomy (see Section 3.1.1), the kinematics and kinetics <strong>of</strong><br />
motions, and the capturing <strong>of</strong> neural activity.<br />
Kinematics<br />
Kinematics describes the spatial and temporal elements <strong>of</strong> motion, i.e. the position,<br />
velocity, and acceleration <strong>of</strong> rigid bodies. In a biomechanical context, this refers to the<br />
translation and rotation <strong>of</strong> body segments relative to a fixed coordinate system or to<br />
one another. Quantitative methods to collect kinematic data during locomotion include<br />
accelerometers or other measurement devices attached to individual body parts, or most<br />
recently X-radiation as used for small mammals. The most common method for obtaining<br />
data uses motion capture systems based on high-speed cameras or optoelectric systems.<br />
These biomechanical capturing units usually operate at 60, 120, 180, or 200 frames per<br />
second. Active or passive markers are fixed on the subject, normally at the end points <strong>of</strong><br />
the body segments to be analyzed (Figure 3.11). The marker positions are then tagged<br />
manually or automatically in the digitized video data. Thus, the global marker trajectories<br />
are known given a calibrated capturing system. Including the kinematic connections <strong>of</strong> the<br />
markers, joint angles can be deduced for each frame. By numerical derivation, velocities<br />
and accelerations can be calculated. Beside the joint angles, parameters <strong>like</strong> stride length,<br />
walking speed, step rate or stance, and swing durations are <strong>of</strong> interest when kinematically<br />
analyzing walking motions.
38 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.12: Joint angles <strong>of</strong> the lower extremities during normal walking (solid line), running<br />
(broken line), and sprinting (dotted line) over the gait cycle. The vertical line represents the<br />
transition from stance (left side) to swing phase (right side). From [Hamill 03], p327.<br />
Many researchers have reported on the kinematics during normal walking in humans.<br />
Figure 3.12 illustrates typical hip, knee, and ankle joints during walking, running, and<br />
sprinting [Hamill 03]. While the role movement in the frontal and transverse plane should<br />
not be neglected, the major segment movement takes place in the sagittal plane. At<br />
ground contact, the body weight and downwards acceleration needs to be absorbed, which<br />
is achieved by hip flexion, knee flexion, and ankle dorsiflexion. These flexions continue<br />
while the body travels over the stance foot. At the end <strong>of</strong> the stance phase, the joint<br />
action reverses into hip extension, knee extension, and ankle plantarflexion.<br />
During walking, the hip flexion at touchdown lies in the range <strong>of</strong> 35 ◦ to 40 ◦ . Until toe-<strong>of</strong>f,<br />
the hip flexion reduces to about 0 ◦ to 3 ◦ . During the swing phase, the hip flexes again<br />
with a maximum <strong>of</strong> 25 ◦ to 50 ◦ .<br />
The knee is flexed to 10 ◦ to 15 ◦ at touchdown to reduce the impact forces. While accepting<br />
body weight at the beginning <strong>of</strong> the stance phase, the knee flexes further and reaches its<br />
maximum at midstance with 20 ◦ to 25 ◦ . The knee then stretches without reaching full<br />
extension, and flexes again during the propulsion phase <strong>of</strong> stance. At toe-<strong>of</strong>f, the knee<br />
angle ranges in between 10 ◦ to 40 ◦ , higher values being reached at faster walking speeds.<br />
The leg length is shortend during swing phase to guarantee ground clearance by further<br />
knee flexion <strong>of</strong> about 50 ◦ to 65 ◦ .<br />
The ankle shows a plantarflexion <strong>of</strong> 5 ◦ to 6 ◦ at heel strike. It then slowly moves to<br />
dorsiflexion <strong>of</strong> 10 ◦ to 12 ◦ until the whole foot touches the ground. During the stance phase,<br />
it gradually returns to plantarflexion <strong>of</strong> about 15 ◦ to 20 ◦ at toe-<strong>of</strong>f. Increasing dorsiflexion<br />
keeps the toes from touching the ground during the swing phase.<br />
The angular kinematics <strong>of</strong> the lower extremities adapt to changes <strong>of</strong> the environment. For<br />
example, walking on non-compliant ground can cause stronger knee flexion at heel strike.<br />
Uphill walking is compensated by additional dorsiflexion, knee flexion, and hip flexion at
3.2. Normal <strong>Walking</strong> in <strong>Human</strong>s 39<br />
Activity Relative Force (N/BW)<br />
Vertical compressive forces in the ankle joint 13<br />
Vertical reaction forces in the ankle joint 3.9–5.2<br />
Vertical reaction forces in the subtalar joint 2.4–2.8<br />
Achilles tendon force 3.9<br />
Peak forces acting in the hip 2.8–4.8<br />
Table 3.1: Maximum relative forces acting on the human body during walking. Forces are given<br />
in newton (N) per body weight (BW) [Hamill 03].<br />
touchdown as well as an increase <strong>of</strong> the motion range in the hip and ankle during stance<br />
phase. When walking downhill, the knees show up to 15 ◦ more flexion at heel strike.<br />
Rotation <strong>of</strong> the pelvis during walking only lies within a few degrees. The same holds true<br />
for the movement <strong>of</strong> the upper trunk. It moves laterally for about 2 to 3cm to the side <strong>of</strong><br />
the stance leg and slightly leans forward after heel strike and back again in the course <strong>of</strong><br />
the stance phase [Murray 64]. Vertical displacement <strong>of</strong> the trunk reaches its maximum <strong>of</strong><br />
about 5cm at midstance <strong>of</strong> each leg.<br />
Kinetics<br />
In biomechanics, kinetics describes the effects <strong>of</strong> internal and external forces and torques<br />
acting on the human body, <strong>of</strong>ten given relative to the body mass or body weight. Typical<br />
relative forces acting on the body during walking are given in Table 3.1.<br />
Forces acting on the human body can be classified into non-contact and contact forces.<br />
The most relevant non-contact forces during locomotion is gravity. Gravity acts at the<br />
center <strong>of</strong> mass <strong>of</strong> each body segment with the gravitational acceleration <strong>of</strong> about 9.81<br />
m/s 2 in vertical direction. Seven contact forces, i.e. forces acting between two bodies, are<br />
normally considered in biomechanics: ground reaction force, joint reaction force, friction,<br />
fluid resistance, inertial force, muscle force, and elastic force [Hamill 03].<br />
The ground reaction force (grf) acts between the ground and an individual body segment<br />
making contact with it. Figure 3.13a shows a typical behavior <strong>of</strong> the grf during the<br />
stance phase <strong>of</strong> a walking cycle. As the grf is a vector, it can be resolved into a vertical,<br />
an anteroposterior (forward-backward) and a mediolateral (side-to-side) component. The<br />
latter two forces act parallel to the ground surface and are referred to as shear forces.<br />
During walking, the vertical component <strong>of</strong> the grf is M-shaped with its first peak during<br />
weight acceptance, and the second peak during push-<strong>of</strong>f. The grf acts at point <strong>of</strong> pressure<br />
in the foot sole. As shown in Figure 3.13b, with the progress <strong>of</strong> the stance phase, the<br />
point <strong>of</strong> pressure travels along the sole from heel to toes [Rodgers 88]. In biomechanical<br />
research, grf is normally measured using a force platform embedded in the ground on<br />
which the subject is performing e.g. walking or jumping.<br />
Two adjoining body segments are connected by a joint at which point equal but opposing<br />
forces act on each segment. These forces are termed joint reaction forces and can be<br />
calculated based on kinematic and kinetic data and known body dimensions.<br />
Friction is mainly <strong>of</strong> interest during the ground contact <strong>of</strong> the foot or shoe. The force<br />
generated by friction is equal to the normal force onto the surface times a friction coefficient.
40 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
(a) (b)<br />
Figure 3.13: (a) Ground reaction forces during normal walking. The vertical ground reaction<br />
force(solidredline)showsthetypicalMshape. Anteroposterior(solidblackline)andmediolateral<br />
(dashed red line) are shear forces in the surface plane. From [Hamill 03], p365. (b) The center <strong>of</strong><br />
pressure travels along the foot sole during stance phase. From [Rodgers 88], p1825.<br />
For producing the necessary propulsion force in the later stance phase and to guarantee a<br />
safe landing at heel strike during walking, the foot friction must be high enough. Overly<br />
high friction can increase joint tension and cause instability or injuries.<br />
As the drag force in air or fluid resistance is proportional to the medium’s viscosity and<br />
to the square <strong>of</strong> the relative velocity, it does not substantially influence the process <strong>of</strong><br />
walking. Rather it is <strong>of</strong> interest in biomechanical studies <strong>of</strong> running, swimming, or other<br />
movement forms <strong>of</strong> faster speed or in viscose medium.<br />
In contrast, inertial forces do play a role in walking and cannot be neglected. An inertial<br />
force occurs between connected body segment as one segment is moving and thus causing<br />
a movement in the next without muscle action. For example during the swing phase, the<br />
tight segment exerts an inertial force on the leg.<br />
Obviously, muscle force is a force <strong>of</strong> major importance during locomotion. As already<br />
described in Section 3.1.2, muscle fibers contract due to stimulation by the motor neurons.<br />
On average, skeletal muscle can contract to about 57% <strong>of</strong> its resting length [Hamill 03].<br />
Only by contraction, a muscle can produce force, so a joint can only be controlled by<br />
opposing muscles, the agonist and antagonist. When a force is produced by an opposing<br />
muscle, or when an external force acts on a joint, a muscle can be extended beyond its<br />
resting length, storing elastic energy in the process.<br />
Depending on the type <strong>of</strong> fibers, muscles can quickly produce high forces, but then fatigue<br />
(Type II), or have slower contraction times and be more enduring (Type I). The force a<br />
muscle produces depends <strong>of</strong> its current length and the velocity <strong>of</strong> movement. The longer<br />
the muscle, the higher the force created. Thus, pre-stretching the muscle before e.g. weight<br />
lifting can increase the force output. The relationship between velocity and force is shown<br />
in Figure 3.14a. Regarding movement, the force produced by muscle action is used for<br />
joint movement, the maintenance <strong>of</strong> posture and positions, and joint stabilization.
3.2. Normal <strong>Walking</strong> in <strong>Human</strong>s 41<br />
(a) (b)<br />
Figure 3.14: (a) Increasing velocity reduces the force output <strong>of</strong> a muscle. This holds true for<br />
the lengthening muscle (eccentric muscle action) as well as the shortening muscle (concentric<br />
muscle action). (b) Hill’s mechanical muscle model in two equivalent forms. From [Hamill 03],<br />
p78f.<br />
Therehavebeenseveralattemptstodescribetheforceproducedbyamuscleinamechanical<br />
model, the most prominent being the model developed by A. V. Hill (Figure 3.14b). It<br />
consists <strong>of</strong> the contractile component (cc), a parallel elastic component (pec) and a series<br />
elastic component (sec). The sec describes the tendon and other elastic elements in series<br />
with the contracting units <strong>of</strong> the muscle. It shows highly nonlinear behavior, as does the<br />
pec expressing parallel elastic elements <strong>like</strong> the fascia surrounding the muscle and its<br />
compartments.<br />
As soon as the line <strong>of</strong> action <strong>of</strong> a force does not pass through the body’s center <strong>of</strong> mass, a<br />
torque, or moment <strong>of</strong> force, is induced. Torques occur when muscle contraction pulls via<br />
tendons at a certain distance away from the joint, when gravity acting on body segments<br />
causes a downward rotation, or when the direction on the ground reaction force does<br />
not pass through the center <strong>of</strong> gravity. The total center <strong>of</strong> mass <strong>of</strong> the body can be<br />
calculated from the segment centers <strong>of</strong> mass and masses. Table 3.2 gives the average<br />
values for both male and female subject as estimated by Plagenhoef et al. using segment<br />
immersion [Plagenhoef 83]. Other researchers examined cadavers for the same purpose.<br />
Using similar techniques, the average moment <strong>of</strong> inertia has been estimated for individual<br />
body segments. The moment <strong>of</strong> inertia necessary to calculate the angular acceleration <strong>of</strong> a<br />
body given an external torque amounts to<br />
T = I ¨ θ (3.1)<br />
where T is the torque, I the moment <strong>of</strong> inertia, and ¨ θ the angular acceleration.<br />
Static and dynamic gait analysis deals with the forces and torques just mentioned as they<br />
act on the human body. Leonard Euler created recursive equations for a dynamic analysis<br />
based on Newton’s laws <strong>of</strong> motion starting with the most distal body segments. Applying<br />
inverse dynamics calculations, the forces and torques acting on body segments can be<br />
concluded from their motions and masses. Motion capture data can provide information
42 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Center <strong>of</strong> Mass Segment Weight<br />
Segment Male Female Male Female<br />
Head, neck 55.0 55.0 8.26 8.20<br />
Trunk 44.5 39.0 46.80 45.22<br />
Whole trunk 63.0 56.0 55.10 53.20<br />
Upper arm 43.6 45.8 3.25 2.90<br />
Forearm 43.0 43.4 1.87 1.57<br />
Hand 46.8 46.8 0.65 0.50<br />
Thigh 43.3 42.8 10.50 11.75<br />
Lower leg 43.4 41.9 4.75 5.35<br />
Foot 50.0 50.0 1.43 1.33<br />
Table 3.2: Average center <strong>of</strong> mass and weight <strong>of</strong> body segments. Center <strong>of</strong> mass location is<br />
given in percent <strong>of</strong> segment length from the proximal end. Weight is given in percent <strong>of</strong> the total<br />
body weight [Plagenhoef 83].<br />
on segment trajectories, masses and inertia can be estimated based on average mass<br />
distributions <strong>of</strong> the human body (Table 3.2). Further variables <strong>of</strong> interest in kinetics are<br />
work, power, or energy being mustered or consumed during motions. For example, the<br />
pendulum-<strong>like</strong> characteristics <strong>of</strong> walking exchanges potential with kinetic energy and vice<br />
versa. This mechanism allows energy savings <strong>of</strong> muscular work <strong>of</strong> up to 65%.<br />
Figure 3.15 illustrates angular kinematic and kinetic joint data during a walking cycle<br />
for the hip, the knee, and the ankle joint [Hamill 03]. At heel strike, the hip produces an<br />
extensor moment to stabilize the trunk. The leg swing is generated by hip flexion before<br />
toe-<strong>of</strong>f and is terminated by an opposing moment at the end <strong>of</strong> swing phase.<br />
Weight acceptance is controlled in the knee joint by an extensor moment. Leg swing is<br />
initiated by a small amount <strong>of</strong> flexion moment and controlled by the following extensor<br />
action. During the swing there is almost no power output in the knee, only towards the<br />
end <strong>of</strong> the swing a flexion is created in preparation for ground contact.<br />
The foot is slowly lowered to the ground after heel strike by a small amount <strong>of</strong> dorsiflexor<br />
moment. Thebody’smovementoverthefootduringstancephaseiscontrolledbyincreasing<br />
plantarflexor moment. The power output <strong>of</strong> the ankle shows its maximum during the<br />
propulsion before toe-<strong>of</strong>f. During swing phase, the ankle produces nearly no power.<br />
As described in the kinematics discussion <strong>of</strong> normal walking, the moment and power<br />
patterns also change due to ground condition or walking speed. For example, higher flexor<br />
and extensor moments can be observed in the knee during faster walking.<br />
Electromyography<br />
Besides the capturing <strong>of</strong> human motion and the kinematic and kinetic analysis <strong>of</strong> that<br />
data, the most frequently used method <strong>of</strong> motion analysis is the electromyography (emg)<br />
recording activation signals <strong>of</strong> muscles. More than the methods mentioned above, emg can<br />
provide inside into the control <strong>of</strong> reflexive or voluntary movements as the muscle action is<br />
directly connected to neural commands. However, analyzing emg plots has its limitations<br />
and thus requires some knowledge on this method, which will be provided in the next few
3.2. Normal <strong>Walking</strong> in <strong>Human</strong>s 43<br />
Figure 3.15: Kinetics during normal walking in the sagittal plane. The toe-<strong>of</strong>f event is<br />
represented by the solid vertical line. From [Hamill 03], p414.<br />
paragraphs. The main sources for this section are the books by Hamill et al. and Vaughan<br />
et al. [Hamill 03, Vaughan 92].<br />
To record an electromyogram, an electrode is placed on the muscle to detect an electrical<br />
signal. This emg signal is a complex combination <strong>of</strong> all action potentials generated by the<br />
muscle neurons connected to the muscle fibers that are gathered by the electrode. The raw<br />
signal is both positive and negative. While the amplitude <strong>of</strong> the signal is influenced by<br />
many factors (see below), in principle it increases with the strength <strong>of</strong> muscle contraction.<br />
However, as indicated in the discussion on muscle properties above, the amplitude is by no<br />
means relative to the produced muscle force or even the joint torque. A somehow direct<br />
correlation between emg signal amplitude and muscle force can only be seen in isometric<br />
contraction. Also, the so-called electromechanical delay between the electrical signal and<br />
the actual muscle contraction can be observed, as the action potential must travel along<br />
the muscle fibers before tension can be developed.<br />
Two types <strong>of</strong> electrodes can be used to detect the electrical signal: indwelling or surface<br />
electrodes. Indwelling electrodes are placed directly in deep muscle in form <strong>of</strong> needles or<br />
fine wire. More commonly used in biomechanics are surface electrodes placed on the skin<br />
and as such used for more superficial muscles. There are two possible arrangements for<br />
surface electrodes: in the monopolar arrangement a single electrode is placed over the
44 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.16: Common representations <strong>of</strong> an emg signal. From [Hamill 03], p84.<br />
muscle, a second one is attached over an electrically neutral place <strong>like</strong> a bony prominence<br />
to get a differential signal. The bipolar arrangement is more precise as another electrode<br />
is placed 1.5 to 2cm next to the first muscle electrode and a differential amplifier can be<br />
used to cancel out common error signals. Obviously, correct placement and orientation<br />
<strong>of</strong> the electrodes on properly prepared skin is important to produce a significant signal<br />
with low crosstalk. As emg signal intensity is very low ranging from 10 �V to 5mV, it<br />
must be amplified by high quality electronics to reduce additional noise or errors. It is<br />
then digitalized by an A/D converter working at least at 1kHz to take the characteristics<br />
<strong>of</strong> neural muscle activity into account.<br />
The technical and physiological factors influencing the emg signal are manifold. They<br />
include factors <strong>like</strong> muscle fiber diameter, the number <strong>of</strong> muscle fibers, the number <strong>of</strong><br />
active motor units, fiber type and location, muscle blood flow, and further effects directly<br />
concerning the muscle. Other factors <strong>like</strong> electrode spacing or electrode-skin interface also<br />
influence the collected data.<br />
Figure 3.16 illustrates different representations <strong>of</strong> an emg signal. The raw signal shows<br />
the composite <strong>of</strong> the multitude <strong>of</strong> action potentials <strong>of</strong> the motor units being active in the<br />
effective range <strong>of</strong> the electrodes. Commonly the raw signal is rectified, i.e. the absolute<br />
value <strong>of</strong> the signal is examined. Filtering out high frequency components, a smooth form <strong>of</strong><br />
the signal called linear envelope can be generated showing more clearly the volume <strong>of</strong> the<br />
activity. In some cases <strong>of</strong> analysis, the integration <strong>of</strong> the emg signal or the transformation<br />
in the frequency domain can be <strong>of</strong> interest.<br />
emg recordings can be used for a number <strong>of</strong> applications. There are attempts to define<br />
a relationship between muscle force and emg signal strength in isometric muscle action.<br />
Also, there is some evidence that frequency changes in emg signals can indicate muscle<br />
fatigue. In ergonomics, muscle activity analysis can help to point out improper sitting<br />
postures, movements, or working conditions. But most interesting for this work is the<br />
clinical gait analysis. Here, the emg signal can be interpreted to identify the contribution<br />
and timing <strong>of</strong> individual muscles or muscle groups during a gait cycle. This allows to<br />
draw certain conclusions regarding the underlying neural control. However, is must be<br />
mentioned that emg gives semiquantitative results at best regarding the strength <strong>of</strong> muscle<br />
contraction. Also it can prove difficult to obtain reliable emg reading during dynamic<br />
movements such as walking or running.
3.2. Normal <strong>Walking</strong> in <strong>Human</strong>s 45<br />
Muscles Footstrike Midsupport Toe-<strong>of</strong>f Forward Swing Deceleration<br />
Dorsiflexors +++ ++ ++ ++ ++<br />
Intrinsic Foot Muscles +++<br />
Gluteus Maximus + ++ +++<br />
Gluteus Medius ++ +++ ++ +<br />
Gluteus Minimus ++ +++ ++ +<br />
Hamstrings +++ ++ ++ + ++<br />
Iliopsoas +++<br />
Plantar Flexors + ++<br />
Quadriceps + +++ ++<br />
Sartorius ++ +<br />
Tensor Fascia Latae + ++ + +++<br />
Thigh Adductors ++ ++ + ++ +<br />
Table 3.3: Contribution <strong>of</strong> the main muscle groups in the lower extremities during normal<br />
walking. +/++/+++ is indicating low/moderate/high muscle activity [Hamill 03].<br />
Many researchers have traced emg signals during normal human walking. As shown in<br />
Figure 3.17, Winter et al. recorded relevant muscle group activities <strong>of</strong> the whole body<br />
during walking [Winter 91]. Table 3.3 lists the contribution to walking <strong>of</strong> the main muscles<br />
groups in the lower extremities [Hamill 03]. The meaning <strong>of</strong> muscle abbreviations, muscle<br />
locations, and their function can be found in Appendix A.<br />
The foot and ankle muscles control the ground contact during walking and create much <strong>of</strong><br />
the necessary propulsion. To keep the front <strong>of</strong> the foot from slapping down after heel strike,<br />
the dorsiflexor muscles <strong>like</strong> the tibialis anterior show maximum activity. This activity then<br />
decreases but nevertheless remains to control the pendulum-<strong>like</strong> tibia movement during<br />
stance phase, assisted by beginning activity <strong>of</strong> the gastrocnemius and soleus. The latter<br />
muscle group mainly contributes to propulsion just before toe-<strong>of</strong>f when it reaches peak<br />
activity. During swing phase, only the dorsiflexors are active to guarantee ground clearance<br />
<strong>of</strong> the foot.<br />
The knee musculature is mainly used for stabilization and force absorption during walking.<br />
At heel strike the hamstrings, biarticular muscles spanning the knee and the hip, get active<br />
to keep the trunk from swinging forward and at the same time to bend the knee to reduce<br />
impact forces. This contraction continues until the foot is flat on the ground. During<br />
weight acceptance, the quadriceps femores work to control the body load and to allow<br />
the knee to flex in a controlled way. As the leg extends towards midstance, this activity<br />
decreases. During propulsion, the knee muscles become active again to add to the forward<br />
force. At toe-<strong>of</strong>f, the hamstrings can flex the knee for increasing ground clearance and<br />
again before heel strike to reduce impact. The quadriceps femores enables leg extension<br />
towards the end <strong>of</strong> the swing phase.<br />
The hip joint and pelvis muscles mainly control trunk and pelvis posture and do not<br />
substantially contribute to propulsion. The gluteus medius provides lateral stability <strong>of</strong><br />
the pelvis and the trunk against the body weight from heel strike to midsupport as the<br />
contralateral leg is swinging and cannot contribute to support. This stabilization is assisted<br />
by activity <strong>of</strong> the gluteus minimus and the adductors. <strong>Control</strong> <strong>of</strong> the trunk in the frontal<br />
plane at heel strike and during stance phase is provided by the hamstrings, the gluteus
46 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Rectus<br />
Femoris<br />
Tibealis<br />
Anterior<br />
prevent foot from slapping down lift foot for ground clearance<br />
Figure 3.17: emg analysis <strong>of</strong> 25 muscles during a cycle <strong>of</strong> normal walking. Exemplary, the<br />
name and location <strong>of</strong> two muscles is indicated, and two significant muscle activities interpreted.<br />
The meaning <strong>of</strong> the remaining muscle abbreviations can be found in Appendix A. emg data<br />
from [Winter 91], plot from [Ivanenko 06], p341.<br />
maximus and the tensor fascia latae. Towards toe-<strong>of</strong>f, the abductors support the propulsion<br />
process. The leg swing is initiated by activity <strong>of</strong> the iliopsoas, sartorius, and tensor fascia<br />
latae. The adductors control lateral movement <strong>of</strong> the swinging limb until it is decelerated<br />
by the hamstrings and the gluteus maximus before the next heel strike.<br />
The trunk muscles mainly control the lateral movement <strong>of</strong> the trunk as it flexes towards the<br />
side where ground contact is made. This is mainly achieved by activity <strong>of</strong> the multifidus<br />
and longissimus. At heel strike, first the contralateral muscle groups prevent the trunk<br />
from flexing to far, then the ipsilateral group stabilizes the trunk. The activity <strong>of</strong> the<br />
leg extensor muscles are synchronized with the activity <strong>of</strong> the erector spinae muscles.<br />
Excessive flexion <strong>of</strong> the trunk is also prevented by the lumbar muscles. An erect head<br />
posture is controlled by relatively low activity <strong>of</strong> the cervical muscles.<br />
Arm movement is coinciding with the leg movement [Wannier 01]. Activity <strong>of</strong> the flexor<br />
and extensor muscles <strong>of</strong> the arm create a contralateral motion contributing to stabilize<br />
trunk rotation. Figure 3.18 graphically recapitulates the contribution <strong>of</strong> the muscles in<br />
the lower extremities during one walking cycle in posterior and lateral views [Vaughan 92].<br />
Darker shading corresponds to higher muscle activity.<br />
Implications for Robotics:<br />
<strong>Human</strong> gait analysis provides valuable insight in bipedal walking mechanisms.<br />
Kinematic data is only partially helpful as direct mapping <strong>of</strong><br />
joint trajectories on a robot cannot work due to differences in mechanics.<br />
At the very least it can serve as benchmark or comparison<br />
basis. Kinetic data and emg recordings, however, allow to draw conclusion<br />
regarding the intention <strong>of</strong> control commands during individual<br />
walking phases or sensor events. Hence they can assist in conceiving<br />
feed-forward and feedback control components.
3.2. Normal <strong>Walking</strong> in <strong>Human</strong>s 47<br />
Figure 3.18: Illustration <strong>of</strong> active muscles in the lower extremities during normal walking in<br />
posterior and lateral view. From [Vaughan 92], p54.<br />
3.2.2 Phases <strong>of</strong> <strong>Walking</strong><br />
Phases <strong>of</strong> walking have been mentioned throughout this chapter, mainly connected to<br />
kinematic or kinetic event <strong>like</strong> heel strike <strong>of</strong> toe-<strong>of</strong>f. It has been shown in Section 3.1 that<br />
neural motor activity and reflex responses depend on the current phase <strong>of</strong> locomotion.<br />
The question <strong>of</strong> how the phases <strong>of</strong> walking are codes in the nervous system is discussed in<br />
the following.<br />
In insects as well as in lower vertebrates, strong evidence for the existence <strong>of</strong> a central<br />
pattern generator (cpg) can be found [Grillner 79, Pearson 93, Bueschges 95, Baessler 98].<br />
Even in the absence <strong>of</strong> sensory feedback and supraspinal commands, rhythmic walking<br />
behavior can be shown. The review by Frigon and Rossignol among others discusses how<br />
sensorimotor interaction affects the output <strong>of</strong> the cpg and thus the motor patterns in<br />
cats [Frigon 06].<br />
Unfortunately, the situation during humans walking is more complicated. While there is<br />
evidence for cpgs in humans, there seems to be much more influence from supraspinal<br />
levels and sensory information [Nielsen 03]. Still, as shown by Vaughan, Ivanenko and<br />
others and already introduced in Section 3.1.4, a substantial part <strong>of</strong> neural control during<br />
human walking is coordinated muscle action at purposefully timed phases <strong>of</strong> the walking<br />
cycle.<br />
Five different components <strong>of</strong> muscle activity can be identified during one cycle <strong>of</strong> human<br />
walking [Ivanenko 04]. Figure 3.19 illustrates the timing <strong>of</strong> the five patterns. The appearance<br />
<strong>of</strong> these activity patterns can be associated with kinematic and kinetic events during<br />
the walking cycle: (1) weight acceptance, (2) loading or propulsion, (3) trunk stabilization<br />
during double support, (4) toe lift-<strong>of</strong>f, and (5) heel strike<br />
The shape <strong>of</strong> the temporal components is Gaussian-<strong>like</strong>, its peak and width showing a<br />
precise timing and stability over the normalized gait cycle [Ivanenko 06]. This implies that<br />
the activity patterns are scaled regarding to the walking speed: at a high speed <strong>of</strong> 9 km/h<br />
the duration <strong>of</strong> on component is about 90ms, at very slow speeds <strong>of</strong> 1 km/h it increases up<br />
to about 250ms. If a central unit <strong>like</strong> a cpg is responsible for these bursts <strong>of</strong> activity, it
48 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.19: The muscle activity during one cycle in human walking can be explained by five<br />
components. From [Ivanenko 06], p342.<br />
only contributes to muscle action at certain fractions <strong>of</strong> the gait cycle. This contradicts the<br />
classic half-center oscillator being active for one half and inhibited for the other half <strong>of</strong> the<br />
cycle. Rather, this implies a stronger influence <strong>of</strong> sensory input, as this would naturally<br />
scale the activity according to biomechanical events.<br />
Neural walking control does also show signs <strong>of</strong> bilateral coordination <strong>of</strong> muscle activity<br />
[Olree 95, Ivanenko 06]. When observing the timing <strong>of</strong> the five components, four <strong>of</strong><br />
them appear in pairs being temporally synchronized: the patterns 1 and 3 and the patterns<br />
2 and 5 match in their onset and are one-half <strong>of</strong> the cycle apart (Figure 3.20). This fact<br />
could also account for the contralateral movement <strong>of</strong> the arms. The synchronized pairs<br />
<strong>of</strong> muscle activity take place at the heel strikes <strong>of</strong> both legs. Only component 4 being<br />
associated with the ipsilateral leg swing appears without contralateral partner. Again,<br />
the fact <strong>of</strong> bilateral synchronization suggests the existence <strong>of</strong> a central origin <strong>of</strong> muscle<br />
patterns and a timing influenced by sensory input.<br />
Implications for Robotics:<br />
<strong>Walking</strong>phasesshouldbecoordinatedbyacentralcontrolunitlocatedon<br />
aninterlayer<strong>of</strong>thecontrolnetwork. Dependingonthecurrentphase, this<br />
unit should stimulate or modulate motor patterns and reflexes.<br />
Phase transitions probably require sensory information and are not<br />
strictly timed. Certain bilateral phases should be synchronized.<br />
Patterns and reflexes should be weighted or scaled depending on the<br />
walking speed.<br />
3.2.3 Reflex Function during <strong>Walking</strong><br />
While muscle patterns in combination with a cpg-<strong>like</strong> structure as described in the<br />
previous section generate basic walking motions, the question remains how reflex action<br />
is incorporated in the neural control. What functions do spinal reflexes perform during<br />
walking? To generate hypotheses on this topic, adequate mechanical data has to be<br />
collected together with neural data, thus enabling a valid interpretation.<br />
Zehr and Stein review literature on the function <strong>of</strong> the stretch reflex, the load receptor<br />
reflexes, and the cutaneous reflexes during locomotion [Zehr 99]. They suggest that the
3.2. Normal <strong>Walking</strong> in <strong>Human</strong>s 49<br />
Figure 3.20: The five muscle patterns during walking show bilateral synchronization visualized<br />
as mirrored polar plots on the left and as superimposed sequence <strong>of</strong> activation timings on the<br />
right. From [Ivanenko 06], p343.<br />
stretch reflex functionally contributes to the force production during walking. By attaching<br />
mechanical devices to subjects during walking, artificial dorsi- and plantarflexion <strong>of</strong> the<br />
ankle can be produced during all phases <strong>of</strong> walking. Thus it is possible to excite the stretch<br />
reflex <strong>of</strong> e.g. the soleus and measure the response. It can be shown that the reflex action<br />
is at its maximum during stance, nearly disappearing in stance-swing transition, and at<br />
about 50% <strong>of</strong> the maximum during late swing. While it is difficult to separate the force<br />
produced by reflex response and by other possible causes, a functional contribution to<br />
walking is assumed.<br />
Only a few experiments on the role <strong>of</strong> load receptor reflexes in human walking have been<br />
carried out. There seems to be evidence <strong>of</strong> a functional contribution, even if somewhat<br />
smaller than what was observed in quadrupedal vertebrates. A phase dependency as well<br />
as significant reflex response in extensor muscles to translational load perturbations can<br />
be shown. Increasing the body load in splitbelt experiments where each leg walks on a<br />
surface <strong>of</strong> different velocity enhances the walking timing and prolongs stance phases.<br />
Some studies exist on the effect <strong>of</strong> cutaneous reflexes during human walking. Stimulation<br />
<strong>of</strong> the sural, tibial, and sp nerves corresponding to the lateral border, and the ventral and<br />
dorsal surface <strong>of</strong> the foot show phase dependent reaction. For instance, stimulating the<br />
tibial nerve during lift-<strong>of</strong>f causes dorsiflexion <strong>of</strong> the ankle. However, during heel strike<br />
it causes plantarflexion. Furthermore it can be shown that cutaneous reflexes generate<br />
kinematic relevant responses. These motions produce reactions to avoid destabilizing<br />
stumbles during the swing phase and adaptation to uneven terrain in stance to avoid<br />
excessive inversion <strong>of</strong> the ankle. Partly, the correcting movement involve muscle groups <strong>of</strong><br />
the whole lower limb.<br />
Zehr and Stein conclude that reflexes ensure balance and a stable walking pattern during<br />
normal walking and in face <strong>of</strong> perturbations. During swing phase, reflexes cause stumbling<br />
correction and trajectory stabilization <strong>of</strong> the swing limb. In the transition from swing to<br />
stance, reflexes work towards stable foot placement and ground adaption. Similar, during<br />
stance, reflexes alter the ankle trajectory depending on terrain structure, stabilize the<br />
body weight support, and enhance cycle timing. Finally in stance to swing transition,<br />
stretch and load reflexes react on unloading by extending the stance phase, and cutaneous<br />
reflexes generate withdrawal motions. Figure 3.21 illustrates the reflex functions during<br />
these four phases <strong>of</strong> walking.
50 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Swing<br />
CUTANEOUS:<br />
stumble correction<br />
MUSCLE:<br />
trajectory stabilization<br />
Swing to Stance<br />
CUTANEOUS<br />
and<br />
MUSCLE:<br />
placing reactions<br />
Stance<br />
MUSCLE:<br />
weight support, stability,<br />
and cycle timing<br />
CUTANEOUS:<br />
stability<br />
Stance to Swing<br />
MUSCLE:<br />
unloading<br />
CUTANEOUS:<br />
withdrawal<br />
Figure 3.21: Function <strong>of</strong> stretch reflex, load receptor reflexes and cutaneous reflexes during<br />
locomotion. Reproduced from [Zehr 99].<br />
Implications for Robotics:<br />
Low-level reflexes help to finely regulate biped walking and to correct<br />
perturbations. Given the necessary sensor systems, control loops similar<br />
to the discussed reflexes can prevent stumbling and stabilize walking.<br />
The reflexes must be stimulated or modulated depending on the<br />
current phase <strong>of</strong> the walking cycle.<br />
3.2.4 Postural <strong>Control</strong><br />
While the reflexes discussed in the last section are mostly <strong>of</strong> the monosynaptic or spinal<br />
type, whole body posture control requires additional information. Supraspinal reflexes or<br />
high-level actions from the motor cortex are necessary to balance the upper body or to<br />
sensibly react to slope changes or lateral body tilts. Postural control must be considered<br />
to be a complex skill rather than a pure combination <strong>of</strong> simple reflexes [Horak 06].<br />
Two thirds <strong>of</strong> the human mass are located at two thirds <strong>of</strong> total height above the ground,<br />
aggregated in the head, arm, and trunk segments. Considering that during normal walking<br />
the trunk shows only an angular displacement <strong>of</strong> about 1-2 ◦ in the plane <strong>of</strong> progression, the<br />
accomplishment<strong>of</strong>thecentralnervoussystemtokeepthisbalanceissubstantial[Winter 95].<br />
Sensory information <strong>of</strong> the vision, the vestibular, and the somatosensory system is necessary.<br />
Winter reviews research on the postural control during quiet standing and normal walking<br />
[Winter 95]. A kinetic analysis <strong>of</strong> the head, trunk, and pelvis movements during<br />
walking show an increasing stabilization in the horizontal plane towards the head. A look<br />
at emg measurements explains this observation as paraspinal muscle activation travels<br />
from the upper neck downwards and reaches the lumbar levels with about 60ms <strong>of</strong>fset.<br />
This suggest a top-down anticipatory posture control <strong>of</strong> the spine.<br />
The main work in sagittal balance control <strong>of</strong> the upper body is raised by the hip extensors<br />
and flexors. Analyzing the dynamics <strong>of</strong> the trunk reveals significant unbalancing moments<br />
about the hip axis <strong>of</strong> about 40Nm. The upper body’s inertia causes a flexion during<br />
weight acceptance and an extension during push-<strong>of</strong>f. The unbalancing moment is nearly<br />
completely compensated by hip muscle action <strong>of</strong> the stance limb, which explains the small
3.2. Normal <strong>Walking</strong> in <strong>Human</strong>s 51<br />
Figure 3.22: The extrapolated center <strong>of</strong> mass (XcoM) lies just within the center <strong>of</strong> pressure<br />
during single support in walking. From [H<strong>of</strong> 07], p253.<br />
changes in trunk angle during walking. But this muscle response occurs practically at the<br />
same moment as head acceleration is measured by the vestibular organ. Thus, considering<br />
the latency <strong>of</strong> the neuromuscular system, this sensory information cannot account for the<br />
full compensation moment. Rather, it suggest that an anticipatory component is involved.<br />
Besides the control <strong>of</strong> the upper body posture in the sagittal plane, the balance system has<br />
to prevent the supporting leg from collapsing. The unbalancing torques <strong>of</strong> the trunk as just<br />
described result in a high variability <strong>of</strong> the hip muscle action, which again influences the<br />
knee and ankle joint and could result in limb instability. However, it can be observed that<br />
the knee joint reacts with additional flexion to extra hip extension and vice versa. This can<br />
partly be explained by biarticular muscles, for instance the rectus femoris muscle causes<br />
simultaneous hip flexion and knee extension. Still the nervous system must contribute to<br />
this fact, probably by corresponding muscle synergies.<br />
Considering the balance in the frontal plane, a single inverted pendulum behavior can be<br />
assumed as the hip ad- and abductors keep the body nearly rigid. These muscles have to<br />
compensate the torque induced by gravity as the CoM always lies medial <strong>of</strong> the subtalar<br />
joint acting as rotation axis in the foot. Further torques are generated by the inertia <strong>of</strong><br />
the trunk at touchdown. Similar torques act at the subtalar joint, which itself can only<br />
produce small correctional torques due to the short support leverage. Hence disturbances<br />
in the frontal plane must be compensated by lateral adaption <strong>of</strong> foot placement that has<br />
significant impact on the torques induced by gravity.<br />
H<strong>of</strong> et al. also investigate stabilization in the frontal plane during walking [H<strong>of</strong> 05, H<strong>of</strong> 07].<br />
They suggest to consider not only the center <strong>of</strong> mass but also an extended version <strong>of</strong> it.<br />
This extrapolated center <strong>of</strong> mass (XcoM) in the frontal plane is defined as<br />
XcoM = CoMz + ˙ CoMz<br />
, ω0 =<br />
ω0<br />
� g<br />
h<br />
(3.2)<br />
CoMx denotes the lateral position <strong>of</strong> the center <strong>of</strong> mass, ω0 the eigen frequency corresponding<br />
to an inverted pendulum model, g the gravity, and h the vertical height <strong>of</strong> the
52 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
center <strong>of</strong> mass. Figure 3.22 illustrates the XcoM during several steps <strong>of</strong> normal walking.<br />
It can be observed that the center <strong>of</strong> pressure which is closely related to the foot position<br />
during single support is always displaced by a small distance lateral <strong>of</strong> the XcoM. This<br />
could imply a simple strategy <strong>of</strong> balance control in walking where foot placement is chosen<br />
based on the XcoM just before heel strike [H<strong>of</strong> 08].<br />
Bauby and Kuo analyze balance control based on a model <strong>of</strong> a passive dynamic walking<br />
(see also Section 3.4.1) [Bauby 00]. They find that passive control in the sagittal plane is<br />
sufficient to achieve stability. However, in the lateral direction, active control by feedback<br />
seems necessary. This control most <strong>like</strong>ly involves visual and vestibular sensory information,<br />
and thus would be originated from higher centers <strong>of</strong> the nervous system, <strong>like</strong> the brain stem<br />
or cerebellum. This assumption is supported by experimental results, as a restriction <strong>of</strong><br />
sensory information <strong>like</strong> walking with eyes closed leads to a significant higher variability in<br />
lateral foot placement, but only small changes in the fore-aft direction. Similar indications<br />
are given by experiments comparing normal walking with an externally lateral stabilized<br />
gait [Donelan 04].<br />
The influence <strong>of</strong> vestibular and visual sensory information is examined in several research<br />
works. The role <strong>of</strong> the vestibular system is analyzed by Bent et al. by phase dependent<br />
galvanic vestibular stimulation [Bent 04]. The strongest changes in foot placement result<br />
from stimulation during the double support phase. This suggests that the decision for limb<br />
positioning is already taken when the foot leaves the ground. Furthermore the information<br />
from the vestibular system must be integrated with somatosensory information to gain an<br />
appropriate representation <strong>of</strong> the body’s pose. During double support the somatosensory<br />
information is more reliable. In contrast, the vestibular sensory information seems to be<br />
used independently during the whole walking cycle for stabilizing the head and trunk.<br />
The influence <strong>of</strong> vision on human locomotion has also been examined by confronting<br />
walking subjects with tunnel-<strong>like</strong> optical flow patterns [Prokop 97]. An effect on stride<br />
length and walking velocity can be observed. The body pose estimation is also integrating<br />
information from the vision system [Patla 97]. This integration depends more strongly on<br />
visual input but can dynamically be adapted based on available perception [Deshpande 05].<br />
Conflicting information from different sensory organs can cause instability or nausea.<br />
As already indicated above, it should again be mentioned that postural control is not<br />
only achieved by purely reactive control components. Rather, the central nervous system<br />
seems to coordinate posture and voluntary movement by anticipatory muscle patterns.<br />
Gahery [Gahery 87] classifies the postural adjustments in three strategies: postural preparations,<br />
postural accompaniments, and postural reactions. Sequences <strong>of</strong> postural muscle<br />
activity can be observed prior to activation <strong>of</strong> focal muscles. Frank et al. [Frank 90] discuss<br />
these postural accompaniments in different motor task, e.g. during elbow flexion-extension<br />
or rising to toes. The postural regulations serve to displace the body’s center <strong>of</strong> mass,<br />
to generate an opposing displacement <strong>of</strong> the center <strong>of</strong> mass, or to position the center <strong>of</strong><br />
mass over a new base <strong>of</strong> support. For example when rising to toes, healthy subjects move<br />
the center <strong>of</strong> mass to the front about 60ms before activation <strong>of</strong> the soleus and medial<br />
gastrocnemius. When pulling a stiff handle, a preceding movement <strong>of</strong> center-<strong>of</strong>-pressure<br />
(cop) and center-<strong>of</strong>-mass (com) counteracting reactive forces can be observed. As different<br />
conditions modulate timing and gain <strong>of</strong> the regulations, Frank et al. argue that the cns<br />
must have learned a simplified but state-dependent model <strong>of</strong> body dynamics to predict the<br />
expected shift <strong>of</strong> mass. The necessary control for this task could be simplified by only using
3.3. Key Aspects <strong>of</strong> Biological <strong>Walking</strong> <strong>Control</strong> 53<br />
a limited set <strong>of</strong> postural synergies that are associated with different focal motor patterns.<br />
The same postural reactions could come to use in response to external perturbations.<br />
Implications for Robotics:<br />
Postural control includes maintaining body stability in the sagittal and<br />
front plane and controlling forward velocity. This is a high-level skill<br />
requiring an estimation <strong>of</strong> the robot’s pose using information on joint angles,<br />
acceleration, and velocity information from an inertial measurement<br />
unit, and optical flow from vision, if available. Adjusting the foot<br />
placement seems to have the major influence on whole body balancing.<br />
Anticipatory torque patterns seem to be necessary to compensate<br />
segment movements resulting from mass inertia during normal walking,<br />
especially in the hip and trunk joints.<br />
3.3 Key Aspects <strong>of</strong> Biological <strong>Walking</strong> <strong>Control</strong><br />
Having reviewed research on human motion control in general and walking in particular<br />
on the preceding pages, this section will shortly summarize the key aspects considered to<br />
be relevant to robotics by the author. The following section will then go into detail on<br />
control approaches for bipedal machines applying one or more <strong>of</strong> the mentioned concepts.<br />
Regarding the structural aspects <strong>of</strong> human motion control, the following significant<br />
conceptions can be identified:<br />
Functional Morphology The human morphology is highly optimized for efficient biped<br />
locomotion regarding its geometry, mass distribution, or actuation. This“intelligent<br />
mechanics”relieves the nervous system <strong>of</strong> some <strong>of</strong> the control burden.<br />
Exploitation <strong>of</strong> Inherent Dynamics The semi-flat gait as exhibited in human walking<br />
takes advantage <strong>of</strong> this functional morphology. Inertia <strong>of</strong> body segments, compliance<br />
<strong>of</strong> the muscle-tendon system, or conversion between static and kinetic energy are<br />
exploited to reduce energy consumption and control effort, and result in natural<br />
looking motions.<br />
Self-Stabilization Suited elastic properties <strong>of</strong> muscles and tendons increase stability<br />
without active control by reacting to perturbations with purposeful joint movements.<br />
This allows for slower communication and higher control delay times.<br />
Hierarchical Network Neural control exhibits a hierarchical layout spanning from nerve<br />
fibers via the spinal cord to the brain. Muscle stimulation and perception run down<br />
respectively up along this network. Nerve cells or groups <strong>of</strong> cells can be gradually<br />
stimulated or inhibited.<br />
Distribution and Spatial Relations <strong>Control</strong> units act in a distributed way and are<br />
located spatially related to their place <strong>of</strong> activity. Like the hierarchical layout, this<br />
reduces signal density and allows to cope with high complexity.
54 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Feed-Forward Motor Patterns Activated at kinetic or kinematic events or due to<br />
learned timing, feed-forward patterns <strong>of</strong> muscle activity create coordinated synergies<br />
<strong>of</strong> movement. Spinal pattern generators manage the correct timing and sequencing<br />
<strong>of</strong> motor patterns to create the desired cyclic motion.<br />
Feedback <strong>of</strong> Varying Complexity Feedback control occurs at various levels <strong>of</strong> complexity<br />
regarding the extend <strong>of</strong> perception and deployment <strong>of</strong> muscle action. Basic<br />
reflexes only affect a single muscle group, while postural reflexes create whole body<br />
motions and rely on a multitude <strong>of</strong> sensing organs.<br />
Phase-dependent Modulation Depending on the current task or phase <strong>of</strong> motion,<br />
reflex action can be modulated, reinforced, or suppressed. Phases <strong>of</strong> locomotion are<br />
originating from spinal pattern generators being part <strong>of</strong> the hierarchical layout <strong>of</strong><br />
control.<br />
While the structural aspects just mentioned provide valuable clues for designing an<br />
appropriate architecture, the functional analysis <strong>of</strong> human walking helps to derive the<br />
actual control units generating a walking bipedal robot. The following functional elements<br />
<strong>of</strong> human gait prove to be meaningful for developing a control for dynamic walking:<br />
<strong>Control</strong> Units from Gait Analysis Especially kinetic analysis and emg recordings <strong>of</strong><br />
human gait can provide information on motor patterns stimulated during walking.<br />
While only qualitative answers can be given, gait analysis still helps in deciding<br />
which basic patterns are necessary to generate the desired movements.<br />
Five <strong>Walking</strong> Phases Analysis <strong>of</strong> emg data shows five basic components <strong>of</strong> muscle<br />
activations <strong>of</strong> which walking is composed. As these components are related to kinetic<br />
or kinematic events, a pattern generator <strong>of</strong> the walking control system can be based<br />
on these five phases. Sensor information can be used to trigger phase transitions.<br />
Bilateral Synchronization In humans, the five phases <strong>of</strong> walking for each side <strong>of</strong> the<br />
body are synchronized. This bilateral coupling can simplify control and guarantee<br />
correct coordination <strong>of</strong> the two legs.<br />
Reflexes during <strong>Walking</strong> By investigating impaired subjects or by specific inhibition<br />
<strong>of</strong> sensing organs, reflex action and its modulation during walking can be identified.<br />
Certain reflexes can be transferred to robotic systems.<br />
Postural <strong>Control</strong> is Supraspinal Postural control requires more than local reflexes.<br />
To a certain degree, estimating the body pose and its dynamics is required for<br />
posture stability. Adjustment <strong>of</strong> foot placement has strong influence on whole body<br />
balancing.<br />
It shall be understood that the features just mentioned do not exhaustively describe<br />
human walking control. On the one hand, this is due to the fact that biomechanical and<br />
neuroscientific knowledge on this problem is still incomplete. On the other hand, some<br />
aspects were deliberately omitted as it was decided not to include them in the control<br />
system developed in this work. Most prominently, this concerns the capability <strong>of</strong> learning<br />
and long-term adaptation <strong>of</strong> the human brain. This topic will be attended to in future
3.4. Biologically Inspired <strong>Control</strong> <strong>of</strong> <strong>Bipedal</strong> <strong>Robots</strong> 55<br />
(a) (b) (c) (d)<br />
Figure 3.23: Derivation <strong>of</strong> passive walking on downwards slope following McGeer’s approach:<br />
(a) simple wheel, (b) rimless wheel, (c) synthetic wheel, (d) simple walker.<br />
work. Furthermore, this thesis will not try to design a control system on neural level but<br />
rather a system based on larger control units. Consequentially, mechanism on the level <strong>of</strong><br />
nerve cells, nerve fibers, or neural oscillators were only treated on a very basic level. As the<br />
next section will show, some researchers try to approach the problem <strong>of</strong> controlling bipeds<br />
at such a fine granularity. And finally, even the parts <strong>of</strong> neurosciences and biomechanics<br />
approached above can certainly not be covered in their vast completeness on the few pages<br />
<strong>of</strong> this introduction.<br />
3.4 Biologically Inspired <strong>Control</strong> <strong>of</strong> <strong>Bipedal</strong> <strong>Robots</strong><br />
Considering the two-legged locomotion capabilities <strong>of</strong> humans, it is not surprising that<br />
robotics researchers are trying to transfer biological concepts as those just discussed to<br />
the control <strong>of</strong> bipedal robots. The remainder <strong>of</strong> this chapter reviews research efforts being<br />
motivated in one or another way by insights on natural motion control. The section is<br />
divided in two parts, one discussing research activities concerning passive control aspects<br />
<strong>like</strong> the exploitation <strong>of</strong> inherent dynamics or elasticities, the other focusing on active<br />
control concepts <strong>like</strong> reflexes or oscillators. In case a research work includes several <strong>of</strong> the<br />
characteristics introduced above, it is listed in the section discussing its most prominent<br />
feature.<br />
3.4.1 Exploitation <strong>of</strong> Inherent Dynamics and Elasticities<br />
One <strong>of</strong> the most important aspect <strong>of</strong> locomotion in biological systems is the exploitation <strong>of</strong><br />
the natural dynamics. As mentioned before, this is done in several ways, e.g. clever mass<br />
distribution, movements that follow the inertia <strong>of</strong> body segments, or energy storage and<br />
self-stabilization by elastic elements. Unfortunately, most actuated bipeds cannot benefit<br />
from these effects due to the high friction <strong>of</strong> their joints.<br />
Beginning in the 1990s, researchers tried to build machines purely relying on inherent body<br />
dynamics. These so called passive dynamic walkers have no actuators and therefore can<br />
exhibit very low joint friction. No active control is taking place, instead these machines<br />
purely rely on well-balanced mechanics and gravity.<br />
McGeer was one <strong>of</strong> the first to investigate the motion laws behind passive dynamic walkers<br />
motivated by simple ramp-walking tinkertoys [McGeer 90, McGeer 93]. He built a machine<br />
l<br />
r<br />
mH<br />
mL
56 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
(a) (b) (c) (d)<br />
Figure 3.24: Passive dynamic walking machines: (a) McGeer’s original walker, (b) Collin’s<br />
Walker, (c) Cornell Biped, (d) Meta from TU Delft.<br />
that can walk down a slope, only using the gained potential energy to compensate for<br />
energy loss (Figure 3.24a). It can be shown that self-stabilizing cycles exist for such<br />
systems, i.e. within small margins they will stay inside stable trajectories. The models for<br />
such a simple walker can be derived starting from a simple wheel as shown in Figure 3.23.<br />
A wheel can roll along a level surface without loss <strong>of</strong> energy as far as friction is neglected.<br />
Removing the rim <strong>of</strong> the wheel leaves an equally spaced set <strong>of</strong> legs dispensing energy<br />
each time the next leg hits the ground. Assuming inelastic and impulsive impacts and<br />
conservation <strong>of</strong> angular momentum, the loss <strong>of</strong> speed can be calculated: on a level surface<br />
the rimless wheel decelerates exponentially. But on a downhill slope it can regain velocity<br />
during the rotation about the stance leg.<br />
Instead <strong>of</strong> removing the rim, the wheel could be reduced to only two spokes that can<br />
vary their angle in a joint at the former axle <strong>of</strong> the wheel (Figure 3.23c). Assuming the<br />
swinging leg would clear the ground, McGeer shows that a solution to the dynamics <strong>of</strong><br />
such a system can be found so that the next swing leg arrives just in time to continue<br />
the rolling motion as next stance leg. A generalization <strong>of</strong> this walker can be found in<br />
Figure 3.23d. McGeer found stable walking cycles for this model considering different<br />
parameters <strong>like</strong> the leg length l, the foot arc radius r, the hip and leg masses mH and mL<br />
as well as <strong>of</strong>fsets <strong>of</strong> the leg mass relative to the leg.<br />
Further research on this topic addresses the extention to three dimensions, adding a passive<br />
knee for implementing ground clearance <strong>of</strong> the swing leg, comparing the motions <strong>of</strong> passive<br />
walkers to human gait, or investigating energy consumption, step length, and stability<br />
issues [Garcia 98, Kuo 99, Kuo 01, Wisse 04]. Figure 3.24 shows some <strong>of</strong> the machines<br />
that emerged from this research.<br />
Despite the elegance <strong>of</strong> its motions and the simplicity <strong>of</strong> the control, the principle <strong>of</strong><br />
passive dynamic walking has some draw-backs and limitations. As the machines are purely<br />
passive, they rely on the potential energy gained while walking down a slope. Furthermore,<br />
the design <strong>of</strong> the robot must be carefully chosen and tuned for it to be able to walk at all.<br />
And as there is no feed-back, the machine cannot react to disturbances, but only walk on
3.4. Biologically Inspired <strong>Control</strong> <strong>of</strong> <strong>Bipedal</strong> <strong>Robots</strong> 57<br />
(a) (b)<br />
Figure 3.25: Jerry Pratt’s Spring Flamingo and the finite state machine <strong>of</strong> its control system.<br />
From [Pratt 00], p68.<br />
very level ground without external forces. It is not possible to walk outside the sagittal<br />
plane as degrees <strong>of</strong> freedom and an active steering mechanism are missing.<br />
The necessity <strong>of</strong> additional energy can be solved by substituting the energy gained while<br />
walking down a slope by simple actuators [Collins 05]. The robots Mike and Denise<br />
developed at TU Delft are powered by two pneumatic actuators in the hip [Wisse 05].<br />
Electrical actuation with series elastic elements is used for hip and ankle actuation <strong>of</strong><br />
the robot Meta shown in Figure 3.24d. Only ankle actuation is used for the Cornell<br />
Biped (Figure 3.24c) having a comparable energy consumption as human walking, whereas<br />
Honda’s Asimo uses at least ten times the energy <strong>of</strong> human walking [Collins 05].<br />
Another work propagating the exploitation <strong>of</strong> inherent control and natural dynamics <strong>of</strong><br />
walking is Jerry Pratt’s control approach for the robot Spring Flamingo (Figure 3.25a).<br />
He states that bipedal walking is a difficult problem only if viewed as a dynamical system<br />
solution but simpler if viewed as a specific mechanism [Pratt 00]. Starting from simplified<br />
models for two-legged walking, intuitive control laws are derived to make sure that five<br />
conditions are met: stabilization <strong>of</strong> height, <strong>of</strong> pitch, and <strong>of</strong> speed; swing leg motion; and<br />
properly timed transition from one support leg to the next. For each leg, a finite state<br />
machine as shown in Figure 3.25b toggles between these controllers. Some <strong>of</strong> the controllers<br />
make use <strong>of</strong> the virtual model control method as described in Section 2.2.2. The approach<br />
is shown to work on the 6 degree <strong>of</strong> freedom planar walking Spring Flamingo as well as for<br />
a 12 degree <strong>of</strong> freedom machine [Pratt 09]. Both robots feature series elastic actuators with<br />
low impedance to allow for the passive dynamics to take effect and for the implementation<br />
<strong>of</strong> a torque joint control [Pratt 95a, Pratt 02].<br />
The main achievements <strong>of</strong> Pratt’s work is to successfully combine feed-back control with<br />
exploitation <strong>of</strong> passive dynamics. A very natural and energy efficient walking gait is
58 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
produced and the system remains stable against small perturbations and changes in slope.<br />
But while the principles <strong>of</strong> exploiting inherent robustness and natural dynamics appear to<br />
beuniversal, thesuggestedalgorithmsandtheirparametershavetobesignificantlychanged<br />
for a robot <strong>of</strong> different mass distribution, size, or shape. Furthermore it is not easily<br />
possible to extend the control to different modes <strong>of</strong> locomotion or adapt characteristics <strong>like</strong><br />
the step height. And for some <strong>of</strong> the controllers, modelling is necessary to a considerable<br />
amount, <strong>like</strong> calculating the Jacobian <strong>of</strong> the direct kinematic for a virtual component or<br />
partly using a dynamic model for fast leg control.<br />
Roa et al. develop simple robots using a design methodology based on models <strong>of</strong> passive<br />
walking [Roa 05]. A dynamic simulation <strong>of</strong> the preliminary mechanical design including<br />
actuation is then used to refine the contruction. The three UNROCA robots originating<br />
from this work use servo motors to track the trajectories resulting from stimulation. While<br />
this approach makes use <strong>of</strong> the system dynamics during the design process, the actual<br />
robots do not exploit it due to their stiff actuators.<br />
A different approach combining the benefits <strong>of</strong> natural system dynamics and actuated<br />
joints is proposed by Katja Mombaur et al. [Mombaur 05b]. The main idea is to use<br />
periodical feed-forward control trajectories that will generate cyclic and stable open-loop<br />
solutions. These trajectories are generated using techniques from numerical optimization<br />
and optimal control. For this approach, a dynamic rigid multibody system model <strong>of</strong><br />
the robot and its interaction with the environment has to be established and periodic<br />
constraints must be formulated. The resulting multi-phase optimal control problem can<br />
efficiently be solved by optimization techniques based on the direct boundary value problem<br />
approach using multiple shooting [Leineweber 03a, Leineweber 03b]. This technique involves<br />
a discretization <strong>of</strong> both state and control variables transforming the optimal control<br />
problem into a nonlinear programming problem (nlp) with simultaneous simulation for<br />
the evaluation <strong>of</strong> objective function and constraints. The approach does not only allow<br />
to calculate an optimal control solution, but also to optimize mechanical parameters<br />
in respect to the target functional. Open-loop stable solutions can be shown for walking<br />
[Mombaur 01], running [Mombaur 05a], and somersaults [Mombaur 05c]. It can even<br />
be shown that human-<strong>like</strong> running with a high degree <strong>of</strong> freedom model can be open-loop<br />
stable [Mombaur 07].<br />
As stability can be included as part <strong>of</strong> the target functional during the optimization process,<br />
self-stabilizing, natural behavior can be achieved. Never-the-less the approach lacks any<br />
feed-back, so robust locomotion over unknown terrain cannot be realized. Furthermore,<br />
the approach depends on a complete mathematical model <strong>of</strong> the robot and its environment<br />
and the resulting trajectories only work for this representation. This makes it difficult<br />
to transfer it to an actual robot, as the optimization process works on a simultaneous<br />
simulation that cannot be easily replaced with a real machine.<br />
As mentioned in Section 3.1.1 exploitation <strong>of</strong> elasticity results in several benefits in<br />
natural locomotion. Alexander suggests three different applications <strong>of</strong> springs in legged<br />
robotics [Alexander 90]. Pogo-<strong>like</strong> springs can store energy during impact that can be<br />
reused for propulsion; return springs can save energy during the reverse <strong>of</strong> direction in<br />
the swing leg; and elastic foot pads can reduce impacts and provide better grip on uneven<br />
terrain. Already in the 1980s Raibert made heavy use <strong>of</strong> pogo-<strong>like</strong> springs in his running<br />
and hopping machines [Raibert 86].
3.4. Biologically Inspired <strong>Control</strong> <strong>of</strong> <strong>Bipedal</strong> <strong>Robots</strong> 59<br />
(a) (b) (c) (d) (e)<br />
Figure 3.26: Bipeds featuring elastic actuation: (a) Lucy and (b) Veronica from University <strong>of</strong><br />
Brussels, (c) the biped developed by the Shadow company, (d) elastic biped developed at fzi,<br />
Germany, (e) Pneumat-BR from Hosoda Lab.<br />
Only a few research projects cover the use <strong>of</strong> elasticity during bipedal walking. The 6 degree<br />
<strong>of</strong> freedom robot Lucy as shown in Figure 3.26a uses pleated pneumatic artificial muscles as<br />
actuation that allow to control joint stiffness [Vermeulen 04, Verrelst 05, Vanderborght 07,<br />
Vanderborght 08]. The aim <strong>of</strong> the project is to combine the versatility <strong>of</strong> robots controlled<br />
by technical methods as discussed in Chapter 2 with exploitation <strong>of</strong> natural dynamics and<br />
thus reducing energy consumption. Joint trajectories are pre-generated using a dynamic<br />
model <strong>of</strong> the robot and the pneumatic muscles. zmp calculations are applied as stability<br />
criterion. A trajectory tracker then controls the pressure within the muscles to follow the<br />
desired motion. In this way walking velocities <strong>of</strong> up to 0.15 m/s could be achieved. By<br />
changing the stiffness <strong>of</strong> the joint during the trajectory tracking depending on the natural<br />
system dynamics, energy usage can be reduced. This approach has so far only be tested<br />
on a pendulum structure actuated by the artificial muscles. While this research work tries<br />
to include passive dynamics to the control, it still depends on a dynamic model <strong>of</strong> the<br />
robot and its environment.<br />
Another project<strong>of</strong> the same groupcombiningpassivedynamic walkingandelasticactuation<br />
is the robot Veronica shown in Figure 3.26b [Ham 06a]. It is powered by six maccepa<br />
(Mechanically Adjustable Compliance and <strong>Control</strong>lable Equilibrium Position Actuator)<br />
actuators in the hip, knee, and ankle. This rotational actuator features controlable stiffness<br />
and equilibrium position by combining two servo motors and a mechanical spring. The<br />
planar robot is 1m in height, weights 5.6kg and is controlled by a concept called <strong>Control</strong>led<br />
Passive <strong>Walking</strong>: the compliant actuators change the natural frequency <strong>of</strong> the mechanical<br />
system thus enabling passive dynamic walking at different velocities. The underlying<br />
controller divides the walking cycle into six phases. For each phase, a set <strong>of</strong> joint control<br />
parameters is determined for the hip, knee, and ankle joints. For instance, the hip joint’s<br />
equilibrium position is either set to the flexed or extended postion, and the controller is<br />
configured to be stiff or compliant. Supported by a human operator, several walking steps<br />
could be achieved. While the actuator has interesting properties, it cannot produce high<br />
stiffness or high torque by design. The control concept lacks feedback mechanisms to react<br />
to disturbances or unpredicted ground conditions.
60 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
At the Locomotion Laboratory in Jena, Seyfarth and his colleagues also investigate the role<br />
<strong>of</strong> compliant actuators on bipedal walking and running [Geyer 04,Iida 07,Blum 09]. In the<br />
scope <strong>of</strong> this research, several basic planar robots with only a few active degrees <strong>of</strong> freedom<br />
are built to verify the models derived from biomechanical analysis. The underactuated<br />
robot Jena Walker II is used to examine the function <strong>of</strong> the elastic muscle-tendon system<br />
during walking [Smith 07]. It features two actuated hip joints and passive knee and ankle<br />
joints. Four major muscle-tendon groups are represented by a spring-cable system, three <strong>of</strong><br />
them spanning two joints. Stable, supported toe-walking can be demonstrated at different<br />
velocities up to 0.6 m/s showing leg compliance via the ankle joint even during stance with<br />
a stretched leg.<br />
Since the pioneer work <strong>of</strong> Kato in 1969, several projects use pneumatic artificial muscles as<br />
actuation for biped, e.g. the biped by the Shadow company in Figure 3.26c, but only a few<br />
machines are actually able to walk, let alone make use <strong>of</strong> the elastic properties. Kerscher et<br />
al. are designing a compliant 3D bipedal robot as shown in Figure 3.26d [Kerscher 07]. The<br />
approach combines electrical actuation in the hip joint with pneumatic muscles produced by<br />
the company Festo in the knee and ankle joints. The control concept combines the Virtual<br />
Model <strong>Control</strong> as describes in Section 2.2.2 with adaptation <strong>of</strong> the stiffness. A detailed<br />
model <strong>of</strong> the pneumatic muscle is developed by using e.g. a quick release experiment to<br />
derive dynamic properties [Kerscher 06]. Based on dynamic simulation <strong>of</strong> the robot and<br />
the model <strong>of</strong> the muscle, first walking steps could be achieved.<br />
Hosoda et al. have built several robots for walking and jumping actuated by McKibben<br />
pneumatic artificial muscles [Hosoda 07a, Hosoda 07b]. The robot Pneumat-BR shown in<br />
Figure 3.26e is able to jump as well as walk in the sagittal plane. The main focus <strong>of</strong> this<br />
work lies in the adjustability <strong>of</strong> the joint compliance depending on the mode <strong>of</strong> locomotion.<br />
The control system consists <strong>of</strong> a simple feed-forward mechanism opening or closing the<br />
valves in a fixed sequence for an experimentally determined time. While indeed passive<br />
walking-<strong>like</strong> locomotion could be achieved, the robot lacks any feedback system and can<br />
only walk on flat terrain without disturbances.<br />
3.4.2 Neuro-, Reflex-, and Oscillator-based <strong>Control</strong><br />
Several research projects developing control approaches for bipedal walking based on<br />
neuroscientific findings can be found in literature. As presented earlier in this chapter,<br />
possible features to be considered are the functionality <strong>of</strong> the neurons, central pattern<br />
generators, reflexes, or muscle synergies. In the following, research work involving one or<br />
several <strong>of</strong> these features will be discussed.<br />
Paul demonstrates that a purely reactive sensorimotor neural network can produce a stable<br />
walking gait for a simulated 8 degrees <strong>of</strong> freedom lower body biped [Paul 05]. Instead<br />
<strong>of</strong> relying on a central pattern generator, simple neural networks directly connect sensor<br />
inputs <strong>like</strong> waist orientation or contact information to actuator control signals. A genetic<br />
algorithm is used to evolve the controllers, resulting in a rhythmic, cyclic gait behavior. It<br />
is shown that the cutaneous sensor information is sufficient to establish control networks<br />
that produce a walking limit cycle, while joint angle and orientation sensing seems to<br />
be less important. It is assumed that a central pattern generator could mainly control<br />
upper body movement to adjust e.g. the step frequency. While the results underline<br />
the importance <strong>of</strong> reflexes and the possibility <strong>of</strong> reactive switching <strong>of</strong> walking phases,
3.4. Biologically Inspired <strong>Control</strong> <strong>of</strong> <strong>Bipedal</strong> <strong>Robots</strong> 61<br />
(a) (b) (c) (d)<br />
Figure 3.27: (a) HOAP-1 and (b) HOAP-3 by Fujitsu, (c) RunBot from bccn Göttingen, (d)<br />
small biped from Nakamura Lab.<br />
it remains to be seen whether this simple control approach would still work on a more<br />
complex machine and in a disturbed environment.<br />
Zaier et al. investigate the combination <strong>of</strong> reflexes with a cpg [Zaier 07, Zaier 08]. On<br />
the small humanoid HOAP-3 (Figure 3.27b) they implement a piecewise linear pattern<br />
generator using gyro sensor information for stabilization during single support. A recurrent<br />
neural network is triggered by sudden sensor events to recognize the disturbance and<br />
initiate a reflex motion. The motion can be adapted on the basis <strong>of</strong> sensor information: in<br />
case the robot steps on an obstacle, its position on the foot sole is calculated using four<br />
force sensors in the foot. Then a roll or pitch motion in the ankle tries to increase the<br />
size <strong>of</strong> the support polygon in order to relocate the current zmp in a stable region. This<br />
approach combines generated trajectories with reflexes. The pattern generation clearly<br />
benefits from the large foot plates and the low weight <strong>of</strong> the robot.<br />
Geng et al. implement a reflexive neural network for a small planar walker [Geng 06,<br />
Manoonpong 07]. They show that fast walking is possible without planing <strong>of</strong> trajectories<br />
but rather by using local reflexes and by exploiting the passive dynamics <strong>of</strong> the mechanical<br />
system. The robot RunBot as shown in Figure 3.27c is 23cm in height, has curved feet<br />
measuring ground contact, and is actuated in hip and knees by four modified servo motors.<br />
An additional servo motor can move a small weight at the upper body to simulate leaning<br />
forward or backwards. Further sensors include an accelerometer and one infrared sensor<br />
pointing to the floor to distinguish between even black floor and sloped white floor. Simple<br />
neural networks locally control the leg and the upper body movement, creating reflex-<strong>like</strong><br />
actions depending on joint angles, ground contact, or acceleration. For instance, when<br />
the swing leg reaches the anterior extreme position (aep), the knee joint is extended to<br />
prepare for touchdown and weight acceptance. An additional adaptive network modifies<br />
the local networks based on the ir information to achieve a predictive change <strong>of</strong> gait on<br />
slopes. As a result, stable planar walking on flat and sloped terrain could be generated<br />
that combines exploitation <strong>of</strong> passive dynamics and active neural control. Scaled by leg<br />
length, the walking velocity is one <strong>of</strong> the fastest observed in bipeds and is comparable
62 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.28: Oscillator control systems as applied by Taga. From [Taga 91], p150.<br />
to fast human walking. However, it still has to be shown whether the simplicity <strong>of</strong> the<br />
control approach scales to larger machines with more degrees <strong>of</strong> freedom.<br />
A combination <strong>of</strong> feed-forward patterns and reflexes accounts for the control approach<br />
developed by Huang et al. [Huang 05]. The feed-forward joint angle trajectories are<br />
pre-calculated <strong>of</strong>fline as third-order splines using zmp as stability criterion. Here, it is<br />
assumed that the dynamics <strong>of</strong> the robot and its environment are known. Three reflexes<br />
add joint angle <strong>of</strong>fsets to the rhythmic trajectories in case disturbances are detected. The<br />
zmp reflex will shift the ankle joints if the actual zmp moves too close to the border<br />
<strong>of</strong> the foot. By considering the <strong>of</strong>fset between the estimated and effective touchdown<br />
time, the landing-phase reflex changes the leg length <strong>of</strong> the stance leg, thus compensating<br />
changes in forward velocity. Finally, the body posture reflex will adapt the hip joints if<br />
the measured body inclination varies from that <strong>of</strong> the calculated trajectory. The control<br />
approach is demonstrated in simulation and using the small biped shown in Figure 3.27d.<br />
While a combination <strong>of</strong> feed-forward and feedback control seems promising, the concept <strong>of</strong><br />
Huang et al. still requires a complete dynamics model for the <strong>of</strong>fline as well as the online<br />
calculation <strong>of</strong> the zmp. Furthermore, the use <strong>of</strong> joint angles as control variable and the<br />
stiff mechanics forbid the use <strong>of</strong> passive dynamics.<br />
Taga was one <strong>of</strong> the first to control biped locomotion by neural oscillators [Taga 91,<br />
Taga 95b, Taga 95a]. In a simulated five and eight link planar biped, neural rhythm<br />
generators similar to those proposed by Matsuoka control each hip, knee, and ankle<br />
(Figure 3.28) [Matsuoka 87]. As passive dynamics are allowed to act, also mechanical<br />
oscillation <strong>like</strong> the pendulum motions <strong>of</strong> the limb is included. Inertial joint angles, joint<br />
velocities, and foot contact information are used in the feedback terms <strong>of</strong> the individual
3.4. Biologically Inspired <strong>Control</strong> <strong>of</strong> <strong>Bipedal</strong> <strong>Robots</strong> 63<br />
Figure 3.29: Hierarchical oscillator control systems as applied by Shan. From [Shan 02].<br />
oscillators. The relation between the oscillators is self-organized as they are mutually<br />
entrained and globally interact via the controlled system and the environment. Stable<br />
walking on even and sloped surfaces and under perturbations is achieved. An important<br />
result <strong>of</strong> Taga’s work is to demonstrate embodied control <strong>of</strong> a biped with rhythmic<br />
locomotion patterns emerging as result from dynamic interaction <strong>of</strong> the global entrainment<br />
between the musculoskeletal system, the neural system, and the environment. Yet it is not<br />
clear if the approach remains valid with more complex models or an actuation similar to real<br />
bipedal machines. Also it has to be decided for each oscillator which sensor systems will be<br />
used as feedback. Similar projects continued Taga’s ideas including slightly more degrees<br />
<strong>of</strong> freedom or a more sophisticated model <strong>of</strong> the neuro-muscular system [Yamazaki 96,<br />
Hase 99, Ogihara 01]. Katayama et al. study the theory <strong>of</strong> neural oscillators for the use in<br />
bipedal locomotion control and show solutions for the stability <strong>of</strong> the nonlinear differential<br />
equations and possible applications for walking pattern generation [Katayama 95].<br />
<strong>Walking</strong> control systems based on neural oscillators do not scale well with increasing<br />
degrees <strong>of</strong> freedom as their parameters do not have a physical interpretation and therefore<br />
are difficult to tune or to learn. Shan et al. approach the problem <strong>of</strong> complexity by using a<br />
hierarchical system <strong>of</strong> cpg sub circuits [Shan 02]. Each <strong>of</strong> these circuits is implemented as<br />
recurrent neural network and represent a certain motor program for walking (Figure 3.29).<br />
Represented by differential equations <strong>of</strong> different order, the oscillator sub circuits create a<br />
lateral roll movement, swing leg lifting, and forward/backward motion. The parameter<br />
space is reduced by inverse kinematics calculations. The control system is tested on the<br />
small biped robot HOAP-1 as shown in Figure 3.27a featuring 20 degrees <strong>of</strong> freedom, force<br />
measurement in the feet, and a three dimensional gyroscope. <strong>Walking</strong> and simple stair<br />
climbing could be achieved. However, as joint position trajectories <strong>of</strong> sine-<strong>like</strong> patterns are
64 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Figure 3.30: Oscillator control system as applied by Aoi et al. From [Aoi 05], p222.<br />
forced on the robots joint, no inherent dynamics can be exploited and only highly tuned<br />
parameters allow the system to walk in an undisturbed environment.<br />
Aoi and his colleagues also control a HOAP-1 robot by a network <strong>of</strong> nonlinear oscillators<br />
[Tsuchiya 03, Aoi 05]. One oscillator for each foot, each leg, and the trunk are<br />
coordinated by an inter-oscillator (Figure 3.30). Together these units form the rhythm<br />
generator <strong>of</strong> the control system. Their phases encode the joint trajectories for the limbs.<br />
Again, inverse kinematics is used to calculate joint positions resulting in ellipsoid trajectories<br />
<strong>of</strong> hands and feet in swing and stance phase. Inverse dynamics and numerical<br />
simulation lead to a trunk motions that allows stable walking. Stability is determined by<br />
analysis <strong>of</strong> Poincaré maps <strong>of</strong> the motion equations. The ground contact measurements<br />
within the feet provide sensory feedback that is used to reset the oscillators and modify<br />
the trajectories e.g. based on the foot position at touchdown. Experiments using the robot<br />
and a simulation environment show that the cyclic motion falls back to its limit cycles at<br />
very small disturbances but cannot cope with larger perturbations. While this approach<br />
employs oscillators at the center <strong>of</strong> its control system, it still relies on many methods <strong>of</strong><br />
technically controlled bipeds and thus inherits the corresponding drawbacks as discuss at<br />
the end <strong>of</strong> Chapter 2.<br />
The application <strong>of</strong> neural oscillators is also examined by Endo, Cheng, et al. for a basic<br />
planar walker and for a small, fully actuated biped [Endo 04, Endo 05]. The control system<br />
based on Matsuoka oscillators is set up in analogy to Kimura’s work on quadrupedal<br />
robots [Kimura 04]. While the oscillators <strong>of</strong> the planar walker directly control the joint<br />
torques, those <strong>of</strong> the control for the small humanoid act on the foot positions (Figure 3.31a).<br />
While this approach reduces the number <strong>of</strong> neurons and parameters, it makes an inverse<br />
kinematics calculation necessary and excludes the possibility to exploit system dynamics.<br />
The vertical leg movement is modulated by two postural reflexes, an extensor response,<br />
and a vestibulo-spinal-<strong>like</strong> reflex that generate feedback terms for the oscillator equations.<br />
Another feedback term synchronized the horizontal leg movement with the body sway. The<br />
approach is tested in simulation and using a QRIO robot by Sony as shown in Figure 3.31b.<br />
Slow walking under small perturbations with a step length <strong>of</strong> approximately the length <strong>of</strong><br />
the feet can be achieved. In doing so, the dynamic effects during walking do play a minor<br />
role and postural stability is easier to obtain.
3.4. Biologically Inspired <strong>Control</strong> <strong>of</strong> <strong>Bipedal</strong> <strong>Robots</strong> 65<br />
(a) (b)<br />
Figure 3.31: (a) Oscillator and reflex control systems as applied by Endo, Cheng et al.,<br />
from [Endo 05], p599. (b) The QRIO robot by Sony.<br />
The forgoing literature survey presents an overview on biological inspired approaches <strong>of</strong><br />
bipedal robots. While not being complete, it still should provide a solid view on this topic’s<br />
research projects. Table 3.4 summarizes these works regarding the application <strong>of</strong> aspects<br />
<strong>of</strong> biological motion control as stated in the previous section. The following chapters will<br />
show how these aspects are integrated in the concept suggested in this work.
66 3. <strong>Human</strong> Locomotion <strong>Control</strong><br />
Approach Details ED HC DC FP RE PG PM PC<br />
[McGeer 90, McGeer 93] planar passive walking � - - - - - - -<br />
[Collins 05, Wisse 05] actuated passive walking � - - - ◦ - - -<br />
[Pratt 00] Spring Flamingo, planar, compliant � - ◦ - - ◦ ◦ ◦<br />
[Roa 05] exploit dynamics during design ◦ - - - - - - -<br />
[Mombaur 01, Mombaur 05b] optimal control, simulation ◦ - - � - - - -<br />
[Vermeulen 04, Vanderborght 08] Lucy, pneumatic muscles ◦ - - ◦ - - - -<br />
[Ham 06a] Veronica, maccepa, variable stiffness � - - ◦ - - - -<br />
[Geyer 04, Smith 07] Jena Walker II, passive compliance � - - ◦ - - - -<br />
[Kerscher 06, Kerscher 07] virtual model control, pneumatic muscles ◦ - ◦ - ◦ - ◦ -<br />
[Hosoda 07a, Hosoda 07b] Pneumat-BR, pneumatic muscles ◦ - - ◦ - - ◦ -<br />
[Paul 05] purely reflex-based, simulation, 8 DoF - - ◦ - � - - -<br />
[Zaier 07, Zaier 08] HOAP-3, recurrent neural network - - ◦ ◦ � � - ◦<br />
[Geng 06, Manoonpong 07] RunBot, planar, neural network � ◦ ◦ - � ◦ - ◦<br />
[Huang 05] small servo biped, zmp - - - � � ◦ - �<br />
[Taga 91, Taga 95b, Taga 95a] simulation, 5/8 DoF, neural oscillators ◦ ◦ � - ◦ � - -<br />
[Shan 02] HOAP-1, hierarchy <strong>of</strong> cpgs, inv. kinematics - � - ◦ ◦ � - -<br />
[Tsuchiya 03, Aoi 05] HOAP-1, neural osc., inv. kinematics, <strong>of</strong>fline - ◦ - - ◦ � - -<br />
[Endo 04, Endo 05] QRIO, neural osc., inv. kinematics - - - - � � - -<br />
this work simulation, 21 DoF, compliance � � ◦ � � � � �<br />
ED: Exploit Inh. Dynamics RE: Reflexes, Feedback <strong>Control</strong><br />
HC: Hierarchical <strong>Control</strong> PG: Central Pattern Generators<br />
DC: Distrib. <strong>Control</strong> Units PM: Phase-dep. Stim. & Modul.<br />
FP: F.-Forw. Motor Patterns PC: High-Level Posture <strong>Control</strong><br />
Table 3.4: <strong>Control</strong> approaches for bipedal robots adapting ideas from biological motion control.
4. A Biologically Supported Concept<br />
for <strong>Control</strong>ling Bipeds<br />
In the previous chapter, key findings <strong>of</strong> biological motion control have been suggested to be<br />
considered worthwhile for robotic bipeds. They concern not only the control system itself<br />
in form <strong>of</strong> the central nervous system. Rather, they affect all aspects <strong>of</strong> the human body,<br />
its morphology, physiology, muscles, and receptors. Even more importantly, these aspects<br />
are interleaved as one cannot function without the other. This leads to a holistic approach<br />
for designing bionical bipeds or other robots strongly based on a biological example. As<br />
illustrated in Figure 4.1, all facets <strong>of</strong> the robot’s design can adopt or transfer ideas from<br />
biology. However, this thesis is focused on the control system for biped locomotion. And<br />
while solutions for the other problems <strong>like</strong> the mechatronics or muscle-<strong>like</strong> actuators<br />
cannot be provided, these topics must be covered nevertheless. A biological inspired<br />
control method as the one suggested here could not function without similar biological<br />
characteristics <strong>of</strong> the mechanical system. In order to test the control concept without the<br />
need <strong>of</strong> developing a full bipedal robot, a suitable simulation is designed (see Chapter 6),<br />
while keeping in mind the requirements for a real robot.<br />
This chapter introduces a methodology for controlling the locomotion <strong>of</strong> complex bipeds<br />
based on above findings from neurosciences and biomechanics. As the approach described<br />
here partly relies on passive dynamics, the following section describes passive control<br />
aspects. These lead to several requirements for the structure <strong>of</strong> the active control system<br />
that will be introduced in the subsequent section. Classes <strong>of</strong> control units that can be<br />
derived from their natural complements will be presented. Thereupon, the hierarchical<br />
layout and the control flow within the emerging network is described. Preliminary versions<br />
<strong>of</strong> this approach have been published in [Luksch 08a, Luksch 08b].<br />
4.1 Passive <strong>Control</strong> Aspects<br />
A strong advantage <strong>of</strong> natural locomotion control is the passive exploitation <strong>of</strong> mechanical<br />
properties. This includes the functional morphology <strong>of</strong> the human body, the inherent<br />
system dynamics, and self-stabilization by elastic elements. All these effects do not require
68 4. A Biologically Supported Concept for <strong>Control</strong>ling Bipeds<br />
Morphology<br />
Kinematical<br />
Layout<br />
Muscles<br />
Actuators<br />
Biology<br />
Bionics<br />
Robotics<br />
Receptors<br />
Sensors<br />
Nervous<br />
System<br />
<strong>Control</strong><br />
System<br />
Figure 4.1: Bionics as guiding principle for the design <strong>of</strong> bipedal robots. This thesis focuses on<br />
the derivation <strong>of</strong> the control system.<br />
active control or feedback. The presented approach tries to make use <strong>of</strong> these benefits.<br />
Naturally, this mainly affects the mechanical properties <strong>of</strong> the simulated or real robot.<br />
However, it also imposes demands on various levels <strong>of</strong> the active control system.<br />
Regarding the mechanical setup, beneficial passive effects can only emerge when certain<br />
requirementsaremet. Themorphology<strong>of</strong>therobotmustbedesignedtosupportthedesired<br />
forms <strong>of</strong> locomotion. This necessitates proper segment lengths and mass distribution.<br />
Besides manually tuning these parameters, a common procedure in the development <strong>of</strong><br />
passive walkers, two further strategies come to mind: as human morphology has been<br />
functionally optimized during millions <strong>of</strong> years <strong>of</strong> evolution, mimicking the masses and<br />
segment lengths <strong>of</strong> human trunk and limbs would be intelligible. This approach is taken<br />
in this work, as a simulated biped is not restricted by constructive constraints. The<br />
second strategy would make use <strong>of</strong> numerical optimization techniques to find a suitable<br />
robot design while taking the target motions and constraints <strong>of</strong> the construction into<br />
account. This idea was also investigates by the author but is not a substantial part <strong>of</strong> this<br />
work [Luksch 05, Luksch 07].<br />
Besides the robot’s morphology, the actuation system must also be suited for passive<br />
control. Especially high joint friction and damping can prevent exploitation <strong>of</strong> inherent<br />
dynamics. In this work, a compliant joint actuator featuring some <strong>of</strong> the characteristics<br />
found in the human muscle-tendon system is assumed. It allows for direct torque control<br />
and position control with adjustable compliance as well as for parallel elastic elements.<br />
This elasticity makes self-stabilization possible. Details on this topic can be found in<br />
Chapter 6.<br />
Finally, the active control system itself must be designed in such a way it does not inhibit<br />
the positive effects <strong>of</strong> passive dynamics. At no point, full body joint position trajectories<br />
should be used. Even if generated using a dynamics model, they can never fully match<br />
actual body motions in a partly unknown environment. Rather, torque control is to be<br />
preferred to position control whenever possible, and control units should act locally and<br />
be distributed. If position control is inevitable, at least a minimum compliance should<br />
remain, and at no time position control should affect more then only a few joints. Active
4.2. <strong>Control</strong> Unit Classes 69<br />
control only occurs to steer the limbs towards the deliberate motions and during reflexive<br />
action. The next section will introduce control units implementing these ideas.<br />
4.2 <strong>Control</strong> Unit Classes<br />
In human motion control, the basic control unit is the neuron. Each neuron collects<br />
incoming activity and fires itself if a certain threshold is reached. All data processing<br />
and muscle control is based on this simple unit. Since decades, researchers are designing<br />
artificial neural network to capture certain properties <strong>of</strong> their natural examples. While<br />
the idea <strong>of</strong> building a control system <strong>of</strong> simple, uniform units is intriguing, the concept<br />
described here chooses a structural abstraction above the neural level. Following the<br />
philosophy <strong>of</strong> behavior-based robotics, each control unit already represents a self-contained<br />
functional unit. Even though the approach is probably not as elegant as artificial neural<br />
networks, it yet shows several advantages: the human nervous system has about 100 billions<br />
<strong>of</strong> neuron, some <strong>of</strong> them handling thousands <strong>of</strong> incoming signal. A robot walking control<br />
system will be much smaller, but still the complexity <strong>of</strong> the network and its communication<br />
would be very high and increasing in size with each new feature. This complexity as well<br />
as the fact that individual neurons and signal have no semantics make it hard to design,<br />
interpret, and debug such a control system. On the other hand, if each control unit has its<br />
own function, these tasks become easier to manage. Furthermore, the parameters <strong>of</strong> the<br />
units have a physical meaning, facilitating the tuning and error handling <strong>of</strong> the control<br />
system.<br />
Nevertheless, some properties <strong>of</strong> neurons can be transferred to control units. A neuron can<br />
only be active if stimulated, and its activation can be decreased or suppressed by inhibiting<br />
signals. This idea <strong>of</strong> gradual stimulation or inhibition is applied to the control units at<br />
hand. The flow <strong>of</strong> activity will indicate which parts <strong>of</strong> the network will be responsible for<br />
the control at a certain point in time. Section 5.1.3 will describe how these features are<br />
implemented within the behavior-based architecture deployed in this work.<br />
The previous chapter, in particular Section 3.1, presented the control units found in human<br />
locomotion control. In nature the distinctions between the classes <strong>of</strong> control units are not<br />
sharply defined. Some might not even exist as a self-contained group <strong>of</strong> neurons, but only<br />
emerge as a unit from consistant effects observed during gait analysis. Still it remains<br />
valid to derive control units for technical systems from these biological finding as they<br />
clearly exist as a functional entity. Thus the following section lists the unit classes <strong>of</strong> the<br />
suggested control concept, succeeded by the descriptions <strong>of</strong> the hierarchical network in<br />
which the units are arranged. For each class, a symbolic representation is introduced which<br />
will be used throughout the remaining chapters <strong>of</strong> this text.<br />
4.2.1 Locomotion Modes<br />
In humans and animals, the decision on which form <strong>of</strong> locomotion is applied in a certain<br />
situation is taken by the brain. The control system in this work leaves this choice to the<br />
operator <strong>of</strong> the bipedal robot. Thus, the highest-level control units to be considered are<br />
the locomotion modes:<br />
Locomotion<br />
Mode
70 4. A Biologically Supported Concept for <strong>Control</strong>ling Bipeds<br />
Examples for locomotion modes could be standing, walking, or running. Selected by the<br />
operator, these units stimulate the corresponding parts <strong>of</strong> the control network. Inputs for<br />
the modulation <strong>of</strong> the locomotion mode could include the desired velocity or direction <strong>of</strong><br />
movement. Locomotion modes directly stimulate the pattern generators introduced next,<br />
but can also modulate control units on a lower level.<br />
4.2.2 Spinal Pattern Generators<br />
Section 3.1.4 showed that muscle activation seems to be coordinated with the phases <strong>of</strong><br />
the walking cycle. This and other evidence brought forth in Section 3.2.2 indicate the<br />
existence <strong>of</strong> a central unit generating rhythmic patterns <strong>of</strong> muscle action. It is commonly<br />
believed that these pattern generators are located within the spinal cord. Consequently,<br />
the corresponding control unit is labeled as spinal pattern generator (spg):<br />
SPG<br />
While many research works model central pattern generators as neural oscillator, another<br />
approach is followed here. spgs are represented as finite state machines, where state<br />
transitions are triggered by sensory events. The drawback <strong>of</strong> this approach is the absence<br />
<strong>of</strong> a strong timing to create periodic movement. Here, the periodicity emerges from the<br />
robots interaction with the environment. As an advantage, the walking phases are always<br />
synchronized to the corresponding kinematic or kinetic events. This can result in higher<br />
robustness <strong>of</strong> the system. Furthermore, this approach is beneficial for the exploitation <strong>of</strong><br />
inherent dynamics as less timing is forced on the motion <strong>of</strong> the segment masses.<br />
4.2.3 Motion Phases<br />
The spgs could directly stimulate all the lower control units working in one phase <strong>of</strong><br />
locomotion. But to support a clear arrangement and to further follow the natural example<br />
<strong>of</strong> hierarchical layout, for each phase its own control unit is introduced:<br />
Motion<br />
Phase<br />
In general, each motion phase corresponds to a section <strong>of</strong> the cyclic locomotion mode<br />
between significant kinetic or kinematic events. Within each phase unit it is coded to<br />
what extend the lower level control units are stimulated or inhibited. Modulation <strong>of</strong> reflex<br />
action is also possible. Furthermore, motion phases set the stiffness and equilibrium point<br />
<strong>of</strong> passive joints.<br />
4.2.4 Motor Patterns<br />
Bizzi, Ivanenko and others showed that stimulation <strong>of</strong> certain regions in the spinal cord<br />
result in muscle action producing coordinated joint or limb motions (Section 3.1.4). These<br />
components or motion primitives seem also to be recruited in phases <strong>of</strong> locomotion. The<br />
corresponding control unit <strong>of</strong> this concept is called motor pattern:
4.2. <strong>Control</strong> Unit Classes 71<br />
Motor<br />
Pattern<br />
Similar to muscle activity measured with emg, these units produce uniform patterns <strong>of</strong><br />
torque for one or more joints in a feed-forward manner. Only a minimum number <strong>of</strong><br />
parameters describe the characteristics <strong>of</strong> the torque function. Motor patterns always act<br />
locally, i.e. they will not affect joints that are located far apart (e.g. a joint <strong>of</strong> an arm and<br />
a joint in one <strong>of</strong> the feet). Should a more global synergy be necessary, it must be provided<br />
at a higher level. For instance a motion phase can stimulate several motor patterns at<br />
a time. While motor patterns are designed without feedback, fortitude and duration <strong>of</strong><br />
the torque output can vary depending on the modulation by motion phases or locomotion<br />
modes. Motor patterns support or shape the passive system dynamics to create the desired<br />
motion. Still, as many joints as possible should act in a purely passive or compliant way.<br />
4.2.5 Local Reflexes<br />
Reflex action provides the basic feedback mechanism in human motion control. It can occur<br />
on various levels <strong>of</strong> complexity, ranging frommonosynaptic and propriospinalto supraspinal<br />
depending on the area <strong>of</strong> the spinal cord and the brain they cover (Section 3.1.3). <strong>Control</strong><br />
units corresponding to the first two types, i.e. those affecting only a few, spatially adjoining<br />
joint, are called local reflexes:<br />
Local<br />
Reflex<br />
Local reflexes show a tight coupling between sensor information and motor action. The<br />
control answer can have different forms: some reflexes show a loopback controller-<strong>like</strong><br />
behavior with a linear or nonlinear relation between sensor data and control output. The<br />
other type <strong>of</strong> reflexes works event-based: as soon as a certain sensor event occurs, the<br />
output state is changed.<br />
4.2.6 Postural Reflexes<br />
As in the natural model, reflexes vary in their spatial and semantic expansion. Most reflexes<br />
regulating the body’s posture during locomotion require a more complex mechanism than<br />
local loopback control. They belong to the class <strong>of</strong> supraspinal reflexes as their neural<br />
activity is not restricted to an enclosed part <strong>of</strong> the spinal cord, but also include the brain.<br />
The analogues to these units are called postural reflexes:<br />
Postural<br />
Reflex<br />
The main characteristics <strong>of</strong> this type <strong>of</strong> control units is the extend <strong>of</strong> their action and<br />
the complexity <strong>of</strong> their internal model: the reflex action at one place <strong>of</strong> the robot can<br />
be the result <strong>of</strong> a sensor event at the opposite end <strong>of</strong> the machine, possibly supported<br />
by a simplified dynamical model. The state variables most frequently used or calculated
72 4. A Biologically Supported Concept for <strong>Control</strong>ling Bipeds<br />
‘Brain’ ‘Spinal Cord’<br />
Locomotion<br />
Modes<br />
Sense <strong>of</strong><br />
Balance<br />
stimulation stimulation<br />
SPGs<br />
Mechatronics<br />
Vestibular<br />
System<br />
(IMU)<br />
modulation signals<br />
Somatosensory<br />
System<br />
Motion<br />
Phases<br />
Environment<br />
Postural<br />
Reflexes<br />
torques, positions, forces<br />
Joint<br />
<strong>Control</strong><br />
Mechanical <strong>Control</strong> (Elasticities, Inerita, ...)<br />
Joint Groups<br />
Local<br />
Reflexes<br />
Motor<br />
Patterns<br />
Sensor<br />
Handling<br />
torque, position,<br />
stiffness<br />
Figure 4.2: The hierarchical organization <strong>of</strong> control units and the interaction <strong>of</strong> the control<br />
system, the robot’s mechatronics and the environment.<br />
by postural reflexes are estimations <strong>of</strong> the upper body orientation, the rough position or<br />
velocity <strong>of</strong> the center <strong>of</strong> mass, or load distribution in the feet. While this information<br />
partly requires some kind <strong>of</strong> reduced model <strong>of</strong> the system dynamics, it can be kept simple<br />
enough to avoid the break <strong>of</strong> the control loop by intensive processing operations. This<br />
is possible because an approximation <strong>of</strong> a single or only a few variables <strong>of</strong> the dynamic<br />
system is sufficient. In collaboration with the local reflexes, the postural reflexes enhance<br />
the global stability <strong>of</strong> the biped.<br />
4.3 Hierarchical Layout<br />
Having defined the basic types <strong>of</strong> control units, the questions remains on how to organize<br />
them as a control network. Section 3.1.4 stated that natural motion control has a<br />
hierarchical layout. As suggested by Ivanenko et al. in the hypothetical scheme shown<br />
in Figure 3.9, stimulation <strong>of</strong> control units runs downwards from higher to lower levels.<br />
Perceptional information feeds back from sensory neurons to various stages <strong>of</strong> the control<br />
network. Figure 4.2 illustrates how these ideas and other conceptions from the previous<br />
chapter are translated to a control concept for bipeds. It also shows how the control system<br />
is integrated with the robot’s mechatronics.<br />
The hierarchy <strong>of</strong> control units is laid out from left to right. From the highest level, i.e. the<br />
locomotion modes, stimulation and modulation signals run along the control units until<br />
motor patterns and local reflexes are reached on the lowest level. As the last-mentioned<br />
units only act locally, they can be pooled in so called joint groups. This corresponds to the
4.3. Hierarchical Layout 73<br />
Locomotion<br />
Mode 1<br />
Locomotion<br />
Mode n<br />
SPG 1<br />
SPG n<br />
1<br />
2<br />
modulation<br />
Motion<br />
Phase 1<br />
Motion<br />
Phase 2<br />
Motion<br />
m Phase m<br />
;<br />
Motion<br />
Phases<br />
Postural<br />
Reflex 1<br />
Postural<br />
Reflex 2<br />
Postural<br />
Reflex l<br />
Joint Group 1<br />
Local<br />
Reflexes<br />
Motor<br />
Patterns<br />
Local<br />
Reflexes<br />
Motor<br />
Patterns<br />
Joint Group q<br />
Figure 4.3: Flow <strong>of</strong> stimulation and modulation signals within the hierarchy <strong>of</strong> control units.<br />
areas <strong>of</strong> the spinal cord where sensor and motor neurons are spatially related depending<br />
on their dedicated region <strong>of</strong> the body (Section 3.1.2 and Figure 3.8). For the biped in<br />
this work, the joints and sensors <strong>of</strong> the upper trunk, the lower trunk, and each leg are<br />
subsumed in such a group. This distribution <strong>of</strong> control units enhances the clearness <strong>of</strong><br />
the control system and enables a possible assignment <strong>of</strong> units to dedicated, distributed<br />
processing hardware <strong>like</strong> small dsp boards [Hillenbrand 09].<br />
Similarly to the somatosensory system <strong>of</strong> the human body, information on torques and<br />
forces acting in joints and feet as well as joint positions are measured. This sensor data<br />
can be pre-processes in the corresponding joint group and forwarded to various levels <strong>of</strong><br />
control. As in human postural control, the sense <strong>of</strong> balance needs to be derived from sensor<br />
information at a higher level. Where nature uses the vestibular system, eyes, or the hairs<br />
on the skin as source <strong>of</strong> perception, a robotic system deploys an inertial measurement unit<br />
(imu), or vision-based sensors. The resulting information is fed to the postural reflexes.<br />
Compared to human locomotion control, the sense <strong>of</strong> balance and the locomotion modes<br />
would be situated within the brain, the rest <strong>of</strong> the control units within the spinal cord.<br />
Reflexes and motor patterns issue control commands for the robot’s joint controller. The<br />
interface consists <strong>of</strong> torque, stiffness, and equilibrium position values. Driven by the joint<br />
controllers, the actuation system applies forces and torques to the robot’s mechanics. In<br />
interaction with parallel elastic elements, external disturbances, and the environment, the<br />
bipeds motions emerge.<br />
In case several control units want to access the same actuator, a fusion <strong>of</strong> the control<br />
signals takes place. Depending on the type <strong>of</strong> the control data and the activity <strong>of</strong> the<br />
unit, one <strong>of</strong> two fusion methods is applied: torque signals are fused by a weighted sum<br />
function, similar to muscle stimulation adding up from different sources. All other control<br />
signals are fused using a weighted average function. More on this topic can be found in<br />
Section 5.1.3 discussing the behavior-based architecture.
74 4. A Biologically Supported Concept for <strong>Control</strong>ling Bipeds<br />
For further clarification <strong>of</strong> the hierarchical structure <strong>of</strong> the control system and <strong>of</strong> the flow<br />
<strong>of</strong> stimulation, Figure 4.3 again shows the layout <strong>of</strong> the control units, this time omitting<br />
the mechatronic part <strong>of</strong> the robot and the environment. Each locomotion mode stimulates<br />
a spinal pattern generator which again stimulates one motion phase at a time, or possibly<br />
one phase per body side. A motion phase activates postural reflexes as well as motor<br />
patterns and local reflexes within the joint groups. Reflexes and motor patterns can be<br />
recruited by more than one phase, and even be shared between locomotion modes. This<br />
matches the fact mentioned in Section 3.1.4 that the control processes <strong>of</strong> human walking<br />
and running seem to share the same control components.<br />
Figure 4.3 also illustrates how one phase <strong>of</strong> a locomotion mode is stimulated at one point<br />
in time. The control units <strong>of</strong> lighter shade indicate inactivity, those <strong>of</strong> darker shade<br />
indicate activation. Exemplary, the dashed line explains the information flow when a<br />
locomotion mode modulates the behavior <strong>of</strong> a motor pattern, e.g. based on the desired<br />
walking velocity. It must be mentioned that while only one phase <strong>of</strong> a locomotion mode<br />
can be stimulated at once for each side <strong>of</strong> the body, more than one locomotion mode can<br />
be activated simultaneously. For instance, during walking initiation, the standing mode<br />
can still continue to work.<br />
As a further remark it can be said that the suggested control concept could also work<br />
for motions other than locomotion. It is conceivable that a spinal pattern generator does<br />
not only create cyclic limb movement, but also voluntary and purposeful motion. For<br />
instance, a grasping process could be subdivided in different phases, each consisting <strong>of</strong><br />
motor patterns and reflexes <strong>like</strong> collision avoidance. Modulation from higher levels could<br />
coordinate the movement to reach in the direction <strong>of</strong> the desired goal. However, future<br />
work is needed to show the implementation <strong>of</strong> such a different task within this control<br />
methodology. The next chapter will describe how stable standing and dynamic walking <strong>of</strong><br />
a two-legged robot can be designed using this approach.
5. <strong>Control</strong>ling Dynamic Locomotion<br />
<strong>of</strong> a Fully Articulated Biped<br />
The preceding chapter presented the structural organization <strong>of</strong> the control concept. Six<br />
classes <strong>of</strong> control units were defined and a hierarchical network structure introduced.<br />
However, to apply this concept to the task <strong>of</strong> controlling the locomotion <strong>of</strong> a robot,<br />
appropriate control units must be found and be integrated within the suggested structure,<br />
thereby creating the desired system behavior. This chapter will demonstrate the design<br />
process for a dynamically walking biped. Methods for finding suitable functional control<br />
units will be discussed, and the resulting network for standing and walking will be<br />
introduced. But first prerequisites and assumptions for the underlying system will be<br />
addressed. These concern the kinematic layout and the actuation system <strong>of</strong> the assumed<br />
robot as well as the behavior-based architecture serving as framework for the control<br />
system.<br />
5.1 System Premises<br />
To achieve human-<strong>like</strong> walking with a bipedal robot, not only the control system but<br />
also the morphology and actuation system must resemble the human body to a sufficient<br />
degree. Nowadays it is impossible to construct a robot featuring the multitude <strong>of</strong> degrees<br />
<strong>of</strong> freedom found in the human body, or an actuation system similar in capabilities to the<br />
sophisticated muscle-tendon system. Likewise, the human perceptual abilities outdo any<br />
available technical sensors. Thus, this work has to agree on a practicable trade-<strong>of</strong>f. The<br />
following paragraphs will outline the characteristics <strong>of</strong> the robotic system upon which the<br />
control system will be established.<br />
5.1.1 Kinematic Layout<br />
As just mentioned, it is not possible to mimic all kinematic degrees <strong>of</strong> freedom the human<br />
body possesses. Instead, a subset <strong>of</strong> joints must be found that is simple enough to be<br />
implemented in a robotic system, but still extensive enough to allow for flexible locomotion.<br />
With dynamic walking being the target mode <strong>of</strong> locomotion, most degrees <strong>of</strong> freedom
76 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
z<br />
x y<br />
(a) (b) (c) (d)<br />
Figure 5.1: Kinematic layout <strong>of</strong> the assumed bipedal robot’s knee and ankle (a), hip (b),<br />
spine (c), and shoulder and elbow (d). Dashed lines denote the rotation axes.<br />
should be contained within the legs and hips. During normal walking, no extensive or<br />
elaborated movement can be observed within the spine, the neck, or the arms, consequently<br />
those parts <strong>of</strong> the robot can be simplified, though not completely ignored.<br />
Section 3.2.1 discussed the human gait with its dominant kinematic characteristics. Originating<br />
from this analysis, necessary joints for the leg design can be found. Figure 5.1a<br />
illustrates the resulting leg kinematics. To make stabilization in the frontal and lateral<br />
direction possible and to allow adaptation to uneven ground, the feet need at least two<br />
rotational degrees <strong>of</strong> freedom along both horizontal axes. The rotation about the vertical<br />
axis is neglected as it is also present in the hip joint where the main rotation about this<br />
axis takes place. The same holds true for the knee joint. During push-<strong>of</strong>f, the foot as well<br />
as the toes bend upwards. This rolling motion can be achieved by an additional joint or a<br />
curved foot shape. The latter solution is chosen for this work. As the knee joint mainly<br />
bends in the frontal plane and shows no other significant motions, only this degree <strong>of</strong><br />
freedom is included.<br />
The hip joint is implemented with all three rotational degrees <strong>of</strong> freedom (Figure 5.1b). All<br />
<strong>of</strong> these are essential for leg swing, lateral postural corrections, and curve walking. Even<br />
though the pelvis rotation during human walking shows only low amplitude, rotational<br />
joints around all three axes are included in the spine (Figure 5.1c). This allows to<br />
compensate the small pelvis motions as well as potentially larger pelvis shifts while e.g.<br />
walking on sloped ground. Furthermore, adjustments <strong>of</strong> the center <strong>of</strong> mass executed by<br />
postural reflexes are possible.<br />
Figure 5.1d illustrates the design <strong>of</strong> the upper trunk. In the scope <strong>of</strong> this work, additional<br />
degrees <strong>of</strong> freedom in the neck are omitted, but could become necessary for head stabilization<br />
should a vision system be included. The shoulder joint enables the arms to swing<br />
forth and back as well as to lift them in lateral direction for posture correction. An elbow<br />
joint is included for a more natural arm swing.<br />
Altogether, this kinematic setup results in a fully articulated biped with 21 degrees <strong>of</strong><br />
freedom to control. While this number requires the control system to cope with a system<br />
<strong>of</strong> considerable complexity, the above analysis suggests that this setup is necessary to<br />
achieve human-<strong>like</strong> three-dimensional walking.
5.1. System Premises 77<br />
5.1.2 Assumed Actuation and Sensor System<br />
Similar to the kinematics, the actuation system must possess certain properties to make a<br />
human-<strong>like</strong> motion control possible. Some properties <strong>of</strong> the muscle-tendon system have<br />
been discussed in Section 3.2.1. Hill’s mechanical muscle model (Figure 3.14b) features<br />
serial and parallel elastics elements, dampers, and a contracting unit for each muscle. A<br />
human joint is actuated by at least two <strong>of</strong> those muscles in an antagonistic setup. This<br />
results in a possible torque control and a position control with a large range <strong>of</strong> stiffness.<br />
Unfortunately, no technical actuator is available that comes even close to its natural<br />
counterpart. Pneumatic muscles at least partly resemble the biological muscle, but are<br />
difficult to model and to control, and the necessity to provide compressed air complicates<br />
the development <strong>of</strong> a self-sustaining system. Electronic actuation in combination with<br />
elastic elements could provide a partial solution. In the scope <strong>of</strong> the research efforts<br />
presented here, some considerations have been put on this topic [Luksch 05, Luksch 07,<br />
Wahl 09, Blank 09b]. Chapter 6 will present a short overview, but otherwise these studies<br />
will not be discussed in depth within this text.<br />
For this work, a direct joint actuation is assumed, neglecting the antagonistic setup.<br />
This has the advantage <strong>of</strong> reducing complexity in design and control. A drawback could<br />
arise as no biarticular structures can be implemented mechanically. In future work, an<br />
antagonistic joint actuation system similar to the human one could be investigated as a<br />
possible extension.<br />
Still, the actuation system applied here features some properties <strong>of</strong> the natural example.<br />
Otherwise, the suggested control concept could not demonstrate all <strong>of</strong> its potential benefits.<br />
It is assumed that each joint can swing freely with low friction if no control commands<br />
are given. A direct torque demand is possible. Beside this, position control with variable<br />
compliance simulates the series elastic elements <strong>of</strong> the muscle. A fusion <strong>of</strong> both control<br />
methods is also provided for. Similar to the muscle-tendon system, a parallel elastic<br />
element with a fixed spring constant and equilibrium point concludes the joint actuation<br />
characteristics. The following chapter will describe how these properties were implemented<br />
in the simulated robotic system.<br />
Furthermore, some requirements have to be met regarding the sensor configuration to<br />
enable the transfer <strong>of</strong> certain biological control strategies to technical systems. As it is the<br />
case in the human muscle, each joint outputs the current angular position and the acting<br />
torque. Cutaneous and load receptor information is required by certain reflexes in human<br />
motion control. Consequently, it is assumed that force sensors in each <strong>of</strong> the robot’s feet<br />
provide data on ground contact and load distribution. Finally, postural reflexes depend<br />
on an estimation <strong>of</strong> the upper trunk’s pose and movements. For this purpose, an inertial<br />
measurement unit (imu) or equivalent sensors have to be installed.<br />
5.1.3 The Behavior-based <strong>Control</strong> Architecture iB2C<br />
Besides the morphology and the sensor-actor system, an appropriate control framework is<br />
a further requirement for implementing a human-<strong>like</strong> locomotion control system. Over the<br />
last 20 years, behavior-based architectures have been established as a preferred control<br />
approach for robotic systems acting in situations and environments that are not known a<br />
priori. Compared to other robot control architectures, they can be classified as a hybrid
78 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
s<br />
�ı<br />
�e<br />
F (�e,s,�ı )<br />
(a)<br />
�u<br />
�a<br />
r<br />
s<br />
�ı<br />
�e<br />
F (�e,s,�ı )<br />
Figure 5.2: The basic behavior module (a) and the fusion behavior module (b) <strong>of</strong> the iB2C<br />
architecture.<br />
system, being located between purely reactive and highly deliberative systems. But in<br />
contrast to normal hybrid systems, behavior-based control shows no conceptual break<br />
between a reactive and deliberative layer. Rather, it is characterized by a homogeneous<br />
layout.<br />
The subsumption architecture by R. Brooks is commonly seen as being the first behaviorbased<br />
strategy [Brooks 86]. Here, mainly reactive control units are arranged in a hierarchical<br />
layout, and suppression signals serve as arbitration method. The subsumption<br />
architecture also shows the feasibility <strong>of</strong> controlling biologically inspired walking machines<br />
by behavior-based architectures in its application to the six-legged robots Genghis<br />
and Attila [Brooks 89, Ferrell 95]. Further biologically motivated robots controlled in a<br />
behavior-based manner include the lobster-<strong>like</strong> machine by Ayers or the quadruped WARP1<br />
by Pettersson et al. [Ayers 00, Pettersson 98]. Arkin provides an extensive overview on<br />
the topic <strong>of</strong> behavior-based architectures, Pirjanian discusses possible coordination mechanisms<br />
[Arkin 98, Pirjanian 99]. Behavior-based control has also been successfully applied<br />
to wheel-driven robots [Arkin 00, Matarić 97]. So far, the control <strong>of</strong> dynamic locomotion<br />
<strong>of</strong> bipedal robots has not been in the focus <strong>of</strong> behavior-based control research.<br />
Considering the key aspects <strong>of</strong> biological locomotion control identified in Chapter 3 and<br />
the understanding <strong>of</strong> the role <strong>of</strong> control units, utilizing a behavior-based architecture<br />
as framework for the suggested control concept seems promising. The behavior-based<br />
control architecture iB2C (integrated Behavior-Based <strong>Control</strong>) is well suited for implementing<br />
the aspired hierarchical layout, the control unit classes, or the stimulation and<br />
inhibition mechanism. It is based on architectural ideas developed for the control <strong>of</strong><br />
multipedal walking machines [Luksch 02, Albiez 03a, Albiez 03b, Albiez 03c, Albiez 07].<br />
Since then the specification <strong>of</strong> its behavioral components has been further refined and<br />
formalized [Proetzsch 07, Proetzsch 10]. The architecture is also applied to the control <strong>of</strong><br />
complex wheeled robots for indoor and <strong>of</strong>f-road applications [Proetzsch 04, Kleinlützum 05,<br />
Proetzsch 05, Schäfer 05, Schmidt 06]. The following paragraphs will give a short introduction<br />
on the ideas <strong>of</strong> the iB2C and will describe how the features required by the control<br />
concept can be implemented.<br />
5.1.3.1 The Basic iB2C Behavior Module<br />
Each individual behavior <strong>of</strong> iB2C is contained in a module as shown in Figure 5.2a. That<br />
way, all behaviors feature the same, common interface. An iB2C behavior B can be<br />
formulated as a three-tuple<br />
(b)<br />
�u<br />
�a<br />
r
5.1. System Premises 79<br />
B = (fa,fr,F) (5.1)<br />
where fa denotes the activity function, fr the target rating function, and F the transfer<br />
function. These functions calculate the activity information �a, a target rating r, and an<br />
output vector �u. The behavior interface is completed by the input vector�e, the stimulation<br />
s, and the inhibition vector�ı.<br />
The stimulation s ∈ [0,1] is used by higher levels <strong>of</strong> the control system to adjust the<br />
influence <strong>of</strong> the behavior. It is complemented by the inhibition i ∈ [0,1] enabling other<br />
control units to actively suppress the behavior. The combined inhibition i <strong>of</strong> a behavior is<br />
calculated based on the inhibition vector as<br />
i = max<br />
j=0,...,k−1 (ij). (5.2)<br />
The stimulation and inhibition determine the activation ι = s·(1−i) <strong>of</strong> the behavior. An<br />
activation <strong>of</strong> ι = 0 corresponds to a fully inactive behavior, ι = 1 to maximum possible<br />
activity and output values. The signals s and�ı correspond to the stimulating and inhibiting<br />
signals <strong>of</strong> control units in neural control. Thus, the requirement stated in Section 4.2 <strong>of</strong><br />
allowing the influence on the activation <strong>of</strong> control units within the network is met.<br />
In addition to these influencing input values, two more behavior signals complete the<br />
module interface. The activity a ∈ [0,1] denotes the influence the behavior wants to exert<br />
on the network in the current state. An activity <strong>of</strong> a = 0 represents an inactive unit,<br />
whereas a = 1 denotes that the behavior intends to have maximum impact with its output<br />
values. It is calculated by the activity function<br />
fa :R m ×[0,1] → [0,1]×[0,1] l , fa(�e,ι) =�a = (a,�a) T<br />
(5.3)<br />
which can also generate an optional vector �a <strong>of</strong> derived activities a i ≤ a used for reduced<br />
stimulation <strong>of</strong> other behaviors. High activity can be interpreted as the firing <strong>of</strong> a neuron,<br />
thus again bridging to natural control concepts. As the activity <strong>of</strong> one behavior, or a<br />
value derived from it, normally serves as stimulation for a lower behavior in the control<br />
hierarchy, a ≤ ι must hold true. As a result, the total activity does not increase as it flows<br />
through the control network.<br />
Thetargetratingr ∈ [0,1]calculatedbythetargetratingfunctionfr statesthecontentment<br />
<strong>of</strong> the behavior with the current situation. A rating <strong>of</strong> r = 0 indicates that the behavior<br />
is satisfied with the state, r = 1 represents maximum discontentment. The target rating<br />
function only refers to the restricted view on the current situation as perceived by the<br />
input vector �e. As with the activity signal, the target rating can prove to be useful during<br />
network debugging, or it can serve as input signal for other control units.<br />
Finally, the transfer function formulates the relation between the input data vector �e and<br />
the output data vector �u:<br />
F :R m ×[0,1] →R n , F (�e,ι) = �u. (5.4)<br />
It further depends on the current activation ι <strong>of</strong> the behavior. In most cases <strong>of</strong> this<br />
work, the activation scales the control values <strong>of</strong> the output vector. The transfer function<br />
implements the actual intelligence <strong>of</strong> the behavior based on its view on the current situation<br />
and a possible internal model. It codes whether the behavior represents a locomotion<br />
mode, a reflex, or one <strong>of</strong> the other possible classes <strong>of</strong> control units. Actual implementations<br />
<strong>of</strong> the behavior functions just described will be found in this and the following chapters.
80 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
B1<br />
5.1.3.2 Behavior Coordination<br />
B2<br />
Fusion<br />
Behavior<br />
Figure 5.3: Example for the fusion <strong>of</strong> three behaviors.<br />
In case several behaviors want to access the same control value, e.g. a motor torque or the<br />
stimulation <strong>of</strong> another behavior, their action must be coordinated. For this purpose, fusion<br />
modules are introduced (Figure 5.2b). Being behaviors themselves, they feature the same<br />
interface, but have a special form <strong>of</strong> input and output vectors as well as transfer function.<br />
A fusion behavior always collects identical outputs <strong>of</strong> competing behaviors and generates<br />
a similar output (Figure 5.3). The input vector �e <strong>of</strong> the fusion behavior is composed <strong>of</strong><br />
the activity ai, the target rating ri, and the output vector �ui for each fused behavior. The<br />
incoming activities are used for arbitration, the target ratings are used to calculate a<br />
meaningful target rating for the fusion behavior itself.<br />
For now, iB2C <strong>of</strong>fers three methods for behavior fusion: maximum fusion, weighted average,<br />
and weighted sum. A fusion module using maximum fusion mirrors the outputs <strong>of</strong> the<br />
behavior with the highest activity as its own. In the case <strong>of</strong> weighted average, the activity,<br />
the target rating, as well as the output values are weighted by the activity <strong>of</strong> the p<br />
competing behaviors:<br />
a =<br />
p−1 �<br />
a<br />
j=0<br />
2 j<br />
p−1 �<br />
ak<br />
k=0<br />
·ι r =<br />
p−1 �<br />
aj ·rj<br />
j=0<br />
p−1 �<br />
ak<br />
k=0<br />
�u =<br />
B3<br />
p−1 �<br />
aj ·�uj<br />
j=0<br />
p−1 �<br />
ak<br />
k=0<br />
(5.5)<br />
In this way, the behavior with the highest activity has the strongest impact on the control<br />
network. The weighted sum fusion method weights the activities and the control outputs<br />
by the activity relative to the maximum activity amax <strong>of</strong> all connected behaviors:<br />
a = min<br />
� p−1<br />
�<br />
a 2 j<br />
amax<br />
j=0<br />
,1<br />
�<br />
·ι r =<br />
p−1 �<br />
aj ·rj<br />
j=0<br />
p−1 �<br />
ak<br />
k=0<br />
�u =<br />
p−1 �<br />
j=0<br />
aj ·�uj<br />
amax<br />
(5.6)<br />
This last fusion method acts similar to motor neurons collecting the incoming activity<br />
<strong>of</strong> connected neurons. Consequently, this fusion method is used when coordinating joint<br />
torque commands as will be described in Chapter 6. For most other control outputs, e.g.<br />
joint stiffness or joint position, weighted average fusion is applied. In relying on a uniform<br />
and established coordination concept for competing control units, the design <strong>of</strong> control<br />
networks is simplified as no additional effort must be invested in arbitration mechanisms.
5.2. Guidelines for Designing <strong>Control</strong> Units 81<br />
5.2 Guidelines for Designing <strong>Control</strong> Units<br />
After selecting a target locomotion mode, functional control units have to be selected<br />
and designed that will achieve the desired motions. The discussion on human walking<br />
in Section 3.2 can serve as source for this process. Gait analysis and neuroscientific<br />
research provide suitable information on selecting feed-forward and feedback control units.<br />
Examining the human gait also helps to find appropriate compliance settings for passive<br />
joints during different phases <strong>of</strong> locomotion. The following section will present some<br />
guidelines on how to design control networks.<br />
5.2.1 Feed-Forward <strong>Control</strong> Units<br />
As mentioned earlier, motor patterns provide the means for feed-forward control. They<br />
allow to shape the passive dynamics according to the target gait, or to initiate limb and<br />
body motions. Fast and promising results in designing these patterns can be achieved<br />
when starting from biomechanical gait analysis. emg data on the muscle activities and<br />
kinetic calculations during the individual phases allow to draw conclusion on the necessity<br />
<strong>of</strong> torque input.<br />
In most cases it is possible to find a semantic interpretation <strong>of</strong> the muscle activity. For<br />
instance, right before the leg swing can be observed, the muscles bending the hip joint are<br />
stimulated. The reason for this can be found in the necessary acceleration <strong>of</strong> the tibia, also<br />
resulting in the passive bending <strong>of</strong> the knee, and thus in ground clearance <strong>of</strong> the swing<br />
foot. Similar patterns can be found in the hip joints during walking initiation, or in the<br />
ankle joint during the push-<strong>of</strong>f phase.<br />
In any case it is necessary to find a suitable function to create torque patterns in a technical<br />
system. It should avoid sudden torque changes creating stress on the mechanics. Also, it<br />
should be possible to define the function with only a few parameters, and still be flexible<br />
enough to allow for a variety <strong>of</strong> torque trajectories. Equation 5.7 presents the sigmoid<br />
function that is suggested as basis for motor patterns:<br />
⎧<br />
1 1 t 1 ⎪⎨ + sin( π( − ) ) 0 ≤ t < T1<br />
2 2 T1 2<br />
ˆτ = A· 1 T1 ≤ t < T2<br />
⎪⎩ 1 1 t−T2 1 − sin( π( − 2 2 T3−T2 2 ) ) T2<br />
(5.7)<br />
≤ t ≤ T3<br />
Using the three parameters T1, T2, and T3 it is possible to define the length <strong>of</strong> the sine-<strong>like</strong><br />
rise <strong>of</strong> the function, the duration <strong>of</strong> the plateau at maximum torque output, and the<br />
time until the sine-<strong>like</strong> fall <strong>of</strong> the function reaches zero. The output value ˆτ ∈ [−1,1] is<br />
normalized to the maximum torque <strong>of</strong> the joint in question, i.e. the effective torque τ<br />
arises to τ = ˆτ ·τmax. Figure 5.4 depicts the sigmoid function and its parameters, and also<br />
gives some examples illustrating how sign and amplitude can be varied by the factor A.<br />
For technical system that do not resemble a biological example, no biomechanical data<br />
is available to be consulted for finding motor patterns. One possibility to obtain similar<br />
data can be optimization techniques. Optimal control theory can generate torque control<br />
patterns for target movements based on a simplified model <strong>of</strong> the robot and its environment.<br />
These torque trajectories can then again be used as foundation for designing motor patterns.<br />
This method has also be investigated by the author and others for a robot <strong>of</strong> reduced<br />
complexity [Luksch 07].
82 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
1.0<br />
-1.0<br />
ˆτ<br />
T1 T2 T3<br />
t<br />
ˆτ<br />
Figure 5.4: Motor patterns generate torque commands as sigmoid function. Three parameters<br />
define the end <strong>of</strong> the rise (T1), the start <strong>of</strong> the fall (T2), and the end <strong>of</strong> the fall (T3). As shown<br />
in the second example, a factor can scale the output.<br />
5.2.2 Feedback <strong>Control</strong> Units<br />
Feedback is introduced by three types <strong>of</strong> control units: spinal pattern generators, local<br />
reflexes, and postural reflexes. One spinal pattern generator exists for each mode <strong>of</strong><br />
locomotion. For designing its phases, findings from the decomposition <strong>of</strong> emg data as<br />
described in Sections 3.1.4 and 3.2.2 can be called on. Each component identified in the<br />
emg analysis can be translated to one locomotion phase. The kinematic or kinetic events<br />
associated with the components provide the conditions for phase transitions.<br />
Local reflexes can partly be adopted from those found during human locomotion (Section<br />
3.1.3). Whether this transition is feasible mainly depends on the availability <strong>of</strong><br />
corresponding sensory information and actuators. Possibly the reflex action has to be<br />
adopted to the robots capabilities. For instance, cutaneous reflexes normally rely on<br />
sensitive skin. If no artificial skin is available, these reflexes could be triggered by isolated<br />
force measurements or data from load cells. Other local reflexes can be deduced by<br />
matching kinematic events with distinctive muscle activities. One example can be found<br />
in the passive knee movement during the swing phase. As soon as the knee is stretched<br />
again before touching down with the swing leg, muscle activity stabilizing the knee can be<br />
observed.<br />
For designing postural reflexes, several ways are conceivable. Some possible reflexive<br />
actions concerning posture stabilization, e.g. the labyrinthine righting reflex, are suggested<br />
in neuroscientific literature (Section 3.2.4). Again, it might prove difficult to adapt these<br />
reflexes due to missing sensor data. Another way to find postural reflexes is based on<br />
simplifying biomechanical models. As discussed in Chapter 3, H<strong>of</strong>, Seyfarth, or Bauby<br />
among others have tried to derive simplified mechanical models explaining correcting<br />
movements or muscle activity observed during human locomotion. These models can be<br />
<strong>of</strong> low complexity and thus be predestined as possible postural reflex. Finally, empirical<br />
validation <strong>of</strong> the robot’s behavior during experiments can point out existing flaws in<br />
posture control, leading to additional reflexes. This strategy, by the way, can be applied<br />
for all other classes <strong>of</strong> control units, too. The common problem in designing postural<br />
reflexes is the requirement for information on the body pose or the behavior <strong>of</strong> the center<br />
<strong>of</strong> mass. The simplified biomechanical models just mentioned can provide a possibility to<br />
derive the necessary data.<br />
t<br />
ˆτ<br />
t<br />
ˆτ<br />
t
5.3. Stable Standing 83<br />
5.2.3 Guidelines for Implementing iB2C Features<br />
The preceding paragraphs focused on the functionality <strong>of</strong> control units. In terms <strong>of</strong> iB2C,<br />
this corresponds to the transfer function F, describing the calculation <strong>of</strong> control signals<br />
based on the behavior activation and the received sensor information. But while iB2C<br />
<strong>of</strong>fers powerful mechanisms and tools, it requires the designer to take care <strong>of</strong> additional<br />
behavior signals, mainly the stimulation, inhibition, and activity. General guidelines and<br />
principles facilitating the development <strong>of</strong> iB2C control systems are discussed by Proetzsch<br />
et al. [Proetzsch 10]. Some rules being <strong>of</strong> importance during the design process following<br />
the control concept suggested here are given in the following.<br />
Stimulation and inhibition <strong>of</strong> one behavior by another should be based on the activity <strong>of</strong><br />
the controlling behavior. In most cases it is sufficient to distinguish between no stimulation<br />
(s = 0) and full stimulation (s = 1). A locomotion mode is fully stimulated by the operator<br />
and shows full activity. Its activity a = 1 will then stimulate a spinal pattern generator,<br />
which again will stimulate motion phases only by a value <strong>of</strong> zero or one. A stimulated<br />
motion phase should show an activity <strong>of</strong> a = 1, and will normally use this activity to<br />
stimulate reflexes and motor patterns. In a few cases it might prove necessary to use<br />
a reduced activity value for stimulation, e.g. when a reflex should only show half <strong>of</strong> its<br />
normal activity during a certain motion phase.<br />
While most higher level behaviors can and should be reduced to activity <strong>of</strong> only one or<br />
zero, reflexes and motor patterns need more sophisticated implementations <strong>of</strong> their activity<br />
function. Motor patterns feature an activity matching their torque output. Reflexes<br />
should increase to full activity as soon as the situation assessment based on their restricted<br />
sensor information indicates a risk <strong>of</strong> loosing stability. Section 6.2.2 <strong>of</strong> the following<br />
chapter will describe how the activity functions <strong>of</strong> the behaviors developed in this work<br />
are implemented.<br />
With control unit classes defined and guidelines for selecting and designing functional units<br />
suggested, control networks for bipedal locomotion can now be developed. The control<br />
units will be arranged following the hierarchical layout described in the previous chapter.<br />
In the remainder <strong>of</strong> this chapter, networks for stable standing and dynamic walking are<br />
presented.<br />
5.3 Stable Standing<br />
Although this work focuses on dynamic walking, stable standing is considered, too. This<br />
allows to observe the transition from standing to walking, and validates the control concept<br />
for a second task <strong>of</strong> different nature. A short review <strong>of</strong> human standing control will<br />
motivate the control network introduced in this section. Additional information on this<br />
part regarded from a slightly different perspective and including further details on the<br />
implementation can be found in [Steiner 08].<br />
5.3.1 Balanced Standing <strong>Control</strong> in <strong>Human</strong>s<br />
<strong>Human</strong>s show a remarkable ability to stand securely on highly unstructured ground and<br />
under considerable disturbances. Generally, postural control is considered to be a complex<br />
skill rather then the result <strong>of</strong> only local reflex action [Horak 06]. Two tasks can be
84 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
Figure 5.5: The ankle and hip strategies for postural balance generate different joint movements<br />
and muscle activities during a movement <strong>of</strong> the support surface. From [Ting 07], p305.<br />
distinguished: postural orientation and postural equilibrium. Postural orientation involves<br />
active adaptation <strong>of</strong> the body segment’s pose considering gravity, structure <strong>of</strong> the support<br />
surface, or additionally body load. Head, trunk, and extremities are aligned in a way that<br />
a relaxed, stable posture emerges. Information <strong>of</strong> the body’s whole sensory apparatus is<br />
necessary to achieve this goal.<br />
Postural equilibrium however implies the reaction to self-induced or external disturbances.<br />
Three basic strategies to achieve this goal can be discerned: the ankle, the hip, and the step<br />
strategy. Which strategy is chosen does not only depend on the kind and magnitude <strong>of</strong> the<br />
disturbance. Personal experience, goals, and current expectations can result in different<br />
responses for each individual. Furthermore, the contribution <strong>of</strong> the human sensory systems<br />
varies from subject to subject [Horak 90]. Most notably this is the case in disabled patients,<br />
e.g. suffering from vestibular loss. One estimation for the distribution <strong>of</strong> the different<br />
senses for balancing in healthy subjects states a partial contribution <strong>of</strong> approximately<br />
70% for the somatosensory system, 20% for the vestibular system, and 10% for the visual<br />
system [Horak 06].<br />
The most basic response strategy being observed at small to medium disturbances is the<br />
ankle strategy. It lends its name from the fact that a correcting movement is issued by the<br />
ankle joint while the rest <strong>of</strong> the body is kept stiff. This <strong>of</strong> course implies muscle action<br />
all along one side <strong>of</strong> the body. Figure 5.5 illustrates the reaction to a backward shift <strong>of</strong><br />
the supporting platform a subject is standing on. Muscles in the back and hip keep the<br />
body rigid while the gastrocnemius and soleus muscles prevent the subject from falling<br />
to the front and create a plantarflexion <strong>of</strong> the ankle for stabilization [Ting 07]. Winter<br />
et al. suggest a simple control scheme for quiet standing where the ankle muscles act as<br />
springs [Winter 98, Winter 01]. This results in a stiffness control for balancing that can<br />
react mechanically and as such almost instantly without a delay caused by the nervous<br />
system. It also explains the body sway that can usually be observed during quiet standing.<br />
The ankle strategy is mechanically constrained by the support area <strong>of</strong> the foot. If the<br />
center <strong>of</strong> preassure moves outside this support area, the ankle strategy alone can no longer<br />
regain balance [Horak 90].<br />
In this case, the hip strategy is able to exert greater influence. In contrast to the ankle<br />
strategy, itgeneratesashift<strong>of</strong>thecenter<strong>of</strong>massintheoppositedirection<strong>of</strong>thedisturbance.<br />
This is accomplished by a coordinated movement <strong>of</strong> the ankle, knee, hip, and spinal column.
5.3. Stable Standing 85<br />
<strong>Walking</strong><br />
Stable<br />
Standing<br />
Standing<br />
States<br />
1<br />
2<br />
3<br />
4<br />
Ground<br />
Adapt.<br />
Stabilization<br />
Optimization<br />
Relaxed<br />
Posture<br />
Figure 5.6: <strong>Control</strong> network for stable standing.<br />
As shown in Figure 5.5, the upper body moves in the direction <strong>of</strong> the disturbance, the<br />
pelvis in the opposite direction. The arm support the posture correction by moving in the<br />
same direction as the trunk. Finally, the step strategy consists <strong>of</strong> an evasive step taken in<br />
the direction <strong>of</strong> the disturbing force. This response has the largest effect on the center <strong>of</strong><br />
mass and can compensate the strongest disturbances.<br />
For the standing control <strong>of</strong> a bipedal robot it is preferable to implement both the postural<br />
orientation and the postural equilibrium task. The first allows to operate not only on<br />
flat surface but also on unstructured ground and with different mass distributions <strong>of</strong> the<br />
robot. At least the ankle strategy should be included for basic functionality <strong>of</strong> the postural<br />
equilibrium task. An extended stiffness control as postulated by Winter et al. seems to<br />
<strong>of</strong>fer the necessary abilities.<br />
5.3.2 Stabilized Standing <strong>Control</strong><br />
The control network for balanced standing suggested in this work does include the postural<br />
orientation and equilibrium task as well as the ankle strategy. Furthermore the assumption<br />
<strong>of</strong> a level ground is discarded in favor <strong>of</strong> an approach for flexible ground adaptation.<br />
Figure 5.6 illustrates the upper layers <strong>of</strong> the resulting control network. As introduced<br />
in the previous chapter, a finite state machine coordinates the different phases occurring<br />
during standing. It stimulates one <strong>of</strong> four phase units depending on the current state <strong>of</strong> the<br />
robot. The Ground Adaptation phase is responsible for setting a sensible posture before<br />
the feet touch the ground and for achieving an appropriate initial posture considering the<br />
terrain geometry as the robot settles on the support surface. As its name suggests, the<br />
Stabilization phase balances the system against disturbances to gain a stable posture. This<br />
phase corresponds to the postural equilibrium task and includes a basic ankle strategy.<br />
The postural orientation task is handled during the Optimization phase. It changes the<br />
target angles to reduce the necessary torques within the joints. In case such a low energy<br />
posture can be found, the joint stiffness is reduced in the Relaxed Posture phase.<br />
5.3.3 Stable Standing State Machine<br />
The spg for stable standing is implemented as the finite state machine shown in Figure 5.7.<br />
Depending on its current state, the corresponding phase is stimulated. The initial state<br />
responsible for ground adaptation is left as soon as full ground contact is achieved. This<br />
information is received from the leg joint groups that preprocess various contact sensor
86 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
Ground<br />
Adaptation<br />
Relaxed<br />
Posture<br />
full ground contact<br />
disturbances<br />
low joint torques<br />
disturbances<br />
Stabilization<br />
Optimization<br />
quite stance<br />
Figure 5.7: Transitions <strong>of</strong> finite state machine managing phases during stable standing.<br />
measurements to a combined ground contact signal per leg. Then the stabilization state is<br />
entered in which the adopted pose is steadied mainly by high joint stiffness.<br />
If a quiet stance can be achieved, the state transition to the optimization state takes place.<br />
This decision is based on measurements from the inertial measurement unit. It provides<br />
three-dimensional acceleration and angular velocity information for the trunk. Based on<br />
the pose estimation the gravitational components <strong>of</strong> the acceleration vector is eliminated.<br />
By integrating this data a rough approximation <strong>of</strong> the trunk’s velocity is calculated. Only<br />
if this velocity and the acceleration stay below a certain threshold, the state transition is<br />
performed.<br />
During the optimization phase several postural behavior modules adapt the robot’s stance<br />
to find a posture consuming only little energy. Following the iB2C specification, these<br />
behaviors calculate a target rating to evaluate the current situation regarding their goal.<br />
Only if all <strong>of</strong> these ratings are low, i.e. all postural reflexes are content, the spg proceeds<br />
to the next state. As now a balanced stance should be adopted, the joint stiffness can be<br />
reduced during the Relaxed Posture phase.<br />
In case disturbances are perceived by the inertial measurement unit or the ground contact<br />
sensors, the state machine switches back to the stabilization state. Similarly, should ground<br />
contact be lost, or the locomotion mode for standing be inhibited, the ground adaptation<br />
state is resumed. In Figure 5.7, the corresponding transition are omitted for clarity. The<br />
following paragraphs will describe the functioning <strong>of</strong> the introduced phases.<br />
5.3.4 Ground Adaptation<br />
The basic idea <strong>of</strong> ground adaptation lies in the compliance <strong>of</strong> the joints. By setting the<br />
joints to a low stiffness, they passively adjust their position to external forces. For instance,<br />
the ankle joint can rotate in a way that the foot settles on uneven ground. As soon as full<br />
ground contact is made, the current joint angles are applied as set point and the stiffness<br />
can be raised in the stabilization phase.<br />
The described functionality is assumed by the Hold Position reflex. An instance <strong>of</strong> this<br />
reflex is included for each joint and stimulated by the standing phase as illustrated in<br />
Figure 5.8. The reflex can be parametrized by an initial angle and three stiffness values:<br />
the initial stiffness stiff init is set at first stimulation and in case there is no ground contact.<br />
The minimal and maximal stiffness parameters stiff min and stiff max define an interval <strong>of</strong>
5.3. Stable Standing 87<br />
Standing<br />
States<br />
1<br />
2<br />
3<br />
4<br />
Ground<br />
Adapt.<br />
Stabilization<br />
Optimization<br />
Relaxed<br />
Posture<br />
Upper Trunk<br />
Hold<br />
Hold<br />
Position<br />
Position<br />
Lower Trunk<br />
Hold<br />
Hold<br />
Position<br />
Position<br />
Left/Right Leg<br />
Hold<br />
Hold<br />
Position<br />
Position<br />
Figure 5.8: <strong>Control</strong> network during the Ground Adaptation phase <strong>of</strong> stable standing.<br />
compliance used during ground contact. A stiffness factor received as modulation input<br />
determines the value within this interval that is actually set as stiffness. Algorithm 5.1<br />
summarizes the behavior <strong>of</strong> the Hold Position reflex.<br />
Algorithm 5.1: Target angle α and stiffness stiff calculation <strong>of</strong> the Hold Position reflex<br />
1<br />
2<br />
3<br />
4<br />
5<br />
6<br />
7<br />
8<br />
9<br />
10<br />
11<br />
12<br />
13<br />
14<br />
15<br />
Initiation:<br />
α = αinit<br />
stiff = stiff init<br />
if a = 0 or no ground contact then<br />
α = αinit<br />
stiff = stiff init<br />
end<br />
else if initial ground contact then<br />
α = αcurrent<br />
stiff = stiff min<br />
end<br />
else if full ground contact then<br />
α = α+∆α<br />
stiff = stiff min +(stiff max −stiff min)·stiffness factor<br />
end<br />
At the start <strong>of</strong> the control system or following a reset command, the target values are set<br />
to the initial angle and stiffness. As soon as first ground contact is measured, the target<br />
angle α follows along the current joint angle αcurrent. When full ground contact is detected,<br />
the target joint angle is fixed, and the compliance is set depending on the stiffness factor.<br />
During the ground adaptation phase, this factor is set to zero resulting in the stiffness<br />
being set to the minimal stiffness parameter.<br />
Beside the stiffness factor, the Hold Position reflex receives a modulation signal ∆α for<br />
changing the set point <strong>of</strong> the joint angle. This angular velocity is integrated by the reflex
88 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
Standing<br />
States<br />
1<br />
2<br />
3<br />
4<br />
Ground<br />
Adapt.<br />
Stabilization<br />
Optimization<br />
Relaxed<br />
Posture<br />
Relax<br />
Joints<br />
Reduce<br />
Tension<br />
Upper Trunk<br />
Hold<br />
Hold<br />
Position<br />
Position<br />
Lower Trunk<br />
Hold<br />
Hold<br />
Position<br />
Position<br />
Left/Right Leg<br />
Hold<br />
Hold<br />
Position<br />
Position<br />
Figure 5.9: <strong>Control</strong> network during the Optimization phase <strong>of</strong> stable standing. The dashed<br />
arrows indicate modulation signals.<br />
and added to the current set point. In case the ground contact is lost or the reflex is no<br />
longer activated, the integral part is set to zero. Using the modulation signal, the posture<br />
optimization control units described below can influence the stance.<br />
5.3.5 Posture Stabilization<br />
The stabilization phase starts as soon as full ground contact is established or when a<br />
disturbance is measured in one <strong>of</strong> the other standing phases. Its control network is laid out<br />
the same way as the one during the Ground Adaptation phase. Only the stiffness factor is<br />
set to a high value to stabilize the stance. In doing so, the joints generate high torques in<br />
case the body is deflected from its target posture. With the trunk and extremities braced,<br />
the compensation will mainly origin from the ankle joints, thus implementing the ankle<br />
strategy. Similar reactions can be observed in humans being disturbed during a relaxed<br />
stance. Muscle activities throughout the body increase and the stiffened body is pushed<br />
against the disturbance by the ankle joint to regain a balanced pose. By only locally<br />
controlling the joints towards a determined target angle, no global feedback loop or model<br />
depending control is necessary and the delay times can be kept low. This strategy can<br />
only work if the target stance retains at least the center <strong>of</strong> mass above the support surface<br />
spanned by the feet. Otherwise, the robot will not be able to remain standing.<br />
5.3.6 Posture Optimization<br />
After the posture is stabilized and a sufficiently quiet stance is achieved, the target pose<br />
can be optimized. This phase corresponds to the postural orientation task. As shown in<br />
Figure 5.9, the Hold Position reflexes are still stimulated. Additionally, postural reflexes<br />
adapt the stance by shifting the joint set points according to the provided modulation<br />
signal. Two types <strong>of</strong> these adaptation reflexes can be distinguished: those trying to relax<br />
joints, i.e. to reduce the necessary torque, and those trying to release tension acting
5.3. Stable Standing 89<br />
<strong>Control</strong> Unit Manipulated Joints<br />
Relax Spine X x-axis <strong>of</strong> spine joint<br />
Relax Spine Y y-axis <strong>of</strong> spine joint<br />
Relax Hip Y y-axis <strong>of</strong> both hip joints<br />
Relax Knee both knee joints<br />
Balance Ankle Pitch y-axis <strong>of</strong> both ankle joints<br />
Reduce Tension Hip Y y-axis <strong>of</strong> both hip joints<br />
Reduce Tension Ankle Y y-axis <strong>of</strong> both ankle joints<br />
Table 5.1: Postural reflexes adapting the posture during the Optimization phase.<br />
because <strong>of</strong> opposing set points. Table 5.1 lists the implemented postural reflexes and notes<br />
the joint angles being adapted by each reflex.<br />
The relax joint control units receive the current joint angles and the corresponding torques<br />
as input. In case the joint limits are not exceeded, a change rate for the joints is forwarded<br />
to the Hold Position reflexes. The change rate is proportional to the torque, thus enabling<br />
a posture adaptation reducing the torques. To keep dynamic effects low during the<br />
adaptation, the change rate is relatively slow. Only the Balance Ankle Pitch follows a<br />
different optimization approach. Instead <strong>of</strong> reducing the joint torque, it tries to optimize<br />
the center <strong>of</strong> pressure acting in the foot. This information is derived from four force sensors<br />
located within the outer parts <strong>of</strong> the foot sole. Based on these measurements the center <strong>of</strong><br />
pressure can be estimated and shifted below the ankle joint by the reflex.<br />
While the relax joint reflexes move one or two joints in the same direction, the reduce<br />
tension control units adjust two paired joints in opposed direction. This strategy is useful<br />
if tension arises due to external forces and limitations by two-legged ground contact. For<br />
instance, concurrent dorsiflexion <strong>of</strong> the one foot and plantarflexion <strong>of</strong> the contralateral<br />
foot causes opposing torques that can be resolved by adjusting the ankle angles without<br />
altering the posture. The same holds true for flexion and extension <strong>of</strong> the hip joints. The<br />
control unit works by trying to minimize the torque discrepancy <strong>of</strong> the two joints being<br />
considered. The generated change rate is proportional to the difference <strong>of</strong> one joint’s<br />
torque and the average torque <strong>of</strong> both joints. Again, the velocity <strong>of</strong> adaptation is low<br />
to reduce dynamic effects. Both the relax joint and reduce tension control units can act<br />
simultaneously on the same joint as it is the case for the y-axes <strong>of</strong> the ankles and the hips.<br />
The change rates from the competeting reflexes are then combined by a fusion behavior<br />
using the weighted average method.<br />
5.3.7 Relaxed Stance<br />
Following the iB2C specification, the angle adjustment reflexes just described indicate<br />
their progress by the target rating signal. The maximum <strong>of</strong> all these ratings can serve as a<br />
reference on the balance <strong>of</strong> the current stance. If this value drops below a certain threshold,<br />
the Relaxed Posture phase <strong>of</strong> stable standing starts. Its control network again mimics the<br />
one <strong>of</strong> the Ground Adaptation or Stabilization phase, i.e. the Hold Position reflexes are<br />
stimulated. But as a balanced posture can be assumed, the stiffness factor can slowly<br />
be decreased to take up a relaxed stance with low energy consumption. If the posture is
90 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
(Running<br />
Initiation)<br />
(Running)<br />
Operator<br />
Standing <strong>Walking</strong><br />
(Cyclic<br />
Running)<br />
Cyclic<br />
<strong>Walking</strong><br />
<strong>Walking</strong><br />
Initiation<br />
Figure 5.10: Coordination <strong>of</strong> three locomotion modes standing, walking, and running.<br />
not as stable as expected, or it is disturbed by external forces, this will be indicated by<br />
raising target ratings <strong>of</strong> the angle adjustments reflexes or by increasing accelerations and<br />
velocities. In this case the stable standing spg changes back to the Stabilization phase to<br />
regain a balanced stance.<br />
5.4 Dynamic <strong>Walking</strong><br />
While stable standing presents a rather static balancing problem, walking is a highly<br />
dynamic motion. The rest <strong>of</strong> this chapter will present a control network for dynamic<br />
walking <strong>of</strong> a human-<strong>like</strong> bipedal robot. First, the transition <strong>of</strong> standing to walking will be<br />
described. In this context, a detailed example <strong>of</strong> how to derive a motor pattern from gait<br />
analysis data will be given. The succeeding main part will introduce the control <strong>of</strong> cyclic<br />
dynamic walking. Its spinal pattern generator determines the phases <strong>of</strong> walking and their<br />
transition conditions. Then the feed-forward and feedback control units <strong>of</strong> each motion<br />
phase will be presented, followed by a discussion <strong>of</strong> the postural reflexes.<br />
Throughout the following pages, the behavior <strong>of</strong> some control units is explained and<br />
illustrated by extracts <strong>of</strong> experimental data. This data is based on the results from the<br />
experiments within the simulation framework introduced in Chapter 6. Basically, the<br />
physical simulation <strong>of</strong> a complex, anthropomorphic bipedal robot following the system<br />
premises stated at the beginning <strong>of</strong> this chapter is used.<br />
5.4.1 Interrelation between Locomotion Modes<br />
Before going into the details <strong>of</strong> the dynamic walking control, the coordination <strong>of</strong> high-level<br />
locomotion modes should be described. Figure 5.10 shows three possible locomotion modes<br />
standing, walking, and running. The latter two are again divided into the cyclic motion<br />
itself, and an initiation or transition mode to switch from standing to walking, and from<br />
walking to running. Switching back to walking or standing is left out for clearer appearance.<br />
The user simply stimulates more and more locomotion modes depending on the desired<br />
form <strong>of</strong> motion. A target velocity and direction is also passed to the control units.
5.4. Dynamic <strong>Walking</strong> 91<br />
(a) (b)<br />
Figure 5.11: (a) Joint angles <strong>of</strong> the stance and swing leg, and (b) movement <strong>of</strong> the center <strong>of</strong> mass<br />
(dotted line) and the center <strong>of</strong> pressure (solid line) during initiation <strong>of</strong> walking. From [Elble 94],<br />
p142f.<br />
During the transition phases, both locomotion modes are activated. As soon as the<br />
transition is finished, the cyclic part <strong>of</strong> the next mode will inhibit the previous one. The<br />
next section will describe this process for the transition from standing to walking in more<br />
detail.<br />
5.4.2 <strong>Walking</strong> Initiation<br />
In many research works on bipedal dynamic walking, the initiation is not considered.<br />
Rather it is assumed that the robot is already moving within the cyclic part <strong>of</strong> the motion.<br />
Here, this assumption is not made. Taking a short look at the initiation <strong>of</strong> human walking,<br />
simple motor patterns are derived to achieve the transition from standing to walking.<br />
5.4.2.1 Gait Initiation in <strong>Human</strong> <strong>Walking</strong><br />
Elble et al. have found a strong stereotypy in the process <strong>of</strong> gait initiation [Elble 94].<br />
Essentially, the center <strong>of</strong> mass is shifted in lateral and anterior direction (Figure 5.11b).<br />
That way, weight is taken from the swing leg, and the body moves forward in preparation<br />
<strong>of</strong> the first step. The forward motion is mainly achieved by the activity <strong>of</strong> the tibialis<br />
anterior, resulting in a dorsiflexion <strong>of</strong> both ankles (Figure 5.11a). A slight flexion <strong>of</strong> the<br />
knee and hip <strong>of</strong> the stance leg can also be observed. This induces a small lateral movement<br />
<strong>of</strong> the trunk in direction <strong>of</strong> the stance leg.<br />
However, the main part <strong>of</strong> lateral weight transfer is initiated by the activity <strong>of</strong> the aband<br />
adductor muscles in the hip joints. This hip muscle function has been investigated<br />
by Kirker et al. during stepping as well as balancing [Kirker 00]. Figure 5.12 plots the<br />
activities <strong>of</strong> the muscle involved when starting to walk with the left leg. Action <strong>of</strong> the<br />
right adductor and the left abductor (gluteus medius) can be observed. This results in the<br />
shearing motion <strong>of</strong> the quadrangle formed by the feet and the two hip joints, which again
92 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
Figure 5.12: Hip muscles activities during gait initiation first stepping with the left leg. The<br />
area marked by the rectangle indicates the initial weight transfer resulting in a lateral torque<br />
and movement <strong>of</strong> the com. From [Kirker 00], p461.<br />
moves the trunk sideways in direction <strong>of</strong> the right stance leg. During this process, muscular<br />
activity in the trunk stabilizes the spine, thus reducing swaying and head movement.<br />
While the center <strong>of</strong> mass only moves anteriorly and in direction <strong>of</strong> the stance leg, the<br />
center <strong>of</strong> pressure follows a more complex trajectory (Figure 5.11b). This is mainly due<br />
to the lateral hip action just described. As the torque in the hip increases, the trunk is<br />
pushed to the side <strong>of</strong> the stance leg. The force that is necessary for this motion connects<br />
to the ground via the swing leg as it pushes downwards during the shearing movement.<br />
Only when the hip torque falls <strong>of</strong>, the weight shifts to the stance leg as the upper body<br />
mass has moved over this leg.<br />
Interestingly enough, in its first half this behavior is counterproductive to the goal <strong>of</strong><br />
transferring the weight onto the stance leg. Only during the second half <strong>of</strong> the initiation<br />
motion, the swing leg is relieved. Consequently, it is not possible to design a simple<br />
controller working on the foot load.<br />
As soon as the walking initiation has finished to shift the weight towards the stance leg,<br />
the activity <strong>of</strong> the swing leg’s adductor and the stance leg’s abductor decreases. In fact,<br />
the direction <strong>of</strong> the hip torque changes to stabilize the pelvis. This is necessary as the foot<br />
leaves the ground and the pelvis can no longer be supported by the swing leg. However,<br />
this behavior is already part <strong>of</strong> the normal cyclic walking phases described later in this<br />
chapter.
5.4. Dynamic <strong>Walking</strong> 93<br />
<strong>Walking</strong><br />
Stable<br />
Standing<br />
Cyclic<br />
<strong>Walking</strong><br />
<strong>Walking</strong><br />
Initiation<br />
<strong>Walking</strong><br />
SPG<br />
Standing<br />
States<br />
...<br />
...<br />
Initiation<br />
Phase L<br />
Initiation<br />
Phase R<br />
Lower Trunk Group<br />
Lateral<br />
Shift R<br />
Lateral<br />
Shift L<br />
Leg Groups<br />
Lean<br />
Forward<br />
Figure 5.13: <strong>Control</strong> network for walking initiation, first step with the left leg.<br />
5.4.2.2 Motor Patterns for <strong>Walking</strong> Initiation<br />
The muscle activity observed during human walking initiation can be translated to motor<br />
patterns. Following the principle <strong>of</strong> control unit distribution and spatially related action,<br />
the muscle activity is allocated to several motor pattern units. As mentioned before, the<br />
local units are distributed in four joint groups representing the upper trunk, the lower<br />
trunk, and each leg. The movement in anterior direction origins from the ankle, hence a<br />
motor pattern is added to each leg group and stimulated during walking initiation. As<br />
lateral weight shift results from muscle action in the hips and the spine, a motor pattern<br />
is added to the lower trunk group, also stimulated during walking initiation. Below, this<br />
control unit will be discussed in more detail.<br />
Figure 5.13 presents the resulting control network for the initiation <strong>of</strong> walking. During<br />
initiation, the standing mode is still active and is combined with the control commands<br />
from the initiation units. The walking locomotion mode signals the initiation mode with<br />
which leg to take the first step. This results in the stimulation <strong>of</strong> one <strong>of</strong> the two initiation<br />
phases. As the initiation process consists <strong>of</strong> only one phase per starting leg, no spg is<br />
necessary. The figure illustrates the activation during initiation with the first step done by<br />
the left leg. The Initiation Phase Left unit is stimulated by the <strong>Walking</strong> Initiation mode,<br />
and itself stimulates the motor patterns for leaning forward and for shifting the weight to<br />
the stance leg’s side (Lateral Shift Right). Similarly, walking initiation with the right leg<br />
as first swing leg would also stimulate the Lean Forward units in both leg groups, and the<br />
Lateral Shift Left to transfer the weight to the contralateral side. The <strong>Walking</strong> mode will<br />
stimulate cyclic walking and gradually deactivate the initiation as soon as the weight is<br />
removed from the swing leg. Then, <strong>Walking</strong> Cyclic will inhibit the standing mode, and<br />
normal walking as described below will be in progress.<br />
A closer look at the control unit for lateral weight shift reveals its similarity to the muscle<br />
activities observed in human walking initiation. Analysis <strong>of</strong> the emg data during this<br />
phase (Figure 5.12) reveals activity <strong>of</strong> the gluteus medius on the swing leg’s side, and<br />
<strong>of</strong> the adductor muscle group on the contralateral side. Knowing the function <strong>of</strong> these<br />
muscles allows to map this muscle action to the corresponding joint action. Appendix A<br />
includes a list <strong>of</strong> the muscles relevant during human walking along with their function and<br />
abbreviation. The main action <strong>of</strong> the gluteus medius is abduction <strong>of</strong> the thigh, meaning an
94 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
Norm. Torque ˆτ<br />
0.00<br />
−0.05<br />
−0.10<br />
−0.15<br />
Left Hip X<br />
0.0 0.25 0.5 0.75 1.0<br />
Time [s]<br />
0.15<br />
0.10<br />
0.05<br />
Right Hip X<br />
0.00<br />
0.0 0.25 0.5 0.75 1.0<br />
Time [s]<br />
0.00<br />
−0.02<br />
−0.04<br />
−0.06<br />
−0.08<br />
Spine X<br />
0.0 0.25 0.5 0.75 1.0<br />
Time [s]<br />
Figure 5.14: Torque output generated by the Lateral Shift Right motor patterns.<br />
outward rotation <strong>of</strong> the hip joint around the x-axis pointing in walking direction. Similarly,<br />
action <strong>of</strong> the adductor muscles result in an inward rotation <strong>of</strong> the hip joint around the<br />
same axis.<br />
Using this information, the muscle action can then be translated to joint torque patterns.<br />
Figure 5.14 illustrates the torques generated by the muscle pattern for lateral weight shift.<br />
The sigmoid function formulated in Equation 5.7 is parametrized and applied to three<br />
joints with individual factors. The torques generated are normalized torque values ranging<br />
from -1 to 1. A positive sign <strong>of</strong> the normalized torque signifies a flexion or adduction <strong>of</strong> the<br />
joint, a negative sign amounts to extension or abduction. Within a hardware abstraction<br />
layer, these values are multiplied by the maximum torque <strong>of</strong> the joint and the sign is<br />
possibly swapped to obtain the mathematically correct rotation direction. The figure<br />
illustrates a negative torque pattern <strong>of</strong> the left hip resulting in an thigh abduction, and a<br />
simultaneous positive torque pattern <strong>of</strong> the right hip leading to adduction <strong>of</strong> the other<br />
thigh. Additionally, a torque about the x-axis <strong>of</strong> the spine joint is generated to compensate<br />
a sideward bending <strong>of</strong> the upper trunk that would occur due to its mass inertia.<br />
It is important to note that all other joints remain passive during the initiation process.<br />
As the motor patterns just mentioned are superimposed on the control <strong>of</strong> stable standing,<br />
a relatively high stiffness and a fixed equilibrium point is set as command for these joints.<br />
Only a few actively controlled joints and the passive dynamics <strong>of</strong> the system result in the<br />
movement preparing for the first step.<br />
Figure5.15comparesthegroundreactionforcesduringwalkinginitiation<strong>of</strong>humansubjects<br />
with results from simulation measured by simulated force plates located under the left and<br />
right body side. As described above, the center <strong>of</strong> pressure first moves to the swing leg<br />
before the weight is shifted fully to the stance leg. When regarding the individual vertical<br />
forces for each leg, a progress as plotted in Figure 5.15a can be observed [Elble 94]. The<br />
vertical forces measured by the force plates during walking initiation <strong>of</strong> the simulated biped<br />
show the same characteristics (Figure 5.15b). The progress <strong>of</strong> the ground reaction forces<br />
is less smooth compared to human measurements as the hip movements <strong>of</strong> the simulated<br />
robot at the beginning <strong>of</strong> the swing phase are slightly jerky. The whole process <strong>of</strong> walking<br />
initiation takes only about 0.1sec longer than in human subjects.<br />
As soon as the load on the swing leg is sufficiently smaller than the load on the stance leg,<br />
the walking locomotion mode switches from walking initiation to cyclic walking. The spinal<br />
pattern generator described in the next section is initialized at those phases responsible
5.4. Dynamic <strong>Walking</strong> 95<br />
Vertical GRF [N]<br />
Vertical GRF [N]<br />
800<br />
600<br />
400<br />
200<br />
0<br />
800<br />
600<br />
400<br />
200<br />
0<br />
Stance Leg<br />
0.0 0.2 0.4 0.6 0.8 1.0<br />
Swing Leg<br />
0.0 0.2 0.4 0.6 0.8 1.0<br />
Time [s]<br />
(a)<br />
Vertical GRF [N]<br />
Vertical GRF [N]<br />
800<br />
600<br />
400<br />
200<br />
0<br />
800<br />
600<br />
400<br />
200<br />
0<br />
Stance Leg<br />
0.0 0.2 0.4 0.6 0.8 1.0<br />
Swing Leg<br />
0.0 0.2 0.4 0.6 0.8 1.0<br />
Time [s]<br />
Figure 5.15: Comparing vertical ground reaction forces <strong>of</strong> human walking initiation (a) with<br />
those produced by the Lateral Shift Right motor pattern in simulated biped (b). <strong>Human</strong> data<br />
reproduced from [Elble 94], p143.<br />
for generating the swing <strong>of</strong> the designated leg and ensuring support <strong>of</strong> the body weight<br />
upon the other leg.<br />
5.4.3 Spinal Pattern Generator for <strong>Walking</strong><br />
After initiation <strong>of</strong> walking, the locomotion mode for cyclic walking will be activated. It<br />
again stimulates the spinal pattern generator for walking which is responsible for the<br />
coordination <strong>of</strong> the different phases during walking. This pattern generator and the<br />
walking phases are derived from the work <strong>of</strong> Vaughan, Ivanenko and others as described in<br />
Section 3.1.4 and Section 3.2.2. Their research results based on emg analysis suggest a<br />
central control unit generating the signals for synergistic muscle activity and reflex action.<br />
The transition from one phase to the next could be triggered in two ways: time-based or<br />
event-based. Due to the high complexity <strong>of</strong> the human nervous system, it cannot clearly<br />
be said how this process works in humans. As presented in Section 3.4 some approaches<br />
utilize artificial neural oscillators to create cyclic motions, thus are based on a fixed timing.<br />
In this work, the phase transition is triggered by sensor events. This complies with the<br />
statement <strong>of</strong> Ivanenko et al. that the components <strong>of</strong> muscle activity during walking are<br />
related to kinematic or kinetic events. The duration <strong>of</strong> each walking phase emerges from<br />
the interaction <strong>of</strong> the dynamic system with the environment.<br />
One advantage <strong>of</strong> this approach is a higher contribution <strong>of</strong> the inherent system dynamics.<br />
By not forcing the robot’s motions into a predefined timing, passive dynamics can be<br />
(b)
96 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
right<br />
leg<br />
left<br />
leg<br />
1 weight acceptance<br />
3<br />
4<br />
2 propulsion<br />
5<br />
3 stab.<br />
4 leg swing<br />
5 heel strike<br />
full contact<br />
toe-<strong>of</strong>f locked knee full contact<br />
toe-<strong>of</strong>f locked knee full contact<br />
Figure 5.16: Phases <strong>of</strong> walking for left and right side and the sensor events triggering the phase<br />
transitions.<br />
exploited more easily. Another benefit can be seen in a potentially higher robustness. As<br />
phase transitions are based on sensor events, less additional mechanisms must be provided<br />
to adapt the control to unexpected disturbances. Rather, the system reacts automatically,<br />
e.g. in case the foot contact after the leg swing occurs a bit earlier or later. A possible<br />
drawback <strong>of</strong> this approach could be that the determining events must be perceived in a<br />
reliable way. For this reason, transition conditions are formulated in a fuzzy and when<br />
possible redundant way. Furthermore the number <strong>of</strong> relevant conditions can be reduced by<br />
bilateral synchronization.<br />
According to the discussed emg analysis, human walking seems to be composed <strong>of</strong> five<br />
phases that can be be associated to kinematic or kinetic events: weight acceptance, loading<br />
or propulsion, trunk stabilization during double support, toe lift-<strong>of</strong>f, and heel strike. Based<br />
on these finding, the spinal pattern generator for walking also stimulates five phases for<br />
both the left and the right side <strong>of</strong> the robot. Figure 5.16 illustrates these phases and the<br />
events triggering the phase transitions. As a reference, snapshots <strong>of</strong> the gait cycle are<br />
depicted on the upper part <strong>of</strong> the figure.<br />
The first phase <strong>of</strong> walking starts after full contact <strong>of</strong> the swing foot, i.e. after heel and toes<br />
touch the ground. The weight <strong>of</strong> the trunk is accepted and then supported by the former<br />
swing leg. During the next phase additionally forward velocity can be inserted into the<br />
system in form <strong>of</strong> propulsion by the stance foot. This process starts as soon as the other<br />
leg finishes its swing and is ready for ground impact. The third phase is characterized by<br />
double support during which stabilization <strong>of</strong> the body posture is facilitated. After toe-<strong>of</strong>f,<br />
the swing phase starts, transferring the leg in front <strong>of</strong> the body. As soon as the swing leg’s<br />
knee is locked or its foot touches the ground, the last phase begins. It is responsible for<br />
managing the foot impact during heel strike and for providing control towards the full<br />
contact <strong>of</strong> the foot.<br />
Figure 5.16 also illustrates the bilateral synchronization <strong>of</strong> the walking phases. As observed<br />
in human walking, phase 1 <strong>of</strong> the one leg and phase 3 <strong>of</strong> the contralateral leg are temporally<br />
coordinated. Thesameholdstruefortheonset<strong>of</strong>phases2and5thattakesplacehalfacycle<br />
1<br />
2
5.4. Dynamic <strong>Walking</strong> 97<br />
<strong>Walking</strong><br />
Stable<br />
Standing<br />
<strong>Walking</strong><br />
Initiation<br />
Cyclic<br />
<strong>Walking</strong><br />
Standing<br />
States<br />
...<br />
...<br />
<strong>Walking</strong><br />
SPG<br />
1<br />
2<br />
Weight<br />
Weight<br />
Accept.<br />
1 Accept.<br />
ProPropulsion<br />
2 pulsion<br />
Trunk<br />
3<br />
Trunk<br />
Stabiliz. 3 Stabiliz.<br />
Leg<br />
Leg<br />
4<br />
4<br />
Swing<br />
Swing<br />
5<br />
left right<br />
Heel<br />
Heel<br />
5Strike<br />
Strike<br />
Figure 5.17: Stimulation flow <strong>of</strong> locomotion modes, spinal pattern generator, and walking<br />
phases during cyclic walking.<br />
later. Only the fourth phase associated with the leg swing begins without a corresponding<br />
phase <strong>of</strong> the other leg. This bilateral synchronization guarantees coordinated movement <strong>of</strong><br />
both legs. It further reduces the number <strong>of</strong> conditions relevant for phase transitions to<br />
three, thus increasing the reliability <strong>of</strong> the pattern generator.<br />
Considering this, the spinal pattern generator can be represented by a state machine <strong>of</strong><br />
three states for the walking phases and a second state machine <strong>of</strong> two states switching<br />
the assignment <strong>of</strong> the phases to the body sides. State one corresponds to phase 1 and the<br />
contralateral phase 3, the next state to phase 1 and phase 4, and the third state to phase<br />
2 and phase 5. Each time one cycle <strong>of</strong> this state machine is completed, the assignment <strong>of</strong><br />
the phases to the left and the right side <strong>of</strong> the body is toggled.<br />
The stimulation flow <strong>of</strong> the locomotion modes, the spinal pattern generator, and the<br />
walking phases during cyclic walking is visualized in Figure 5.17. The locomotion mode for<br />
cyclic walking is inhibiting the standing mode and stimulating the spinal pattern generator.<br />
Depending on its state, the pattern generator activates a matching pair <strong>of</strong> walking phases,<br />
one for the left and one for the right body side, each being equipped with its own set <strong>of</strong><br />
the five phases. The figure illustrates the stimulation <strong>of</strong> phase 1 for the left and phase 3<br />
for the right side <strong>of</strong> the body. This pairwise activation <strong>of</strong> phases progresses as the relevant<br />
sensor events described above are perceived.<br />
Each active walking phase is responsible for stimulating the appropriate control units and<br />
for managing the joints being passive during the phase. The passive joints have a constant<br />
stiffness and equilibrium point set throughout the phase. In case a joint or the action <strong>of</strong> a<br />
control unit cannot unambiguously be associated to one body side, it will be controlled by<br />
the phase that is semantically closer related to it. The next sections will name the passive<br />
joints and describe the active control units for each walking phase in detail.<br />
5.4.4 <strong>Walking</strong> Phase 1: Weight Acceptance<br />
Phase 1 <strong>of</strong> cyclic walking begins as soon as the foot <strong>of</strong> the swing leg fully touches the<br />
ground. As in human walking, this phase is responsible for accepting the body weight<br />
with the new stance leg, generating the semi-flat walking gait and shifting the task <strong>of</strong>
98 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
<strong>Walking</strong><br />
SPG<br />
1<br />
2<br />
3<br />
4<br />
5<br />
left<br />
Weight<br />
Accept.<br />
Propulsion<br />
Trunk<br />
Stabiliz.<br />
Leg<br />
Swing<br />
Heel<br />
Strike<br />
Forward<br />
Velocit.L<br />
Upright<br />
Trunk L<br />
Lat. Bal.<br />
Ankle L<br />
Lower Trunk<br />
Stabilize<br />
Pelvis L<br />
Left Leg<br />
Weight<br />
Accept.<br />
Figure 5.18: <strong>Control</strong> units stimulated during phase 1 <strong>of</strong> cyclic walking.<br />
stabilizing the pelvis and the trunk from one leg to the other. Figure 5.18 illustrates the<br />
control units being stimulated in this phase for the left body side. The locomotion modes<br />
and the control units <strong>of</strong> the right body side are omitted for sake <strong>of</strong> clarity and readability.<br />
A trailing ‘L’ or ‘R’ in the unit’s name denotes that it is responsible for action on the left<br />
or right body side. The postural reflexes that aim for suitable forward velocity, an upright<br />
trunk, and lateral stabilization will be discussed separately in Section 5.4.9. Thus, the<br />
passive joints and two control units called Stabilize Pelvis and Weight Acceptance remain<br />
to be described.<br />
The motor pattern Weight Acceptance controls the knee joint to guarantee a smooth weight<br />
acceptance and a semi-flat gait during and after heel strike. This is achieved by actively<br />
bending the knee, already starting in walking phase 5, i.e. just before the foot touches the<br />
ground (Figure 5.19a). Similar to what can be observed in human gait analysis, the leg is<br />
bent preventively even before ground contact, thus reducing impact energy. The motor<br />
pattern receives the desired walking velocity as modification signal. The faster the walking<br />
speed, the stronger the knee is bent. The duration <strong>of</strong> the pattern is set to last until the<br />
trunk has traveled beyond the foot <strong>of</strong> the stance leg in a normal stride. After the pattern<br />
has ended, the knee joint remains in a mostly extended position with high stiffness. As a<br />
result, only little energy must be invested despite <strong>of</strong> the knee having to support the whole<br />
body weight. Figure 5.19b illustrates the resulting semi-flat gait by plotting the z-position<br />
<strong>of</strong> the head’s center. Close to what is found in human walking, the height <strong>of</strong> the head<br />
oscillates only a few centimeters at twice the frequency <strong>of</strong> the gait cycle.<br />
To stabilize the pelvis via the stance leg, a second control unit is stimulated during walking<br />
phase 1. As the pelvis would rotate about the x-axis <strong>of</strong> the hip joint as soon as the swing<br />
leg leaves the ground, this joint must be kept stiff. This corresponds to the activity <strong>of</strong> the<br />
abductor muscles <strong>of</strong> the stance leg observed in human walking where the pelvis is kept<br />
almost horizontal throughout the walking cycle.<br />
Unfortunately, it is not possible to stabilize the pelvis by simply setting a constant joint<br />
angle during the whole stance phase. As the position <strong>of</strong> the stance leg’s foot in lateral<br />
direction will shift depending on disturbances or during walking sidewards, another control<br />
strategy has to be found. Two possible ways come into mind and have been examined
5.4. Dynamic <strong>Walking</strong> 99<br />
Left Knee Angle [ ◦ ]<br />
60<br />
40<br />
20<br />
Heel Strike<br />
0<br />
0.0 0.5 1.0 1.5 2.0 2.5<br />
Time [s]<br />
(a)<br />
Head Height [m]<br />
1.8<br />
1.6<br />
1.4<br />
1.2<br />
0.0 1.0 2.0<br />
Time [s]<br />
3.0 4.0<br />
Figure 5.19: (a) The Weight Acceptance motor pattern starts to bend the knee before heel<br />
strike to reduce impact. (b) The height <strong>of</strong> the head’s center illustrates the semi-flat walking gait.<br />
in the scope <strong>of</strong> this work. The first possibility assumes that the hip angle in the x-axis<br />
does not have to change during stance phase. Then the Stabilize Pelvis reflex can stiffen<br />
the joint at its current angle as soon as the leg touches the ground. To gain additionally<br />
ground clearance for the swing leg, a small <strong>of</strong>fset can be added to the hip angle, raising<br />
the contralateral side <strong>of</strong> the pelvis.<br />
A second strategy to stabilize the pelvis can be implemented by actually controlling the roll<br />
angle <strong>of</strong> the pelvis. Assuming the pose <strong>of</strong> the trunk is known, this roll angle can be derived<br />
and adjusted by changing the x-angle <strong>of</strong> the hip joint. This method has the advantage <strong>of</strong><br />
being more flexible, as it keeps an appropriate pelvis orientation no matter what situation<br />
occurs. But as this reflex needs to hold a stiff position during strong disturbances and<br />
relatively high cycle time, it easily inclines to oscillate.<br />
In addition to the joints controlled by the two units just described, the postural reflexes<br />
actively influence the ankle pitch and roll angles, and the hip roll angle. The remaining<br />
joints, namely the hip joint about the vertical axis, the spine joints, and the arm joints<br />
are passive and set to a medium, low, and high compliance, respectively. The equilibrium<br />
points <strong>of</strong> these joints are set to their neutral position, correlating to an upright, relaxed<br />
standing posture.<br />
5.4.5 <strong>Walking</strong> Phase 2: Propulsion<br />
The next walking phase starts as soon as the contralateral leg has finished the swing phase<br />
and has stretched the knee in preparation to heel strike. The main task <strong>of</strong> this phase is to<br />
insert additional energy to the system so the forward velocity can be maintained. As the<br />
body mass has already traveled beyond the stance leg, this propulsion can be achieved by<br />
plantarflexion <strong>of</strong> the ankle. Furthermore, the leg swing is already initialized by active leg<br />
flexion in the hip joint. The Stabilize Pelvis control unit as well as the postural reflexes<br />
from phase 1 are kept stimulated. Figure 5.20 illustrates the resulting control network<br />
during phase 2.<br />
The motor pattern Leg Propel creates a plantarflexion <strong>of</strong> the ankle. Thus it corresponds to<br />
the strong muscular activity <strong>of</strong> the gastrocnemius and soleus before toe-<strong>of</strong>f. As in human<br />
walking, the amplitude <strong>of</strong> the motor pattern increases with the walking velocity that it<br />
receives as modulation signal. Additionally, the motor pattern output is scaled by a factor<br />
(b)
100 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
<strong>Walking</strong><br />
SPG<br />
1<br />
2<br />
3<br />
4<br />
5<br />
left<br />
Weight<br />
Accept.<br />
Propulsion<br />
Trunk<br />
Stabiliz.<br />
Leg<br />
Swing<br />
Heel<br />
Strike<br />
Forward<br />
Velocit.L<br />
Upright<br />
Trunk L<br />
Lat. Bal.<br />
Ankle L<br />
Lower Trunk<br />
Stabilize<br />
Pelvis L<br />
Initialize<br />
Swing L<br />
Left Leg<br />
Leg<br />
Propel<br />
Figure 5.20: <strong>Control</strong> units stimulated during phase 2 <strong>of</strong> cyclic walking.<br />
determined by the ankle angle at the beginning <strong>of</strong> the pattern. Advancing dorsiflexion <strong>of</strong><br />
the ankle results in an amplification <strong>of</strong> the motor pattern torque. As a result, a longer step<br />
size automatically leads to stronger propulsion by the stance leg. To prevent excessive<br />
plantarflexion, the output <strong>of</strong> the motor pattern is reduced by the increasing pitch angle <strong>of</strong><br />
the ankle.<br />
Gait analysis <strong>of</strong> human walking shows that leg swing not only emerges passively by the<br />
weight <strong>of</strong> the leg segments after toe-<strong>of</strong>f. Rather, energy is added by the hip joint to actively<br />
start the leg swing and to increase the leg’s velocity even before the foot leaves the ground.<br />
The more energy is added, the more the swing duration can be shortened, thus allowing<br />
for higher walking speeds. The motor pattern Initialize Swing corresponds to this muscle<br />
activity generated by the iliopsoas, sartorius, and tensor fascia latae. As in the Leg Propel<br />
control unit, its amplitude is modulated by the desired walking velocity. The duration <strong>of</strong><br />
the pattern is chosen to last well into walking phase 4.<br />
The torque induced in the hip joint does not only cause a flexion <strong>of</strong> the leg, but also bends<br />
the trunk forward. This trunk movement would be corrected by the postural reflexes, but<br />
only after a deflection has occurred which is big enough to trigger a reflexive response. By<br />
then, the trunk already has started to sway. To prevent this outcome, the motor pattern<br />
additional generates a torque in the contralateral hip. Properly dimensioned, this torque<br />
compensates the unwanted trunk deflection. A corresponding muscle activity can also be<br />
observed in human walking.<br />
The leg flexion generated by Initialize Swing induces a flexion <strong>of</strong> the knee that is set to high<br />
compliance during walking phase 2. This would lead to contra-productive shortening <strong>of</strong> the<br />
stance leg which still is responsible for supporting the body weight. Only in combination<br />
with the plantarflexion <strong>of</strong> the ankle produced by the Leg Propel motor pattern, body<br />
support and propulsion is possible. This synergistic effect is created by the synchronous<br />
stimulation <strong>of</strong> the two control units, coordinated by the motion phase unit.<br />
As already mentioned, the knee joint acts passively with high compliance during this phase.<br />
The other passive joints are similar to those <strong>of</strong> the previous phase.
5.4. Dynamic <strong>Walking</strong> 101<br />
<strong>Walking</strong><br />
SPG<br />
1<br />
2<br />
3<br />
4<br />
5<br />
left<br />
Weight<br />
Accept.<br />
Propulsion<br />
Trunk<br />
Stabiliz.<br />
Leg<br />
Swing<br />
Heel<br />
Strike<br />
Upright<br />
Trunk L<br />
Lat. Bal.<br />
Ankle L<br />
Upper Trunk<br />
Arm<br />
Swing L<br />
Lower Trunk<br />
Stabilize<br />
Pelvis L<br />
Initialize<br />
Swing L<br />
Lateral<br />
Shift R<br />
Left Leg<br />
Leg<br />
Propel<br />
Figure 5.21: <strong>Control</strong> units stimulated during phase 3 <strong>of</strong> cyclic walking.<br />
5.4.6 <strong>Walking</strong> Phase 3: Stabilization<br />
During the third phase <strong>of</strong> walking the robot’s posture can be stabilized as both feet touch<br />
the ground. It begins as soon as the foot <strong>of</strong> the contralateral leg has full contact with the<br />
ground after its swing phase. As the stance phase is nearly finished, the postural reflexes<br />
are gradually diminished in their stimulation. The forward velocity is now controlled by<br />
the former swing leg, and lateral balancing by the ankle joint becomes more difficult as the<br />
ground contact lessens. For similar reasons, the reflex stabilizing the pelvis is only partly<br />
stimulated. Still, the Leg Propel motor pattern pushes the body forward until the foot<br />
leaves the ground. The Initialize Swing pattern started in the previous phase continuous<br />
its action, too.<br />
As illustrated in Figure 5.21, two additional control units are stimulated in phase 3: the<br />
Lateral Shift Right pattern already introduced during walking initiation is stimulated<br />
depending on the body posture. This allows to direct the movement <strong>of</strong> the center <strong>of</strong> mass<br />
to the next stance leg. Additionally, the Arm Swing motor pattern controls the rotation<br />
about the y-axis <strong>of</strong> the ipsi- and contralateral shoulder joint. By adding contrary torque<br />
impulses, a synchronized arm flexion respectively extension is generated. As in human<br />
walking, this arm swing compensates possible trunk rotation disturbing the walking cycle.<br />
The remaining arm joints stay passive.<br />
Figure 5.22 visualizes the torques generated by the Arm Swing motor pattern and the<br />
resulting trajectories. The upper plots represent the y-axis <strong>of</strong> left, the lower plots the<br />
y-axis <strong>of</strong> the right shoulder joint. On the left side, the effective motor torques illustrate<br />
the synchronous but opposite action <strong>of</strong> both shoulder joints. This results in sine-<strong>like</strong> angle<br />
trajectories <strong>of</strong> the swinging arms despite the fact that only short torque impulses are<br />
created. This behavior is possible as the shoulder joints can move passively throughout<br />
the rest <strong>of</strong> the walking cycle.
102 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
Left Shoulder<br />
Right Shoulder<br />
Torque [Nm]<br />
Torque [Nm]<br />
10<br />
0<br />
−10<br />
10<br />
0<br />
−10<br />
0.0 0.5 1.0 1.5 2.0 2.5<br />
0.0 0.5 1.0 1.5 2.0 2.5<br />
Time [s]<br />
Angle [ ◦ ]<br />
Angle [ ◦ ]<br />
40<br />
20<br />
0<br />
−20<br />
−40<br />
0.0 0.5 1.0 1.5 2.0 2.5<br />
40<br />
20<br />
0<br />
−20<br />
−40<br />
0.0 0.5 1.0 1.5 2.0 2.5<br />
Time [s]<br />
Figure 5.22: Angle and torque progress <strong>of</strong> the arm swing generated by the Arm Swing motor<br />
pattern.<br />
5.4.7 <strong>Walking</strong> Phase 4: Leg Swing<br />
The fourth phase <strong>of</strong> walking covers the actual swing <strong>of</strong> the leg. It begins as soon as the<br />
foot has left the ground and ends when the knee <strong>of</strong> the swing leg is stretched again. The<br />
task <strong>of</strong> this phase is tw<strong>of</strong>old: the swing leg has to be brought forth to accept the body<br />
weight while ensuring ground clearance <strong>of</strong> the foot; and the foot must be positioned in a<br />
way that postural stability can by retained. The latter function is performed by the local<br />
reflex Lock Hip and the postural reflex Lateral Foot Placement which will be described<br />
later on. Active control <strong>of</strong> the upper body’s posture is not possible as the leg does not<br />
touch the ground and no forces can be induced into the trunk.<br />
As shown in Figure 5.23, the Arm Swing and Initialize Swing motor patterns continue<br />
their action and three new reflexes are introduced. The Lock Knee reflex is responsible for<br />
ensuring the knee is stretched at the end <strong>of</strong> the leg swing. This is necessary as only an<br />
extended leg can create the pendulum-<strong>like</strong> walking gait aimed for. A bended leg would<br />
allow the center <strong>of</strong> mass to fall too low, and additional joint work would be required to lift<br />
the trunk again.<br />
Before the knee can be stretched to prepare it for weight acceptance, it must bend to<br />
guarantee ground clearance <strong>of</strong> the foot while it travels forward. In human walking, no<br />
muscle action affecting the knee joint can be observed during the main part <strong>of</strong> the leg<br />
swing. Rather, the knee bends passively due to mass inertia <strong>of</strong> the lower leg and the foot.<br />
The same holds true for this approach: during phase 4, the knee joint is allowed to move<br />
freely until the end <strong>of</strong> the swing when the Lock Knee reflex reacts. It bends passively as<br />
an effect <strong>of</strong> the inherent dynamics.<br />
In case the momentum <strong>of</strong> the lower leg is high enough, the knee would extend by itself and<br />
the Lock Knee reflex would not be needed. But if the momentum is too low, active control
5.4. Dynamic <strong>Walking</strong> 103<br />
<strong>Walking</strong><br />
SPG<br />
1<br />
2<br />
3<br />
4<br />
5<br />
left<br />
Weight<br />
Accept.<br />
Propulsion<br />
Trunk<br />
Stabiliz.<br />
Leg<br />
Swing<br />
Heel<br />
Strike<br />
Lat. Foot<br />
Placem.L<br />
Upper Trunk<br />
Arm<br />
Swing L<br />
Lower Trunk<br />
Lock<br />
Hip L<br />
Initialize<br />
Swing L<br />
Left Leg<br />
Lock<br />
Knee<br />
Cutan.<br />
Reflex<br />
Figure 5.23: <strong>Control</strong> units stimulated during phase 4 <strong>of</strong> cyclic walking.<br />
<strong>of</strong> knee joint will be necessary. This control takes place as soon as the angle <strong>of</strong> the knee<br />
joint draws near to the stretched state. The reflex then starts to increase the stiffness <strong>of</strong><br />
the knee joint with the equilibrium point set to the stretched angle. If the leg extends by<br />
itself, no additional energy will be expended. Otherwise, a torque will be generated by the<br />
knee motor to support the leg extension.<br />
Figure 5.24 shows the knee angle emerging during a step <strong>of</strong> the simulated biped and<br />
compares it to human walking. It can be seen that similar trajectories arise. The knee<br />
passively bends to an angle <strong>of</strong> about 60 ◦ during the swing phase.<br />
The Lock Hip reflex controls the flexion <strong>of</strong> the hip joint, i.e. the rotation about the y-axis<br />
by applying a damping torque. It aims at stopping the swing <strong>of</strong> the leg to achieve a<br />
suitable angle <strong>of</strong> attack at heel strike. This follows the ideas <strong>of</strong> Blum, Seyfarth et al. who<br />
show a correlation <strong>of</strong> the swing leg’s angle <strong>of</strong> attack and a stable forward velocity in human<br />
walking and running [Blum 07]. Varying step length at the same kinetic forward energy <strong>of</strong><br />
the trunk influences the forward velocity. Longer steps result in slowing down, shorter<br />
steps in accelerating the upper body.<br />
To set a suitable angle <strong>of</strong> attack, the Lock Hip (lh) reflex has to know the pitch angle φ <strong>of</strong><br />
the trunk. It also receives the desired walking velocity. The resulting normalized target<br />
hip angle ˆ φhip y, lh amounts to<br />
ˆαhip y, lh = ˆαhip y, max ·vtarget +Kpitch ·φ (5.8)<br />
where the maximum hip angle ˆαhip y, max and the body pitch factor Kpitch are set experimentally.<br />
This calculation results in shorter steps when the body leans backwards and<br />
longer steps when the body leans forward. The more the hip flexion <strong>of</strong> the swing leg<br />
approaches the target angle, the higher the applied damping. The damping torque is<br />
proportional to the rotational velocity <strong>of</strong> the hip joint, thus falling to zero as soon as the
104 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
Knee Angle [ ◦ ]<br />
60<br />
40<br />
20<br />
<strong>Human</strong> <strong>Walking</strong><br />
0<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
(a)<br />
Knee Angle [ ◦ ]<br />
60<br />
40<br />
20<br />
Simulated Biped<br />
0<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 5.24: Comparison <strong>of</strong> the knee angle trajectory in human walking (a) and in the biped<br />
simulation, averaged over 20 steps (b). <strong>Human</strong> data reproduced from [Hamill 03].<br />
leg swing is stopped. Then the reflex stimulates the position control to fix the hip joint at<br />
the desired angle <strong>of</strong> attack.<br />
The Cutaneous Reflex is motivated by its namesake discussed in Chapter 3. Its task is to<br />
re-establish ground clearance in case the foot touches down during the swing phase. To<br />
this end, it receives the force measurements from the toe and heel sensors. In case the<br />
toe sensors indicate ground contact, ankle dorsiflexion is generated by an ankle torque<br />
proportional to the measured force. Similar, ankle plantarflexion is initiated as soon as heel<br />
contact is conceived. In both cases, an accompanying torque to bend the knee supports<br />
the necessary ground clearing reaction.<br />
As long as the cutaneous reflex does not become active, the knee joint acts purely passively<br />
during this motion phase. Furthermore, both ankle joints are set to a fixed, neutral<br />
equilibrium point with medium compliance. The spring-<strong>like</strong> behavior <strong>of</strong> the ankle pitch<br />
angle is sufficient to lift the toes <strong>of</strong>f the ground after the Leg Propel motor pattern <strong>of</strong> the<br />
previous phases has finished the plantarflexion <strong>of</strong> the ankle. Hip ab- and adduction is not<br />
passive but controlled by the postural reflex Lateral Foot Placement. The flexion <strong>of</strong> the hip<br />
is passive between the end <strong>of</strong> the Initialize Swing pattern and the action <strong>of</strong> the Lock Hip<br />
reflex. As in the phases before, hip rotation and the spine joints are set to low compliance.<br />
5.4.8 <strong>Walking</strong> Phase 5: Heel Strike<br />
The last phase <strong>of</strong> walking takes place around the heel strike event. As soon as the swing<br />
leg is extended, it must prepare for touching the ground. This phase is responsible for<br />
reducing the ground impact and for generating a controlled lowering <strong>of</strong> the toes after heel<br />
strike. Figure 5.25 illustrates the involved control units. Compared to the previous phase,<br />
the knee joint is no more controlled by the Lock Knee reflex but by the Weight Acceptance<br />
motor pattern already described above. Additionally, the Heel Strike reflex controls the<br />
ankle dorsiflexion. <strong>Control</strong> <strong>of</strong> the posture and <strong>of</strong> the leg’s angle <strong>of</strong> attack remain the same.<br />
Due to the body weight resting on the foot after touch-down, the ankle joint would<br />
plantarflex and the foot would rotate about the heel contact point. In human walking,<br />
activity <strong>of</strong> the tibialis anterior muscle prevents the toes from hitting the ground too<br />
(b)
5.4. Dynamic <strong>Walking</strong> 105<br />
<strong>Walking</strong><br />
SPG<br />
1<br />
2<br />
3<br />
4<br />
5<br />
left<br />
Weight<br />
Accept.<br />
Propulsion<br />
Trunk<br />
Stabiliz.<br />
Leg<br />
Swing<br />
Heel<br />
Strike<br />
Lat. Foot<br />
Placem.L<br />
Lower Trunk<br />
Lock<br />
Hip L<br />
Left Leg<br />
Heel<br />
Strike<br />
Weight<br />
Accept.<br />
Figure 5.25: <strong>Control</strong> units stimulated during phase 5 <strong>of</strong> cyclic walking.<br />
forcefully. Here, the Heel Strike reflex assumes this task. As a force is measured by the heel<br />
force sensors <strong>of</strong> the foot, a damping torque is produced to s<strong>of</strong>ten plantarflexion. The torque<br />
is proportional to the rotational velocity <strong>of</strong> the ankle joint. In contrast to the biological<br />
ankle joint, technical systems already introduce joint damping, e.g. by gear friction. The<br />
simulation used in this work also includes damping within the joints. Depending on the<br />
amount <strong>of</strong> damping that acts within the ankle joint, the Heel Strike reflex can be omitted.<br />
Otherwise, the ankle joint remains in a passive, relaxed state as no other control unit<br />
affects its action. Again, hip rotation and the spine joints are set to low compliance at a<br />
neural equilibrium position.<br />
5.4.9 Posture <strong>Control</strong><br />
Postural reflexes provide additional body stabilization based on global sensor information.<br />
The main source <strong>of</strong> information on the current body pose is provided by the inertial<br />
measurement unit. It is able to measure accelerations in all three directions as well as<br />
three rotational velocities. In this work it is assumed that the upper body orientation can<br />
be derived from this data. While this assumption might not be easily implemented, it<br />
would go beyond the scope <strong>of</strong> this thesis. In literature, a few approaches can be found on<br />
deriving the orientation based on an inertial measurement unit and certain heuristics or<br />
additional model knowledge [Koch 04, Gienger 02].<br />
The main challenges <strong>of</strong> postural control are threefold: the upper body should be kept erect<br />
or slightly bend forward depending on the walking velocity; the forward velocity must be<br />
controlled to keep the robot from stumbling or falling forward or backwards; finally, lateral<br />
stability must be ensured.<br />
To a certain degree, passive dynamics and compensating motor patterns work towards these<br />
challenges. For instance, parallel elasticities in the ankle joint help in lateral stabilization<br />
and in controlling the forward velocity: larger steps result in stronger dorsiflexion during<br />
push-<strong>of</strong>f, thus stretching the ankle elasticities and adding more energy to the system.<br />
The motor pattern for initiating the leg swing also inserts an opposing torque in the<br />
contralateral hip to stabilize the trunk. However, postural reflexes still need to generate<br />
correcting motions to compensate self-induced or external disturbances.
106 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
φtarget<br />
−<br />
eφ<br />
˙φtarget e ˙ φ ˆτhip<br />
P PI<br />
φ<br />
−<br />
˙φ<br />
Process<br />
Figure 5.26: <strong>Control</strong> block diagram <strong>of</strong> the postural reflex Upright Trunk.<br />
5.4.9.1 Upper Body Balance<br />
In human walking, the upper body is kept remarkably stable. Despite significant accelerations<br />
caused by hip movements, ground impact, or foot push-<strong>of</strong>f, the trunk remains upright.<br />
Especially the head shows only small deflections in the horizontal plane, facilitating the<br />
processing <strong>of</strong> visual information, assisted by the vestibulo-ocular reflex [Ito 82].<br />
The postural reflex Upright Trunk assumes the task <strong>of</strong> upper body stabilization in the<br />
frontal plane. It receives the current estimation on the body pitch as sensor information.<br />
The walking velocity is passed as modulation signal to achieve a forward inclination <strong>of</strong> the<br />
trunk when walking faster.<br />
As described above, there is the need to have one instance <strong>of</strong> the reflex for each body<br />
side to enable specific stimulation during different walking phases. Each <strong>of</strong> the two reflex<br />
instances will generate torque values acting on the hip joint <strong>of</strong> its particular body half.<br />
The activity <strong>of</strong> the reflex is further scaled by the ground contact derived from the force<br />
sensors <strong>of</strong> the respective foot. This guarantees that the torque applied at the hip joint<br />
only affects the orientation <strong>of</strong> the trunk as the leg is securely rooted to the ground.<br />
TheUpright Trunk reflexisdesignedasacascadedposition-velocityloop-backcontroller. As<br />
illustrated in Figure 5.26, the position control is implemented as P-control, the underlying<br />
velocity part as PI-control. The target pitch angle φtarget, i.e. the rotation <strong>of</strong> the trunk<br />
about the y-axis, is slightly increased with the walking velocity to boost the forward<br />
momentum. Depending on the resulting error <strong>of</strong> body pitch, a target change <strong>of</strong> pitch<br />
˙φtarget is calculated and passed to the PI loop. The controller then generates a normalized<br />
torque ˆτhip being applied to the hip joint <strong>of</strong> the corresponding body side.<br />
The action <strong>of</strong> the left Upright Trunk reflex during six consecutive steps and the resulting<br />
posture <strong>of</strong> the upper body is depicted in Figure 5.27. The activity a <strong>of</strong> the reflex illustrates<br />
the dependency <strong>of</strong> its reaction on the ground contact information. During the swing phase,<br />
the reflex shows no activity as it is not stimulated by the corresponding walking phase.<br />
The plotted normalized torque ˆτhip will only be applied to the hip joint if the reflex is<br />
active.<br />
As indicated by the head’s pitch angles, swaying <strong>of</strong> the upper body in the frontal plane<br />
can be kept within a few degrees. The head shows slightly more rotation than the inertial<br />
measurement unit being attached to the pelvis. This is caused by the elastic action <strong>of</strong> the<br />
spine joint. The plotted angles also illustrate that the upper body is leaning forward by<br />
a few degrees during walking. Depending on the aspired walking velocity, this <strong>of</strong>fset is<br />
raised or decreased.
5.4. Dynamic <strong>Walking</strong> 107<br />
Head Pitch Angle [ ◦ ]<br />
IMU Pitch Angle [ ◦ ]<br />
10<br />
0<br />
−10<br />
10<br />
0<br />
−10<br />
0.0 1.0 2.0 3.0<br />
0.0 1.0 2.0<br />
Time [s]<br />
3.0<br />
Reflex Activity a<br />
Norm. Hip Torque ˆτhip<br />
1.0<br />
0.5<br />
0.0<br />
1.0<br />
0.0<br />
−1.0<br />
0.0 1.0 2.0 3.0<br />
0.0 1.0 2.0<br />
Time [s]<br />
3.0<br />
Figure 5.27: The postural reflex Upright Trunk regulates the pitch angle <strong>of</strong> the upper body.<br />
The imu is mounted within the pelvis.<br />
5.4.9.2 Estimation <strong>of</strong> Center <strong>of</strong> Mass Position<br />
Regulation <strong>of</strong> the stability in lateral direction and adjustments <strong>of</strong> the forward velocity<br />
require additional information processing. As discussed in Section 3.2.4, postural control<br />
in human walking could be based on the movement <strong>of</strong> the center <strong>of</strong> mass (com). H<strong>of</strong> et al.<br />
suggest a control strategy for foot placement relying on the extrapolated center <strong>of</strong> mass<br />
(xcom) [H<strong>of</strong> 08]. To adopt a similar approach for the functioning <strong>of</strong> postural reflexes, an<br />
estimation <strong>of</strong> the current position <strong>of</strong> the com becomes necessary.<br />
The com calculations used in this work only provide a coarse estimation <strong>of</strong> its position. It is<br />
assumed that there is no elaborate dynamic model coded within the human cerebellum, but<br />
rather a simplified model that is sufficient for postural regulation. Figure 5.28 illustrates<br />
the approach <strong>of</strong> a reduced model <strong>of</strong> the com for one vertical plane. It disregards all<br />
motions <strong>of</strong> the upper body <strong>like</strong> e.g. arm swing that are changing the mass distribution<br />
and are introducing additional dynamic effects. Variation <strong>of</strong> the stance leg’s length is also<br />
neglected. The calculations are equivalent for the frontal and the sagittal plane, so the<br />
following considerations can be limited to two dimensions.<br />
The center <strong>of</strong> mass is assumed to be located at a constant distance l1 from the hip joint,<br />
aligned by an angle δ. These variables can be derived from the horizontal and vertical<br />
shift ∆com <strong>of</strong> the com from the hip joint as:<br />
l1 =<br />
�<br />
∆comhoriz 2 +∆comvert 2 , (5.9)<br />
tanδ = ∆comvert<br />
∆comhoriz<br />
. (5.10)<br />
The rotational deflection φ <strong>of</strong> the pelvis from the neutral vertical position is provided by<br />
the pose estimation <strong>of</strong> the imu. The stance leg <strong>of</strong> length l2 is rotated by the known angle
108 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
φ<br />
CoM l1<br />
l3<br />
δ<br />
d<br />
β<br />
α<br />
β<br />
γ<br />
l2<br />
β +δ + π<br />
2<br />
Figure 5.28: Simplified model for the estimation <strong>of</strong> the center <strong>of</strong> mass position.<br />
β about the hip joint. From these values, the distance l3 <strong>of</strong> the com from the foot contact<br />
point can be calculated as<br />
�<br />
l3 = l1 2 +l2 2 �<br />
−2l1l2cos β +δ + π<br />
�<br />
. (5.11)<br />
2<br />
To derive the wanted distance d <strong>of</strong> the projection <strong>of</strong> the com from the foot contact point,<br />
the angle α = β +γ +φ is necessary. With γ and φ already known, the complementing<br />
angle γ can be found as<br />
tanγ = l1sin � β +δ + π<br />
�<br />
2<br />
l2 −l1cos � β +δ + π<br />
�. (5.12)<br />
2<br />
This results in the distance d being<br />
d = l3sinα. (5.13)<br />
These calculations are done for both the left and right leg and for the frontal and sagittal<br />
plane, resulting in four values comx,left, comx,right, comy,left, and comy,right. They provide<br />
an estimation <strong>of</strong> the projection <strong>of</strong> the static com position to the ground plane relative to<br />
the position <strong>of</strong> the left and right ankle joint. Following H<strong>of</strong>’s suggestions, the extrapolated<br />
center <strong>of</strong> mass (xcom) can be derived from these values by including the velocity ˙ d <strong>of</strong> the<br />
respective com projection normalized by the eigen frequency ω0 <strong>of</strong> the assumed inverted<br />
pendulum model:<br />
xcom = d+ ˙ d<br />
(5.14)<br />
ω0<br />
with the eigen frequency ω0 for the pendulum length l3 <strong>of</strong> the com above the the foot<br />
point given as<br />
�<br />
g<br />
ω0 = . (5.15)<br />
l3
5.4. Dynamic <strong>Walking</strong> 109<br />
comx [m]<br />
comy [m]<br />
comy,fusion [m]<br />
1.0<br />
0.0<br />
−1.0<br />
0.2<br />
0.0<br />
−0.2<br />
0.2<br />
0.0<br />
−0.2<br />
0.0 1.0 2.0 3.0 4.0 5.0<br />
0.0 1.0 2.0 3.0 4.0 5.0<br />
0.0 1.0 2.0 3.0 4.0 5.0<br />
Time [s]<br />
xcomx [m]<br />
xcomy [m]<br />
xcomy,fusion [m]<br />
1.0<br />
0.0<br />
−1.0<br />
0.2<br />
0.0<br />
−0.2<br />
0.2<br />
0.0<br />
−0.2<br />
0.0 1.0 2.0 3.0 4.0 5.0<br />
0.0 1.0 2.0 3.0 4.0 5.0<br />
0.0 1.0 2.0 3.0 4.0 5.0<br />
Time [s]<br />
Figure 5.29: Estimation <strong>of</strong> the com movement. Solid lines represent the left side, dashed line<br />
the right side. The lower two plots show merged (x)com values in y-direction weighted by ground<br />
contact.<br />
Again, equation 5.14 can then be applied for both legs and directions resulting in the four<br />
values xcomx,left, xcomx,right, xcomy,left, and xcomy,right. The extrapolated interpretation<br />
<strong>of</strong> the com projection can be used in case the static calculations are insufficient for<br />
maintaining stability.<br />
Figure 5.29 illustrates the progression <strong>of</strong> the estimated center <strong>of</strong> mass for undisturbed<br />
walking. The solid lines in the upper two rows represent the com and xcom values relative<br />
to the left leg, the dashed lines those corresponding to the right leg. The phase shift <strong>of</strong><br />
half a cycle between the left and the right side is clearly visible. During stance phase, the<br />
comx value increases as the center <strong>of</strong> mass swings over the supporting leg. It decreases<br />
again as the leg swings forward. The absolute value <strong>of</strong> comy has its minimum during the<br />
stance phase as the body mass sways in the direction <strong>of</strong> the support leg. During leg swing,<br />
the value is <strong>of</strong> only minor significance as it depends on the lateral foot position controlled<br />
by the related postural reflex.<br />
The extrapolated com values on the right side <strong>of</strong> the plot reflect the integration <strong>of</strong> the<br />
com’s velocity. Both directions exhibit larger amplitudes. The additional noise in both<br />
signals origins from the oscillation <strong>of</strong> the upper body that inflicts the measurements <strong>of</strong> the<br />
imu. Both the xcomx and the xcomy values show a negative phase shift compared to their<br />
com counterparts due to their velocity component. Thus their interpretation by a postural
110 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
xcomx [m]<br />
1.0<br />
0.0<br />
−1.0<br />
0.0 1.0 2.0 3.0 4.0 5.0<br />
Time [s]<br />
Correction Value<br />
0.5<br />
0.0<br />
−0.5<br />
0.0 1.0 2.0 3.0 4.0 5.0<br />
Time [s]<br />
Figure 5.30: <strong>Control</strong> <strong>of</strong> forward velocity by approximating the xcomx trajectory during normal<br />
walking and calculating the derivation.<br />
reflex not only allows for integrating dynamic properties but also gives a temporal benefit.<br />
This advantages must be weighted against the drawback <strong>of</strong> additional noise.<br />
The lower two plots <strong>of</strong> Figure 5.29 show merged values <strong>of</strong> the comy and xcomy <strong>of</strong> both<br />
the left and right leg. The fusion is calculated using the normalized ground contact force<br />
ˆFz ∈ [0,1] measured by the load cells as weights:<br />
comy,fusion = comy,left · ˆ Fz,left +comy,right · ˆ Fz,right<br />
ˆFz,left + ˆ Fz,right<br />
(5.16)<br />
This combined value illustrates the lateral sway <strong>of</strong> the robot during normal walking. During<br />
single support the center <strong>of</strong> mass travels to the side <strong>of</strong> the supporting leg. With both legs<br />
on the ground, the merged com value levels out at about zero, as the left and right com<br />
estimations show similar absolute values and both legs have full ground contact. As soon<br />
as the swing leg lifts <strong>of</strong>f, the merged com value again moves to the side <strong>of</strong> the stance leg.<br />
5.4.9.3 <strong>Control</strong>ling the Forward Velocity<br />
The control <strong>of</strong> forward velocity relies on three control units: the local reflex Lock Hip, the<br />
motor pattern Leg Propel, and the postural reflex Forward Velocity, each <strong>of</strong> those existing<br />
for both body sides. The postural adaptation <strong>of</strong> the former control unit has already been<br />
discussed above: the step length is varied depending on the pitch <strong>of</strong> the upper body. The<br />
latter <strong>of</strong> the three control units calculates a correction value for the forward velocity that<br />
is used to generate an suitable ankle torque. It is also passed to the leg propulsion control<br />
unit as modulation value scaling the amplitude <strong>of</strong> the motor pattern.<br />
The computation <strong>of</strong> the correction value relies on the xcomx estimation <strong>of</strong> the respective<br />
leg as shown on the upper right plot in Figure 5.29. The plot depicts the xcomx during<br />
undisturbed, normal walking on level ground. Assuming that a deviation from this<br />
trajectory stems from external or self-induced disturbances, the correction factor is based<br />
on this deviation. Therefore, the xcomx trajectory over the time interval during which<br />
the corresponding leg has ground contact is approximated by the first quarter <strong>of</strong> a sine<br />
function:<br />
xcomx,target = vtarget<br />
�<br />
xcomx,start +(xcomx,end −xcomx,start)sin<br />
�<br />
π<br />
2 t<br />
��<br />
(5.17)<br />
where xcomx,start and xcomx,end denote the interval defining the amplitude, vtarget the<br />
desired walking velocity passed as modulation signal, and t ∈ [0,1] indicating the time
5.4. Dynamic <strong>Walking</strong> 111<br />
comy [m]<br />
0.2<br />
0.1<br />
0.0<br />
0.0 2.0 4.0 6.0<br />
Time [s]<br />
Correction Value<br />
0.1<br />
0.0<br />
−0.1<br />
0.0 2.0 4.0 6.0<br />
Time [s]<br />
Figure 5.31: <strong>Control</strong> <strong>of</strong> lateral stability by approximating the comy trajectory during normal<br />
walking and calculating the derivation.<br />
progression over the average duration <strong>of</strong> the reflex’s activity. Figure 5.30 illustrates the<br />
approximated trajectory and the calculated correction value. Both values are only relevant<br />
during full ground contact <strong>of</strong> the foot as only then the leg can influence the robot’s posture.<br />
Hence the calculations are limited to walking phases one and two, during the other phases<br />
the values are set to zero.<br />
The correction value is then applied as torque to the ankle joint to achieve an appropriate<br />
dorsi- or plantarflexion. The maximum absolute torque is limited to prevent lifting <strong>of</strong> the<br />
heel or toes <strong>of</strong> the foot. In case the forward velocity is too high, i.e. the xcomx value is<br />
greater than the approximated trajectory, plantarflexion <strong>of</strong> the foot will slow down the<br />
pendulum movement <strong>of</strong> the upper body over the stance leg. Likewise a small xcomx value<br />
will result in an ankle dorsiflexion and increase the velocity <strong>of</strong> the upper body.<br />
5.4.9.4 Lateral Stability<br />
Similar to the control <strong>of</strong> forward velocity, lateral stability is improved by foot placement<br />
and by correcting ankle torque. As the xcom estimation in y-direction is strongly influenced<br />
by the lateral sway <strong>of</strong> the upper body and the pelvis rotation during hip stabilization, the<br />
com estimation is utilized to calculate reflex action. Again, the trajectory <strong>of</strong> comy during<br />
normal walking is approximated, in this case by a forth order polynomial:<br />
�<br />
comy,target = vtarget comy,start +(comy,end −comy,start) � 1−(2t−1) 4��<br />
(5.18)<br />
The variables are defined similar to the trajectory approximation for forward velocity<br />
control. Figure 5.31 illustrates the resulting correction value. The dashed line in the left<br />
plot denotes the estimated comy values, the solid line the approximated trajectory.<br />
The postural reflex Lateral Balance Ankle uses the correction value to generate an ankle<br />
torque about the x-axis. Again, the absolute torque values are limited to maintain full<br />
ground contact <strong>of</strong> the foot. The resulting inversion or eversion <strong>of</strong> the foot can only produce<br />
a small correction motion as the leverage <strong>of</strong> toes and heel in y-direction is relatively short.<br />
Nevertheless the reflex provides a small amount <strong>of</strong> lateral balance.<br />
Foot placement has much stronger influence on the movement <strong>of</strong> the center <strong>of</strong> mass in the<br />
sagittal plane. Similar to what is suggested by H<strong>of</strong> et al., the postural reflex Lateral Foot<br />
Placement (lfp) uses the correction value just described to adapt the hip angle during leg<br />
swing in motion phases four and five. As the leg influenced by the reflex is in its swing
112 5. <strong>Control</strong>ling Dynamic Locomotion <strong>of</strong> a Fully Articulated Biped<br />
phase, the com estimation relative to the opposite leg is considered for foot placement<br />
adaptation. The normalized hip angle ˆαhip, lfp passed to the joint controller amounts to<br />
ˆαhip x, lfp = ˆαhip x, normal +g ·σ ·Kcom ·(comy,target −comy) (5.19)<br />
where ˆαhip, normal denotes the hip angle for the undisturbed case, σ the change <strong>of</strong> sign due<br />
to the different directions <strong>of</strong> normalized hip angles <strong>of</strong> the left and right leg, Kcom a factor<br />
to translate the com error to a normalized angle change, and g a gradual activation <strong>of</strong> the<br />
angle correction rising from 0 to 1 to prevent a jerky movement <strong>of</strong> the leg at the start <strong>of</strong><br />
its swing phase. The reflex activity indicating both the behavior influence and desired<br />
joint stiffness quickly rises with an increasing correction value to enforce the adjustment<br />
<strong>of</strong> the foot placement.
6. Implementation <strong>of</strong> <strong>Bipedal</strong><br />
<strong>Walking</strong> <strong>Control</strong><br />
To validate the suggested control concept and its application to dynamic walking and<br />
standing as described in the previous chapters, it is implemented as control system for<br />
a simulated biped. The simulation environment must support the dynamics calculation<br />
<strong>of</strong> the robot and its interaction with the environment. As already mentioned before, the<br />
bipedal robot has to show some properties <strong>of</strong> human morphology, muscles, and perception.<br />
This chapter will introduce the test environment as well as the biped model and its features.<br />
Some aspects <strong>of</strong> the implementation <strong>of</strong> the control system are discussed.<br />
6.1 Simulation Environment<br />
As this thesis focuses on the control <strong>of</strong> bipedal walking, it cannot also provide a concept<br />
for a suitable mechanical construction and actuation system. But while the design <strong>of</strong> a<br />
biped with human-<strong>like</strong> properties is subject to current research activities, there still is<br />
no satisfactory solution for this problem. To nevertheless validate the suggested control<br />
approach, it is implemented and tested within a simulation environment. In doing so, the<br />
essential features for the functioning <strong>of</strong> the biologically inspired control can be provided<br />
without the need <strong>of</strong> a mechanical implementation. Still, attention is paid to the fact that<br />
the simulated biped should potentially be realizable as a prototype. Additional information<br />
on the simulation environment can be found in Appendix B, preliminary studies to this<br />
topic can be found in [Chiderova 05, Lamp 05, Gilsdorf 06].<br />
6.1.1 Embedding the Physics Engine<br />
The control system and simulation <strong>of</strong> this work is implemented using the framework<br />
mca2 (modular controller architecture) 1 [Scholl 02]. Its basic control entities are modules<br />
featuring an interface <strong>of</strong> control and sensor inputs and outputs. Modules are connected<br />
by edges transferring processed data between their interfaces. Additionally, a blackboard<br />
1 The RRLab version <strong>of</strong> mca2 can be downloaded at http://rrlib.cs.uni-kl.de
114 6. Implementation <strong>of</strong> <strong>Bipedal</strong> <strong>Walking</strong> <strong>Control</strong><br />
mechanism allows the exchange <strong>of</strong> larger data objects without the need <strong>of</strong> edges. Modules<br />
can be subsumed in groups that feature the same interface as modules. The interconnection<br />
<strong>of</strong> modules and groups defines a control hierarchy <strong>of</strong> layers and the order in which their<br />
processing methods are called during the control cycle running with a fixed timing.<br />
The behavior-based framework iB2C is also implemented within mca2. Each behavior<br />
is represented by a module, the behavior signals and the input and output vectors are<br />
transferred via edges. mca2 comes with an extensive tool set to support the developing<br />
process. In particular, the behavior-based design is assisted by visualization and debugging<br />
tools, e.g. the mcabrowser allows to show the flow <strong>of</strong> stimulation and activity between<br />
behaviors during runtime.<br />
mca2 already provides a library called SimVis3D for the simulation and visualization <strong>of</strong><br />
robots and their environment [Braun 07]. Its visualization part is based on Coin3D 2 , a free<br />
implementation <strong>of</strong> the OpenInventor standard. SimVis3D features a comfortable way to<br />
define the simulation scene via a description file, dynamic object management, separation<br />
<strong>of</strong> simulation and visualization, and <strong>of</strong>fers support for various sensor systems <strong>like</strong> cameras<br />
or laser range finders.<br />
In the scope <strong>of</strong> this work, SimVis3D has been supplemented with dynamical simulation<br />
capabilities. To achieve this, two possible methods are possible: either the dynamics<br />
equation can be derived manually for each robot, or a physics engine can be used that<br />
automates this process. While the first approach allows to describe more specialized<br />
models, the second approach has been chosen due to its versatility. Furthermore, changes<br />
<strong>of</strong> the model can be transferred straightforward to the simulation without the need to<br />
re-derive the equations <strong>of</strong> motion. The free Newton physics engine 3 used in this work is<br />
developed by Julio Jerez. Its main advantages are easy adaptability by a function callback<br />
mechanism, the possibility to extract various information <strong>like</strong> acting forces or torques,<br />
and a flexible universal joint implementation system. Newton’s penalty-based contact<br />
calculation features adjustable elasticity, s<strong>of</strong>tness, and coulomb-<strong>like</strong> static and kinetic<br />
frictions. These parameters can be defined for each pair <strong>of</strong> materials.<br />
To embed the physics engine into the simulation environment, the so-called elements <strong>of</strong><br />
SimVis3D are used. In contrast to parts that define the visualization <strong>of</strong> objects, elements<br />
provide the means to insert sensors or other specialized entries into the scene description<br />
graph. In the context <strong>of</strong> the physics engine, three new types <strong>of</strong> elements are defined:<br />
static physical objects, dynamic objects, and joints. Physical objects define the association<br />
between the visualization parts and colliding objects within the physical simulation. Static<br />
objects describe the environment, they only need to provide a collision geometry and a<br />
material type, and are assumed to be unmovable and to have infinite mass. Dynamic<br />
objects will move within the environment, and therefore a transformation matrix node is<br />
added to the scene graph. During run-time, this matrix is modified by the physics engine<br />
to set the pose <strong>of</strong> the visual object. Besides their collision geometry, dynamic objects<br />
additionally are defined by a mass and a material changing the contact interaction between<br />
objects. It is assumed that the mass is distributed evenly within the collision geometry<br />
and an inertia tensor is calculated accordingly.<br />
2 http://www.coin3d.org<br />
3 http://www.newtondynamics.com
6.1. Simulation Environment 115<br />
axis <strong>of</strong> rotation<br />
motor<br />
series spring<br />
segment i segment i+1<br />
parallel spring<br />
Figure 6.1: The layout <strong>of</strong> the simulated joint is assumed as a combination <strong>of</strong> a motor, a series<br />
spring, and a parallel spring.<br />
A third element type is used to add joints to the simulation model. Each joint defines<br />
constraints acting between two objects. Besides several standard joint types, Newton <strong>of</strong>fers<br />
so called universal joints to allow a high flexibility in joint design. Using the universal<br />
joint type, six constraints for the three linear and the three rotational motions between<br />
two objects can be specified. These constraints can either detain the movement along<br />
respectively about the corresponding axis, or induce an acceleration or torque on the<br />
two connected objects. This enables the implementation <strong>of</strong> loopback control mechanisms.<br />
In addition it is possible to read the force or torque that is necessary to maintain each<br />
constraint. Appendix B gives further details on the implementation <strong>of</strong> the simulation<br />
environment and presents an example <strong>of</strong> the scene description file.<br />
6.1.2 Actuators and Joint <strong>Control</strong><br />
In accordance to the system premises discussed in Section 5.1, a suitable model for joint<br />
actuation needs to be simulated. Its main characteristics are adjustable compliance,<br />
ranging from freely moving to high stiffness, an additional parallel elastic element, and<br />
direct torque control as well as position control. All joints used in the biped model <strong>of</strong> this<br />
work are revolute joints, i.e. rotational joints with five <strong>of</strong> their six degrees <strong>of</strong> freedom fixed.<br />
The ball joints <strong>of</strong> hip and spine and the ankle joints are simulated by a concatenation <strong>of</strong><br />
these revolute joints.<br />
The principle <strong>of</strong> the joint design suggested for the simulation is illustrated in Figure 6.1.<br />
The joint connects two robot segments i and i+1. In series with a revolving motor an<br />
elastic element with adjustable stiffness connects to the actuated axis. Another spring<br />
with fixed stiffness and constant equilibrium point is attached in parallel.<br />
Figure 6.2 presents the torque calculation used for implementing the constraint <strong>of</strong> the<br />
joint’s rotational degree <strong>of</strong> freedom. The controller receives a target torque τtarget and a<br />
target angle αtarget as inputs. Following the ideas <strong>of</strong> the behavior-based architecture iB2C,<br />
each input value is complemented by a stimulation value. The stimulation sτ is used to<br />
scale the target torque, thus only control units with full activity can generate the maximum<br />
torque output. For the position control part, sα is interpreted as stiffness. If the position<br />
controller is stimulated less, the compliance <strong>of</strong> the joint will be higher. This behavior is
116 6. Implementation <strong>of</strong> <strong>Bipedal</strong> <strong>Walking</strong> <strong>Control</strong><br />
sτ<br />
τtarget<br />
sα<br />
αtarget<br />
−<br />
Limit P P<br />
α<br />
α<br />
“compliance”<br />
˙αtarget<br />
−<br />
˙α<br />
τpos<br />
×<br />
×<br />
α0 = const.<br />
� wi<br />
sτ, sα<br />
Nonlinear<br />
Limit<br />
parallel spring<br />
damping<br />
P<br />
τspring<br />
τdamping<br />
τcontrol<br />
Figure 6.2: <strong>Control</strong> block diagram for the constraint <strong>of</strong> the rotational degree <strong>of</strong> freedom used<br />
for the simulated revolute joint.<br />
implemented by scaling the output τpos <strong>of</strong> the position control by the stimulation value.<br />
The controller itself is designed as a cascaded P-P control, with the outer position loop<br />
generating the target value ˙αtarget for the inner velocity loop. Resembling the iB2C fusion<br />
behaviors, the two torques resulting from the stimulation multiplication are combined by<br />
weighted summation, using the stimulation values as weights:<br />
τcontrol = sτ(τtargetsτ)+sα(τpossα)<br />
sτ +sα<br />
−<br />
−<br />
τ<br />
(6.1)<br />
This weighted sum is symbolized by � wi in Figure 6.2. The output <strong>of</strong> the loopback<br />
control part is given as τcontrol and limited by the maximum torque <strong>of</strong> the simulated motor.<br />
The parallel elasticity as it is found in the biological muscle is modeled as nonlinear spring.<br />
Given the constant equilibrium position α0 <strong>of</strong> the spring and the current joint angle α, the<br />
resulting torque is calculated as<br />
τspring = sgn(α0 −α)·Kspring ·(α0 −α) 2 . (6.2)<br />
with Kspring being the spring constant. Despite the fact that damping is nearly absent<br />
in biological joints, it is by all means present for technical systems. Thus, an additional<br />
torque τdamping proportional to the joint’s rotational velocity is calculated. All three torque<br />
values τcontrol, τspring, and τdamping are then combined and used as the acting torque τ for<br />
the rotational constraint <strong>of</strong> the simulated joint.<br />
This joint setup allows to create various joint behaviors as needed by the biologically<br />
motivated control concept. If both stimulation values sτ and sα are set to zero, the joint<br />
can rotate freely except for the parallel spring and the damping. Setting the position<br />
stimulation to zero, a direct torque command can be implemented. With sα > 0, an elastic,
6.1. Simulation Environment 117<br />
(a) (b)<br />
Figure 6.3: (a) Joint construction with (from top to bottom) the motor, the gearbox, and the<br />
gas spring highlightened. (b) Monopod prototype attached to a vertical slider.<br />
passive joint action with the given equilibrium point αtarget is achieved. As described<br />
below, precedence <strong>of</strong> the torque command over the position command is guaranteed by an<br />
adequate layer <strong>of</strong> fusion behaviors.<br />
In the antagonistic setup <strong>of</strong> two muscle group acting on a human joint, information on<br />
the current status <strong>of</strong> the joint is perceived by the muscle spindles, the golgi tendon organ,<br />
the pacinian corpuscle, the Ruffini endings, and the surrounding skin. The joint used in<br />
this simulation emits the current joint angle and the torque acting in the joint as sensor<br />
information. Both values can be extracted from the physics engine. In a real robotic joint,<br />
the current angle can be measured by e.g. encoders. The torque can be captured by using<br />
a load cell. Given an appropriate loopback control, the torque can also be derived by<br />
measuring the motor current, but then a low ration gear is necessary. Otherwise, external<br />
forces would not be transferred to the motor.<br />
In the scope <strong>of</strong> this work, some consideration has also been put towards the development <strong>of</strong><br />
an actuator implementing the characteristics just described [Luksch 05, Luksch 07]. The<br />
preliminary prototype follows the joint layout presented in Figure 6.1. A dc motor with<br />
disc-shaped rotor is used as main actuator. The serial elastic element is omitted in the<br />
first prototype. Instead, active compliance is implemented by a suitable controller similar<br />
to the one presented above [Wahl 09, Blank 09b]. A low friction gear box with a ratio <strong>of</strong>
118 6. Implementation <strong>of</strong> <strong>Bipedal</strong> <strong>Walking</strong> <strong>Control</strong><br />
(a) (b)<br />
Figure 6.4: (a) Inertial measurement unit, and (b) three-axis load cell developed at the Robotics<br />
Research Lab.<br />
1:32 still allows the joint to move freely. In total, the setup can produce a peak torque <strong>of</strong><br />
more than 150Nm. Figure 6.3a depicts the resulting joint construction, with the main<br />
components marked in red.<br />
In the first setup <strong>of</strong> the prototype joint, the parallel spring is designed as a novel rotatory<br />
gas spring [Flörchinger 05]. By changing the volume being compressed by the rotating<br />
piston, the stiffness <strong>of</strong> the spring would be adaptable. Also, the elasticity would be<br />
nonlinear as in biological muscles. Unfortunately, the construction turned out to be very<br />
difficult to manufacture. Remaining air leaks permit to produce the desired torque. Thus<br />
the gas spring is complemented by a conventional linear coil spring that is stretched during<br />
the flexion <strong>of</strong> the joint.<br />
Using this actuator, the monopod prototype shown in Figure 6.3b is developed [Roth 08,<br />
Schumann 08]. The active hip and knee joints allow the robot to jump on the spot. The<br />
upper body is guided by a passive linear slider to neglect the problem <strong>of</strong> stabilization. The<br />
setup is intended for the evaluation <strong>of</strong> the joint construction and the controller in a highly<br />
dynamic task. For more details on this ongoing research, please refer to the cited papers.<br />
While the presented actuator is still under development and not implementing all features<br />
preferable for the suggested control concept, it at least shows that the design <strong>of</strong> such an<br />
actuator should be possible.<br />
6.1.3 Simulation <strong>of</strong> Sensors<br />
Similar to the joint actuation, a suitable sensor setup must be provided by the simulation<br />
framework. Senses necessary for the suggested control system include a sense <strong>of</strong> balance,<br />
load perception, and cutaneous sensor information <strong>of</strong> the foot soles. These senses are<br />
implemented as inertial measurement unit (imu), load cells, and force sensors in the feet.<br />
To stay as close as possible to real sensor systems, the imu and the load cell developed at<br />
the Robotics Research Laboratory were modeled (see Figure 6.4).<br />
The imu is able to measure three linear accelerations and three rotational velocities. To<br />
model the functionality <strong>of</strong> the imu within the simulation, an object <strong>of</strong> known mass is
6.1. Simulation Environment 119<br />
Joint min. angle [rad] max. angle [rad] max. torque [Nm]<br />
Spine X -1.0 1.0 180<br />
Spine Y -1.0 1.0 180<br />
Spine Z -1.0 1.0 100<br />
Shoulder X left 0.0 2.0 80<br />
Shoulder X right -2.0 0.0 80<br />
Shoulder Y -1.0 1.0 80<br />
Elbow Y -2.0 0.0 30<br />
Hip X -1.0 1.0 220<br />
Hip Y -0.85 0.15 220<br />
Hip Z -1.0 1.0 150<br />
Knee Y 0.0 2.0 150<br />
Ankle X -0.5 0.5 80<br />
Ankle Y -0.5 0.5 150<br />
Table 6.1: Minimum and maximum angles and the maximum torque for all degrees <strong>of</strong> freedom<br />
<strong>of</strong> the simulated biped.<br />
attached to the mount point <strong>of</strong> the imu by a joint fixing all six degrees <strong>of</strong> freedom. The accelerations<br />
are calculated by dividing the forces necessary to maintain the linear constraints<br />
by the objects mass. This method is similar to the working <strong>of</strong> real microelectromechanical<br />
acceleration sensors using a small suspended mass and measuring its deflection via a change<br />
<strong>of</strong> capacitance. The rotational velocities can be calculated by transforming the velocities<br />
<strong>of</strong> the imu object provided by the physics engine to the current coordinate system <strong>of</strong> the<br />
imu.<br />
Similar to the imu, the load cell is implemented by a fixed joint attached between two<br />
robot segments. The load cell shown in Figure 6.4b measures the force in z-direction and<br />
the torque about the x- and y-axis. These values <strong>of</strong> interest can directly be read from<br />
the physics engine as it provides the forces and torques produced to preserve the joint<br />
constraints. The force sensors placed within the foot soles are <strong>of</strong> equal design, only they<br />
just return the force in one direction and no torque values.<br />
6.1.4 Model <strong>of</strong> Simulated Biped<br />
Deploying the joint actuation and sensors just described, the model for the simulated biped<br />
can be designed. The kinematic layout corresponds to the compromise <strong>of</strong> joint selection<br />
described in Section 5.1. The ball joints mentioned there are implemented as chained<br />
revolute joints. Table 6.1 summarizes the range <strong>of</strong> movement and the maximum torques<br />
for each joint. Segment lengths and masses are similar to what can be found in human<br />
subjects. Masses were taken from Table 3.2, but in contrast to human segments made <strong>of</strong><br />
bone, muscle, and tissue, the mass distribution is assumed to be uniform for reasons <strong>of</strong><br />
simplicity. In total, the number <strong>of</strong> degrees <strong>of</strong> freedom amounts to 21, the robot’s weight<br />
adds up to 76kg, and its overall height is 1.8m. Details on the exact masses and the<br />
placement <strong>of</strong> all segments can be found in Appendix B where the scene description file for<br />
the robot setup and the environment is given.
120 6. Implementation <strong>of</strong> <strong>Bipedal</strong> <strong>Walking</strong> <strong>Control</strong><br />
(a)<br />
z<br />
x y<br />
Figure 6.5: (a) Simulated biped as visualized by the simulation framework. (b) Joint layout <strong>of</strong><br />
the biped model. The hip and spine joints are modeled by three, the shoulder and ankle joints as<br />
two subsequent revolute joints.<br />
Figure 6.5 illustrates the visualization and the joint layout <strong>of</strong> the biped model. The<br />
coordinate system depicts the direction <strong>of</strong> the axes, namely the x-axis pointing in walking<br />
direction, the y-axis pointing sidewards to the left, and the z-axis pointing upwards,<br />
respectively. The visible shapes correspond to the collision geometries used by the physics<br />
engine. The trunk and pelvis are modeled in such a way that the center <strong>of</strong> mass is located<br />
slightly in front <strong>of</strong> the hip joints. Similarly, the head position is shifted in x-direction. This<br />
position <strong>of</strong> the center <strong>of</strong> mass facilitates the forward motion while walking, in particular<br />
during the stance phase as the trunk travels over the supporting foot.<br />
In contrast to the vestibular system located in the human head, the inertial measurement<br />
unit is attached to the pelvis <strong>of</strong> the biped model. This has the advantage <strong>of</strong> circumventing<br />
the oscillation <strong>of</strong> the upper body, facilitating the stabilization <strong>of</strong> the pelvis. Knowing the<br />
angles <strong>of</strong> the spine joint, the trunk can still be balanced at an upright pose.<br />
The foot geometry is shown as a close-up in Figure 6.6. The white-colored part between<br />
the ankle joint and the actual foot represents the load cell. It measures the force acting in<br />
z-direction and the torques about the x- and y-axis. The elliptical shape <strong>of</strong> the toe objects<br />
allows the foot to roll over the ground during push-<strong>of</strong>f, creating a behavior similar to the<br />
bending <strong>of</strong> the forefoot and the toes. This geometry can save an additional joint in the<br />
foot. Each <strong>of</strong> the round toe and heel objects is attached to the central foot object by a<br />
fixed joint measuring the force acting in z-direction. By knowing these four load values for<br />
each foot, the center <strong>of</strong> pressure can be estimated. The force sensors in the feet correspond<br />
to the cutaneous perception found in the human foot.<br />
(b)
6.2. Notes on the Implementation 121<br />
Figure 6.6: Shape <strong>of</strong> the foot model allowing to roll over the toes.<br />
6.2 Notes on the Implementation<br />
As mentioned above, the control concept postulated in this work is implemented within<br />
the behavior-based architecture iB2C and the robot control framework mca2. Both <strong>of</strong><br />
these systems <strong>of</strong>fer special features, but also pose certain restrictions on the design. Some<br />
<strong>of</strong> the resulting decision necessary during the development process will be discussed in the<br />
following.<br />
6.2.1 Group Layout and Phase Representatives<br />
As illustrated in Figure 6.7, the control and simulation system is arranged within three<br />
main groups. The mca2 framework executes all processing and data transportation<br />
routines <strong>of</strong> these groups and the contained modules once for each control cycle. For the<br />
experiments done in this work, this cycle runs at 40Hz. This results in a delay time for<br />
reflex action <strong>of</strong> at least 25ms, thus the control system has to manage similar dead times<br />
as found in neural pathways. The group gSimulation contains the modules responsible<br />
for the dynamical simulation and the three-dimensional visualization <strong>of</strong> the current scene.<br />
The iteration step size for the dynamics calculation is set to 1ms, resulting in 25 iterations<br />
per control cycle. As the low level joint controller described above is embedded within the<br />
physics simulation cycle, it also runs at 1kHz.<br />
The interface <strong>of</strong> the simulation group is designed in a way to enable its replacement by<br />
a real robot. The control interface is composed <strong>of</strong> the inputs for the joint controllers,<br />
i.e. the target torque and position as well as the two corresponding stimulation values.<br />
On its sensor side, the simulation provides the current joint positions and torques, the<br />
accelerations and velocities measured by the inertial measurement unit, and the forces and<br />
torques measured by the load cells. To abstract from actual limits <strong>of</strong> joint angles, motor<br />
torques, or sensor information, the gAbstractionLayer group introduces a normalization<br />
layer between the simulation and the control system.<br />
The group gBiped<strong>Control</strong> contains the control system as described in the previous chapter.<br />
Its control units are distributed to six groups: the locomotion modes are located within<br />
the brain group, the spgs and the postural reflexes within the spinal cord group. As local<br />
reflexes and motor patterns only act on a few joints and do not receive sensor information<br />
from other parts <strong>of</strong> the robot, they can be separated in four joint groups for the upper<br />
and lower trunk and the legs.
122 6. Implementation <strong>of</strong> <strong>Bipedal</strong> <strong>Walking</strong> <strong>Control</strong><br />
gBiped<strong>Control</strong><br />
gAbstractionLayer<br />
gSimulation<br />
(a)<br />
gBiped<strong>Control</strong><br />
gBrain<br />
gSpinalCord<br />
gUpperTrunk gLowerTrunk gLeftLeg gRightLeg<br />
Figure 6.7: (a) Main layout <strong>of</strong> the control and simulation system. (b) The control units are<br />
arranged within six groups. The four joint groups at the lower end contain the motor interface.<br />
The motion phases are located in the spinal cord group. But to improve clarity, to reduce<br />
communication bandwidth and interface complexity, and to increase local coherence, a<br />
representative <strong>of</strong> each motion phase is introduced in each joint group. These units are<br />
stimulated by their counterpart in the spinal cord and again manage the stimulation <strong>of</strong><br />
local reflexes and motor patterns <strong>of</strong> their joint group. They also set the compliance and<br />
equilibrium point for the passive joints.<br />
6.2.2 Application <strong>of</strong> iB2C Features<br />
The joint groups also contain the interface to the joint controllers in form <strong>of</strong> iB2C fusion<br />
behaviors. They provide the means to coordinate concurrent access to the same joint<br />
by several control units. Only units <strong>of</strong> the classes motion phase, postural reflex, motor<br />
pattern, and local reflex generate control commands for the joints, with motion phases<br />
only setting a fixed equilibrium point and compliance. As a behavior’s activity signal is<br />
used for calculating its influence during the fusion, only control units stimulated by the<br />
active motion phase will be considered.<br />
Two different fusion methods are applied for the joint interface: position commands are<br />
fused by the weighted average method, thereby finding a compromise between the joint<br />
angle demands <strong>of</strong> active control units. Torque commands are combined by the weighted<br />
sum function. As the target torque for a joint roughly corresponds to muscle activity,<br />
several possible torque demands are added up as a motor neuron would add up neural<br />
activity. The resulting torque command must be limited as it can extend the maximum<br />
value.<br />
Figure 6.8 illustrates the behavior-based joint control interface using the example <strong>of</strong> the<br />
leg groups. The left and right leg group each manage the knee and the two ankle joints.<br />
For each <strong>of</strong> the group’s joints, two fusion behaviors are inserted, one being responsible<br />
for position, the other for torque commands. The torque fusion behavior inhibits the<br />
position fusion behavior using its activity. This design decision is based on the assumption<br />
that control units generating torque commands have higher priority than those providing<br />
(b)
6.2. Notes on the Implementation 123<br />
Motor Pattern<br />
(F) Knee<br />
Torque<br />
sτ,knee<br />
ˆτknee<br />
(F) Knee<br />
Position<br />
sα,knee<br />
ˆαknee<br />
Local Reflex<br />
(F) Ankle X<br />
Torque<br />
sτ,ankle x<br />
ˆτankle x<br />
(F) Ankle X<br />
Position<br />
sα,ankle x<br />
ˆαankle x<br />
(F) Ankle Y<br />
Torque<br />
sτ,ankle y<br />
ˆτankle y<br />
(F) Ankle Y<br />
Position<br />
sα,ankle y<br />
ˆαankle y<br />
Figure 6.8: Interface to joint controllers implemented as layer <strong>of</strong> fusion behaviors. Precedence<br />
<strong>of</strong> torque fusion is achieved by inhibiting edges.<br />
position and stiffness commands. This also agrees to the suggested design guideline that<br />
torque control should be preferred to position control.<br />
Each fusion behavior forwards the resulting control value and its activity to the joint<br />
controllers described above. The normalized torque and angle commands ˆτi and ˆαi are<br />
scaled to effective values while passing the abstraction layer. The activity <strong>of</strong> the torque<br />
fusion behavior serves as stimulation sτi for the torque part <strong>of</strong> the controller, <strong>like</strong>wise the<br />
activity <strong>of</strong> the position fusion behavior is used as stimulation sαi<br />
for the position part. As<br />
the fusion behavior’s activity results from the activity <strong>of</strong> the connected control units, these<br />
units can use their own activity signal to influence the desired compliance or to scale the<br />
effective torque value.<br />
The activity <strong>of</strong> motor patterns is based on the sigmoid function used to calculate the<br />
torque output. Similar to Equation 5.7, the signal is depending on the three parameters<br />
describing the temporal progress <strong>of</strong> the torque value, only a factor for scaling the amplitude<br />
is missing as the activity will always rise up to the reflex activation ι and fall back to zero:<br />
⎧<br />
1 1 t 1 ⎪⎨ + sin( π( − ) ) 0 ≤ t < T1<br />
2 2 T1 2<br />
a = ι· 1 T1 ≤ t < T2<br />
⎪⎩ 1 1 t−T2 1 − sin( π( − 2 2 T3−T2 2 ) ) T2<br />
(6.3)<br />
≤ t ≤ T3<br />
In contrast to the uniform activity <strong>of</strong> motor patterns, the activity <strong>of</strong> postural and local<br />
reflexes depends on sensory information. For instance, the postural reflex Upright Trunk<br />
calculates a normalized hip torque ˆτhip to balance the upper body based on the trunk<br />
pitch angle and its velocity. The activity signal <strong>of</strong> this reflex is derived from the output<br />
torque, but is then scaled by the normalized ground contact value ˆ Fz ∈ [0,1] measured by<br />
the force sensors:<br />
a = ι·|ˆτhip|· ˆ Fz<br />
(6.4)
124 6. Implementation <strong>of</strong> <strong>Bipedal</strong> <strong>Walking</strong> <strong>Control</strong><br />
This ensures that the activity decreases with the load on the stance leg as torque applied<br />
to the hip joint can only act on the upper body if the leg is firmly connected to the ground.<br />
The multiplication by the reflex activation ι corresponds to the iB2C principle stating that<br />
the activity <strong>of</strong> a behavior must never exceed it activation. As activity signals are used to<br />
stimulate other behaviors, this principle guarantees a limitation <strong>of</strong> the activity throughout<br />
the behavior network.<br />
This principle is also obeyed by the activity calculation <strong>of</strong> the motion phase control<br />
units. As described in Chapter 4, these units are responsible for stimulating the motor<br />
patterns and reflexes being active during the respective phase <strong>of</strong> motion, and for setting<br />
the compliance and equilibrium points <strong>of</strong> the passive joints. As just described, setting<br />
the stiffness <strong>of</strong> a joint corresponds to the appropriate stimulation <strong>of</strong> the associated fusion<br />
behavior. Thus stimulating a reflex or motor pattern and setting a joint compliance<br />
functions by the same mechanism. Consequentely it is possible to implement all motion<br />
phases as instance <strong>of</strong> the same behavior class called mbbStimulationBehavior. Each<br />
behavior or joint k controlled by the motion phase is registered by passing a stimulation<br />
factor fs,k along with a possible modulation value or equilibrium point. The activity <strong>of</strong><br />
the motion phase itself is simply set to its activation (a = ι), but the stimulation signal a k<br />
used for the controlled units is calculated as<br />
a k = a·fs,k. (6.5)<br />
By setting fs,k <strong>of</strong> a passive joint to zero, it is allowed to move freely during the motion<br />
phase, only the passive elastic element and external forces will influence its action. A<br />
factor fs,k > 0 results in compliant joint behavior around its equilibrium point. Setting<br />
fs,k <strong>of</strong> a motor pattern or reflex to a value smaller than one will restrict its influence in the<br />
control network during this motion phase. The actual compliance for each joint during all<br />
motion phases <strong>of</strong> walking will be given in Chapter 8 when discussing passive joint action<br />
during normal walking.<br />
The target ratings <strong>of</strong> the control units do not play as crucial a role as their activity. Still,<br />
an analysis <strong>of</strong> the target rating can be used during implementation and testing to better<br />
understand the working <strong>of</strong> the behaviors in a given situation. For this purpose, the target<br />
rating should have a meaningful value representing the contentment <strong>of</strong> the behavior. To<br />
continue the above example <strong>of</strong> the postural reflex Upright Trunk, its target rating r is<br />
given as<br />
r = min(1,|φ−φtarget|) (6.6)<br />
with φ being the current body pitch angle in radians and φtarget the target pitch angle<br />
depending on the desired walking velocity. This kind <strong>of</strong> target rating calculation allows to<br />
interpret the state <strong>of</strong> the robot regarding the goal <strong>of</strong> an individual control unit.<br />
A further use <strong>of</strong> the target rating is its application as pre-processed sensor value. This<br />
method can reduce the extend <strong>of</strong> sensor information that must be passed to higher control<br />
levels. An example for this kind <strong>of</strong> usage will be given below, where the target rating<br />
<strong>of</strong> the Lock Knee reflex serves as indication for switching the state <strong>of</strong> the cyclic walking<br />
spinal pattern generator.
7. Balanced Standing Experiments<br />
Before discussing the performance <strong>of</strong> the implemented control system during dynamic<br />
walking, this chapter will present its capability for stable standing [Steiner 08]. Several<br />
experiments will demonstrate different aspects <strong>of</strong> the control introduced in Section 5.3.<br />
The adaptation to different ground geometries becomes apparent when letting the robot<br />
fall on inclined terrain or steps. The control <strong>of</strong> joint stiffness can be observed by applying<br />
external forces to body segments during standing or by moving the platform the robot<br />
is standing on. Posture optimization takes place after ground contact, when tilting the<br />
ground platform, or in case the robots mass distribution changes, e.g. by adding weight to<br />
a backpack mounted on the robot. Some <strong>of</strong> these experiments are inspired by studies on<br />
human postural control.<br />
The setup used for the following experiments is composed <strong>of</strong> the robot standing on or<br />
falling on a square plate with an edge length <strong>of</strong> 1m. The plate can be moved along and<br />
rotated about all three axis to apply disturbances. Additionally, arbitrary forces can be<br />
deployed to individual body segments. Sequences <strong>of</strong> platform motions or external forces<br />
can be programmed and executed automatically to generate repeatable runs.<br />
7.1 Adaptation to the Ground Geometry<br />
In order to test the ground adaptation capabilities <strong>of</strong> the standing control, the robot<br />
is dropped from a height <strong>of</strong> about 20cm on different ground geometries as exemplified<br />
in Figure 7.1. The actual shape <strong>of</strong> the terrain is unknown to the control system. The<br />
adaptation relies on the initially moderate compliance in most joints and on the high<br />
compliance <strong>of</strong> the ankle joints. This strategy enables a passive matching to the ground<br />
geometry. Then, high joint stiffness is used to stabilize the posture.<br />
Figure 7.2 illustrates the control behavior during a drop on sloped ground. The platform<br />
the robot is landing on is inclined by 6 ◦ about the y-axis. In fact, the robot remains stable<br />
at inclinations <strong>of</strong> up to 30 ◦ , but the parallel springs <strong>of</strong> the ankle joints act with increasing<br />
torque and the joint relaxing phase cannot be observed anymore.<br />
While still in the air, the spinal pattern generator for stable standing stimulates the first<br />
phase called Ground Adaptation. The local Hold Position reflexes are stimulated, but the
126 7. Balanced Standing Experiments<br />
(a) (b) (c) (d)<br />
Figure 7.1: Experiment on ground geometry adaptation. The robot is dropped from about<br />
20cm height on sloped ground with both feet (a,b) and on a step with just the toes <strong>of</strong> one foot<br />
(c,d), then the posture is stabilized.<br />
stiffness modulation factor is zero. The activity <strong>of</strong> the reflexes is medium for most joints<br />
and near zero for the ankle joints as shown on the lower right side <strong>of</strong> the figure. As the<br />
reflexes connect to the position fusion nodes, their activity is interpreted as joint stiffness,<br />
resulting in compliant ankles.<br />
At point in time t1 the robot touches the ground, easily recognizable by the force peak in<br />
z-direction measured by the ankle load cells. In the short time interval until full contact,<br />
the joints passively adapt to the ground shape, with the major adaptation taking place<br />
in the ankle joint. As seen in the lower left plot, the ankle compensates for most <strong>of</strong> the<br />
6 ◦ <strong>of</strong> ground inclination. With full foot contact at t2, the standing spg switches to the<br />
stabilization phase. The stiffness factor increases to one in order to brace the joints at<br />
their current angles. With the raising activity <strong>of</strong> the Hold Position reflexes, the position<br />
control stabilizes the joint angles.<br />
As the taken stance is relatively steady, i.e. no strong accelerations are measured, the<br />
spg directly moves on to the next phase trying to optimize the posture. This phase<br />
will be described in detail below, but Figure 7.2 exemplary shows the activity <strong>of</strong> the<br />
postural reflex Relax Spine Y to clarify the processes during stable standing. The posture<br />
optimization causes minor joint movements resulting in accelerations recorded by the<br />
inertial measurement unit (imu). As soon as the joint torques have reached a lower<br />
threshold at t3, the Relaxed Posture phase is entered. The stiffness factor is reduced,<br />
resulting in lower activity <strong>of</strong> the Hold Position reflexes and thus in higher joint compliance.<br />
7.2 External Forces and Platform Movements<br />
The stabilization phase <strong>of</strong> the standing control mainly relies on passing favorable joint<br />
position and high stiffness values to the joint controllers. This results in a stance stabilization<br />
similar to the human ankle strategy. Two kind <strong>of</strong> experiments will validate the
7.2. External Forces and Platform Movements 127<br />
Loadcell Force Z [kN]<br />
Acceleration [ m/s 2 ]<br />
Spine Y Angle [ ◦ ]<br />
Hip Y Angle [ ◦ ]<br />
Knee Angle [ ◦ ]<br />
Ankle Y Angle [ ◦ ]<br />
3.0<br />
2.0<br />
1.0<br />
0.0<br />
0.4<br />
0.2<br />
0.0<br />
2.0<br />
1.0<br />
0.0<br />
−1.0<br />
5.0<br />
4.0<br />
3.0<br />
t1t2 t3 t1t2 t3<br />
0.0 1.0 2.0 3.0 4.0<br />
0.0 1.0 2.0 3.0 4.0<br />
0.0 1.0 2.0 3.0 4.0<br />
2.0<br />
0.0 1.0 2.0 3.0 4.0<br />
7.0<br />
6.0<br />
5.0<br />
4.0<br />
0.0 1.0 2.0 3.0 4.0<br />
0.0<br />
−2.0<br />
−4.0<br />
−6.0<br />
0.0 1.0 2.0<br />
Time [s]<br />
3.0 4.0<br />
Stiffness Factor<br />
Relax Spine Y a<br />
Hold Pos. Spine Y a<br />
Hold Pos. Hip Y a<br />
Hold Pos. Knee a<br />
Hold Pos. Ankle Y a<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0 3.0 4.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0 3.0 4.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0 3.0 4.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0 3.0 4.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0 3.0 4.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0<br />
Time [s]<br />
3.0 4.0<br />
Figure 7.2: Experiment on ground geometry adaptation. t1: ground contact, t2: full contact,<br />
t3: joint relaxation.
128 7. Balanced Standing Experiments<br />
Figure 7.3: Experiment on stabilization against external forces. A force <strong>of</strong> 100N in direction <strong>of</strong><br />
the x-axis is applied to the head for 300ms. The arrow above the head indicates the acceleration<br />
measured by the imu.<br />
performance <strong>of</strong> this part <strong>of</strong> the control system. External forces are applied to different<br />
segments <strong>of</strong> the robot, and the platform it is standing on is moved horizontally. Both<br />
<strong>of</strong> these setups can frequently be found in studies on human balancing capabilities. The<br />
following analysis is limited to movements in the frontal plane. Lateral disturbances can<br />
be compensated more easily as the feet are placed side by side in normal stance.<br />
Figure 7.3 shows the setup during the application <strong>of</strong> an external force to the head segment.<br />
Beginning with a quiet stance, the force is pushing the robot forward. The resulting<br />
acceleration is visualized by the arrow above the robot’s head. The low compliance <strong>of</strong> the<br />
joints in the stabilization phase only allows for small joint movements before the robot is<br />
moving back to a stable posture.<br />
The results <strong>of</strong> a run applying an external force <strong>of</strong> 100N in x-direction to the head segment<br />
for 300ms are shown in Figure 7.4. The gray bar starting at t = 0.65sec is indicating<br />
the time span during which the force is effective. The impact <strong>of</strong> the force is clearly<br />
demonstrated by the acceleration in x-direction measured by the imu, or by the change <strong>of</strong><br />
the pitch angle <strong>of</strong> the torso as it is leaning forward.<br />
Before the external force is applied, the robot is standing in a relaxed posture and the<br />
spg is stimulating the fourth motion phase. This results in a low stiffness factor and<br />
moderately compliant joints. As soon as the disturbance is measured by the imu, the spg<br />
switches to the stabilization phase. The stiffness factor is pulled up and the compliance<br />
<strong>of</strong> the joint position control is reduced. The center <strong>of</strong> pressure moves to the front <strong>of</strong> the<br />
feet as the maximum leverage is applied to move the body back into an upright position.<br />
The plot marked“CoP Position”in Figure 7.4 indicates the movement <strong>of</strong> the center <strong>of</strong><br />
pressure. Being based on the four force measurement in each foot, a value <strong>of</strong> 1 denotes<br />
that all vertical force is shifted to the front <strong>of</strong> the foot, at a value <strong>of</strong> −1 it is located at<br />
the heels. A cop position <strong>of</strong> zero will occur if the center <strong>of</strong> pressure lies below the ankle<br />
joint, i.e. in case the system is statically balanced.<br />
Analysis <strong>of</strong> the arising torques <strong>of</strong> the spine, hip, knee, and ankle joints reveals the reaction<br />
<strong>of</strong> the joint controllers to the disturbance. As soon as the external force deflects the trunk,<br />
an opposite torque can be observed. The reaction is propagated with a small delay to the
7.2. External Forces and Platform Movements 129<br />
Accel. X [ m/s 2 ]<br />
Torso Pitch [ ◦ ]<br />
Spine Y Torque [Nm]<br />
Hip Y Torque [Nm]<br />
5<br />
0<br />
−5<br />
10<br />
0<br />
0.0 2.0 4.0 6.0<br />
−10<br />
0.0 2.0 4.0 6.0<br />
50<br />
0<br />
−50<br />
50<br />
0<br />
−50<br />
0.0 2.0 4.0 6.0<br />
0.0 2.0 4.0 6.0<br />
Time [s]<br />
Stiffness Factor<br />
CoP Position<br />
Knee Torque [Nm]<br />
Ankle Y Torque [Nm]<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0<br />
1.0<br />
0.0<br />
−1.0<br />
0.0 2.0 4.0 6.0<br />
50<br />
0<br />
−50<br />
50<br />
0<br />
−50<br />
0.0 2.0 4.0 6.0<br />
0.0 2.0 4.0 6.0<br />
Time [s]<br />
Figure 7.4: Experiment on stabilization against external forces. The gray bar marks the time<br />
interval <strong>of</strong> 300ms during which an external force <strong>of</strong> 100N is pulling the head segment forwards.<br />
Experiment Torque [Nm] Acceleration<br />
Force [N] Time [ms] spine y hip y knee ankle y x-axis [ m/s2] 1000 25 160 82 68 64 75.0<br />
100 300 57 30 37 50 7.6<br />
50 600 38 22 30 46 4.1<br />
25 ∞ 24 14 23 40 2.0<br />
−750 25 −130 −62 −61 −45 −57.0<br />
−70 300 −39 −22 −32 −35 −5.0<br />
−40 600 −30 −17 −30 −34 −2.9<br />
−25 ∞ −23 −14 −28 −34 −2.0<br />
Table 7.1: Experiment on stabilization against external forces. The columns give the maximum<br />
forces and the resulting accelerations at which the robot does still keep standing.
130 7. Balanced Standing Experiments<br />
Figure 7.5: Major muscle activity <strong>of</strong> human subjects during movements <strong>of</strong> the supporting<br />
platform. From [Ting 07], p302.<br />
joints more distant to the disturbance. The external force pulling at the head segment<br />
results in the robot standing solely on its toes. During this timespan, the lower joints have<br />
to support a larger amount <strong>of</strong> the machine’s weight, consequently the torque in the ankle<br />
joints is higher than in the other joints. The robot then shifts back and is again supported<br />
by the whole foot. After only a short oscillation, the posture is stabilized and the joint<br />
torques fall back to a low value.<br />
The control system can only handle disturbances up to a certain threshold. If the intensity<br />
<strong>of</strong> the external force is increased, the timespan for which this force may act without<br />
the robot falling down decreases, and vice versa. Table 7.1 lists some <strong>of</strong> these limits.<br />
The first two columns give the force value and the interval during which the force was<br />
applied. A negative force indicates that the head segment was pulled backwards. Small<br />
disturbances can be compensated continuously. The remaining columns list the resulting<br />
maximum torques and the maximum acceleration in x-direction measured during the<br />
corresponding experiment. As expected, stronger forces result in higher torques and<br />
accelerations. Disturbances pushing the robot backwards must not be as intense due to<br />
the shorter leverage <strong>of</strong> the foot on the heel side. Applying the force to other segments<br />
yields similar results. When pulling or pushing the pelvis segment, the sign <strong>of</strong> the spine<br />
torque changes because <strong>of</strong> the mass inertia <strong>of</strong> the upper body.<br />
A further series <strong>of</strong> experiments analyzes the control behavior at linear movements <strong>of</strong> the<br />
platform the robot is standing on. Similar to the studies on human subjects by Ting et al.<br />
(Figure 7.5), the platform is moved by about 12cm with a gradual acceleration in forward<br />
and backward direction [Ting 07].<br />
Figure 7.6 illustrates the reaction <strong>of</strong> the control system to a 12cm platform movement in<br />
forward direction accelerating to a maximum velocity <strong>of</strong> 0.25 m/s. The upper row outlines<br />
the platform motion, the gray bar denotes the time interval during which the platform<br />
is moving. The robot’s behavior basically resembles the one <strong>of</strong> the previously described<br />
experiments. As soon as the disturbance is perceived by the acceleration sensor, the joint
7.2. External Forces and Platform Movements 131<br />
Platform Vel. [ m/s]<br />
Accel. X [ m/s 2 ]<br />
Torso Pitch [ ◦ ]<br />
Spine Y Torque [Nm]<br />
Hip Y Torque [Nm]<br />
0.3<br />
0.2<br />
0.1<br />
0.0<br />
0.0 1.0 2.0 3.0 4.0<br />
5<br />
0<br />
−5<br />
5<br />
0<br />
−5<br />
50<br />
0<br />
−50<br />
50<br />
0<br />
−50<br />
0.0 1.0 2.0 3.0 4.0<br />
0.0 1.0 2.0 3.0 4.0<br />
0.0 1.0 2.0 3.0 4.0<br />
0.0 1.0 2.0<br />
Time [s]<br />
3.0 4.0<br />
Platform Pos. [m]<br />
Stiffness Factor<br />
CoP Position<br />
Knee Torque [Nm]<br />
Ankle Y Torque [Nm]<br />
0.15<br />
0.10<br />
0.05<br />
0.00<br />
0.0 1.0 2.0 3.0 4.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0 3.0 4.0<br />
1.0<br />
0.0<br />
−1.0<br />
0.0 1.0 2.0 3.0 4.0<br />
50<br />
0<br />
−50<br />
50<br />
0<br />
−50<br />
0.0 1.0 2.0 3.0 4.0<br />
0.0 1.0 2.0<br />
Time [s]<br />
3.0 4.0<br />
Figure 7.6: Experiment on stabilization against platform movement. The gray bar marks the<br />
time interval during which the platform is moving for 12cm at a maximum velocity <strong>of</strong> 0.25m/s.<br />
stiffness is raised to stabilize the posture. While the upper body sways backwards due<br />
to the platform acceleration, the center <strong>of</strong> pressure completely moves to the heel side<br />
<strong>of</strong> the feet. As the body swings forwards again during platform deceleration, the center<br />
<strong>of</strong> pressure moves to the toe and then levels out at its equilibrium point as the robot<br />
stabilizes.<br />
The joint torques correspond to the muscle activities observed by Ting in her experiments<br />
with human subjects (Figure 7.5). The main work is done by the tibialis anterior which
132 7. Balanced Standing Experiments<br />
Max. platform Torque [Nm] Acceleration<br />
velocity [ m/s] spine y hip y knee ankle y x-axis [ m/s2] 2.0 −110 −60 −65 −46 16.0<br />
1.0 −75 −45 −54 −44 11.0<br />
0.5 −24 −15 −31 −35 3.1<br />
0.25 −19 −12 −30 −35 2.6<br />
−2.0 115 62 62 60 −16.0<br />
−1.0 80 45 50 55 −11.0<br />
−0.5 33 20 30 45 −4.2<br />
−0.25 22 14 24 42 −3.0<br />
Table 7.2: Experiment on stabilization against forward and backward platform movement. The<br />
first column states the maximum platform velocity during a displacement <strong>of</strong> 12cm. The following<br />
columns list the maximum torques and x-acceleration during the respective experiment.<br />
is active throughout the disturbances. Similarly, Figure 7.6 shows the prominent torque<br />
<strong>of</strong> the ankle joint lasting until the robot sways forward due to platform deceleration.<br />
As in human subjects, the reaction <strong>of</strong> the distal muscles respectively joint actuators is<br />
increasingly delayed with the distance to the ankle joint. The knee, hip, and spine joints<br />
apply a torque to prevent the body from bending backwards. A <strong>like</strong>wise reaction can be<br />
observed in the activity <strong>of</strong> the quadriceps and abdominal muscles.<br />
<strong>Human</strong> subjects manage to compensate the disturbance with less sway <strong>of</strong> the upper<br />
trunk. As the center <strong>of</strong> mass displacement shown in Figure 7.5 illustrates, the body stays<br />
in a backward position and slowly moves back to an upright pose after the platform<br />
movement stops. The pitch angle <strong>of</strong> the robot’s torso visualizes the slight overreaction<br />
<strong>of</strong> the joint controllers due to strong movements <strong>of</strong> body masses. This also leads to the<br />
change <strong>of</strong> direction in joint torques after the platform motion, a reaction not visible in<br />
the corresponding muscles <strong>of</strong> human subjects. A less aggressively tuned controller would<br />
reduce the body sway, but would also decrease the maximum platform velocities that can<br />
still be stabilized. Furthermore, the experiment just described pushes the control systems<br />
to its limits. Slower platform movements result in considerably less overshooting <strong>of</strong> the<br />
upper body.<br />
After the robot has stabilized its posture again, the joint torques and the measured<br />
accelerations decline. As the remaining torques rest within the limits being accepted as<br />
optimized posture, the standing control system switches back to the relaxed posture phase<br />
and slowly decreases the joint stiffness.<br />
Asinthepreviousexperiment, aseries<strong>of</strong>runswithdifferentdisturbanceintensitieshasbeen<br />
performed. Table 7.2 lists the torques and accelerations occurring at forward and backward<br />
platform movement <strong>of</strong> different velocities. At the evaluated platform displacement <strong>of</strong><br />
12cm, the maximum forward velocity the robot can still compensate is about 2.0 m/s, the<br />
maximum backward velocity about 2.5 m/s. The difference stems from the longer foot<br />
leverage in toe direction, as most stabilization origins from ankle torque. With decreasing<br />
platform velocity, the observed ankle torque is only slightly reduced, whereas the reaction<br />
<strong>of</strong> the more distal joints strongly declines. This behavior can be explained by the fact<br />
that stronger platform motions induce greater displacement <strong>of</strong> the center <strong>of</strong> mass. This
7.3. Posture Optimization 133<br />
again results in greater body pitch angles and thereby in higher torque requirements for<br />
the joints closer to the center <strong>of</strong> mass.<br />
7.3 Posture Optimization<br />
A last series <strong>of</strong> experiments shall illustrate the behavior <strong>of</strong> the posture optimization control<br />
units. To this end, two different types <strong>of</strong> disturbances are applied to the robot: on the one<br />
hand, the platform the robot is standing on is rotated about the y-axis, on the other hand<br />
the robot is equipped with a backpack <strong>of</strong> changing weight. In both cases, the robot starts<br />
with an already optimized posture and has to adapt to the changing situation.<br />
Figure 7.7 shows the control behavior during a modification <strong>of</strong> the support surface. The<br />
platform the robot is standing on rotates at an angular velocity <strong>of</strong> 1.15 ◦ /s about the y-axis,<br />
i.e. it tilts forward. The rotation is stopped after three seconds at an angle <strong>of</strong> about 3 ◦ ;<br />
the time interval <strong>of</strong> the platform motion is marked by the gray bar. As the accelerations<br />
remain below the threshold for switching to the stabilization motion phase, the angle<br />
adjustments control units are continuously stimulated. The units only show activity if the<br />
robot is standing still, stronger motions induced by their own adjustments result in short<br />
intervals <strong>of</strong> inactivity. The two Relax Joint reflexes plotted in the figure try to reduce the<br />
torque acting in the corresponding joint, whereas the Balance Ankle Pitch reflex tries to<br />
keep the relative cop position shown in the upper right at its equilibrium point below the<br />
ankle joint. All three control units adjust the posture by passing an angle change rate to<br />
the appropriate Hold Position reflex.<br />
It can be observed that most <strong>of</strong> the change in angle and the highest reflex activity is<br />
accomplished in the ankle joint, compensating most <strong>of</strong> the rotation <strong>of</strong> the supporting<br />
platform. Additional adaptation is done in the hip and spine joints, the angle <strong>of</strong> the<br />
knee joint remains constant. In contrast to what could be expected, the sum <strong>of</strong> angle<br />
adjustments exceeds the amount <strong>of</strong> platform rotation. The posture assumed after the<br />
optimization is slightly shifted to the back. But actually, this posture is superior to the<br />
one with an upright trunk, as the rotation <strong>of</strong> the platform and thereby the rotation <strong>of</strong> the<br />
ankle joint shifts the cop in direction <strong>of</strong> the toes. This reduces the stability margin in<br />
forward direction and can be compensated by the observed backward recline.<br />
The second experiment on posture optimization deals with different weight distributions <strong>of</strong><br />
the robot itself. For this purpose, a virtual backpack is mounted to the torso <strong>of</strong> the robot.<br />
The weight <strong>of</strong> the backpack can be changed at random. Figure 7.8 depicts the setup <strong>of</strong><br />
the experiments and shows the final postures after increasing backpack weight to 5, 10,<br />
and 15kg. Figure 7.9 illustrates the control behavior with increasing backpack weight up<br />
to 20kg in step <strong>of</strong> 5kg.<br />
The postural reflexes are parametrized identically to the previously described experiment.<br />
Nonetheless the adapted posture differs significantly. Instead <strong>of</strong> compensating the disturbance<br />
mainly by change <strong>of</strong> angle in the ankle, the spine and hip joint show the strongest<br />
adjustments. The reason for this can be found in the optimization objective to minimize<br />
joint torques. Compensating the additional backpack weight purely by changing the ankle<br />
joint to regain equilibrium while keeping the body rigid would maintain considerable<br />
torques in spine and hip. The final posture at a backpack weight <strong>of</strong> 20kg results in a torso<br />
pitch <strong>of</strong> approximately 13 ◦ , a fact also visible in the raw acceleration values in x-direction<br />
which increasingly includes a gravitational component.
134 7. Balanced Standing Experiments<br />
Platform Rot. [ ◦ ]<br />
Torso Pitch [ ◦ ]<br />
Spine Y Angle [ ◦ ]<br />
Hip Y Angle [ ◦ ]<br />
Ankle Y Angle [ ◦ ]<br />
Hip Y Torque [Nm]<br />
3.0<br />
2.0<br />
1.0<br />
0.0<br />
2.0<br />
0.0<br />
−2.0<br />
4.0<br />
2.0<br />
0.0<br />
0.0<br />
−2.0<br />
−4.0<br />
2.0<br />
0.0<br />
−2.0<br />
10.0<br />
5.0<br />
0.0<br />
−5.0<br />
0.0 4.0 8.0 12.0<br />
0.0 4.0 8.0 12.0<br />
0.0 4.0 8.0 12.0<br />
0.0 4.0 8.0 12.0<br />
0.0 4.0 8.0 12.0<br />
0.0 4.0 8.0 12.0<br />
Time [s]<br />
CoP Position<br />
Accel. X [ m/s 2 ]<br />
Relax Spine Y a<br />
Relax Hip Y a<br />
Bal. Ankle Pitch a<br />
Spine Y Tor. [Nm]<br />
1.0<br />
0.0<br />
−1.0<br />
0.0 4.0 8.0 12.0<br />
1.0<br />
0.0<br />
−1.0<br />
0.0 4.0 8.0 12.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 4.0 8.0 12.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 4.0 8.0 12.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 4.0 8.0 12.0<br />
10.0<br />
5.0<br />
0.0<br />
−5.0<br />
0.0 4.0 8.0 12.0<br />
Time [s]<br />
Figure 7.7: Experiment on posture optimization during platform rotation. The gray bar marks<br />
the duration <strong>of</strong> the platform motion. The angular velocity <strong>of</strong> the platform rotation is 1.15 ◦ /s.
7.3. Posture Optimization 135<br />
Figure 7.8: Experiment on posture optimization while changing weight distribution by different<br />
weights <strong>of</strong> a backpack.<br />
As illustrated in Figure 7.9, the posture adaptation is generated by reflex activity appearing<br />
as soon as the backpack weight is increased. The activity abates as the robot approaches<br />
a balanced posture. Indeed, the necessary torque in the spine and the hip cannot be<br />
completely eliminated, but only a small amount <strong>of</strong> a few Nm remains. The cop position is<br />
shifted back to zero by respective adjustment <strong>of</strong> the ankle joint, thus bringing the robot<br />
back to equilibrium.<br />
The experiment has been continued with increasing backpack weight. Starting at a weight<br />
<strong>of</strong> about 30kg the postural reflexes cannot fully stabilize the posture any longer. The<br />
robot starts to sway. At a backpack load <strong>of</strong> about 70kg, i.e. nearly the weight <strong>of</strong> the<br />
whole robot, standing cannot be sustain and the robot falls over.<br />
It should again be noted that the posture adaptation relies purely on local reflexes acting<br />
at a balanced rate <strong>of</strong> change. The optimization process does neither require a whole body<br />
model nor a global assessment <strong>of</strong> the posture. As a drawback, the suggested method might<br />
stabilize in a local minimum and takes relatively long to reach it as a static posture is<br />
assumed. Too fast changes would induce dynamics distorting the measured joint torques<br />
that are evaluated for postural corrections. The method also depends on equal rates <strong>of</strong><br />
adaptation <strong>of</strong> all reflexes involved to reduce oscillation and to facilitate the stabilization <strong>of</strong><br />
the process. In return, it allows to cope with different and unforeseen kinds <strong>of</strong> disturbances<br />
in a robust and intuitive way.<br />
Comparing the robot’s postures after optimization with those assumed by human subjects<br />
in similar situations, a strong resemblance can be observed. This might justify the<br />
conclusion that humans use analog, local strategies focused on necessary muscle work while<br />
optimizing their posture against static disturbances <strong>like</strong> ground variations or additional<br />
weight attached to the body.
136 7. Balanced Standing Experiments<br />
Backp. Weight [kg]<br />
Torso Pitch [ ◦ ]<br />
Spine Y Angle [ ◦ ]<br />
Hip Y Angle [ ◦ ]<br />
Ankle Y Angle [ ◦ ]<br />
Hip Y Torque [Nm]<br />
20<br />
10<br />
0<br />
15<br />
10<br />
5<br />
0<br />
0<br />
−5<br />
−10<br />
0<br />
−5<br />
−10<br />
0<br />
−5<br />
−10<br />
0<br />
−10<br />
−20<br />
0.0 5.0 10.0 15.0<br />
0.0 5.0 10.0 15.0<br />
0.0 5.0 10.0 15.0<br />
0.0 5.0 10.0 15.0<br />
0.0 5.0 10.0 15.0<br />
0.0 5.0 10.0 15.0<br />
Time [s]<br />
CoP Position<br />
Accel. X [ m/s 2 ]<br />
Relax Spine Y a<br />
Relax Hip Y a<br />
Bal. Ankle Pitch a<br />
Spine Y Tor. [Nm]<br />
1.0<br />
0.0<br />
−1.0<br />
0.0 5.0 10.0 15.0<br />
0.0<br />
−1.0<br />
−2.0<br />
1.0<br />
0.5<br />
0.0 5.0 10.0 15.0<br />
0.0<br />
0.0 5.0 10.0 15.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 5.0 10.0 15.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 5.0 10.0 15.0<br />
0<br />
−10<br />
−20<br />
0.0 5.0 10.0 15.0<br />
Time [s]<br />
Figure 7.9: Experiment on posture optimization while changing weight distribution by different<br />
weights <strong>of</strong> a backpack. The dashed lines mark the changes <strong>of</strong> weight ranging from 0 to 20kg.
8. Dynamic <strong>Walking</strong> Experiments<br />
To evaluate the performance <strong>of</strong> the suggested control concept for dynamic walking, experiments<br />
have been performed in the test environment as presented in Chapter 6 and<br />
Appendix B. Normal walking on flat ground is analyzed in depth, and the robustness <strong>of</strong> the<br />
control system is examined by changing the ground geometry or by applying other external<br />
disturbances. Throughout all experimental runs, the same set <strong>of</strong> control parameters is<br />
used, and no adaptations are made to handle any particular situation.<br />
8.1 Normal <strong>Walking</strong><br />
Thefirstpart<strong>of</strong>thischapterfocusesonnormalwalkingoneventerrainwithoutthepresence<br />
<strong>of</strong> external disturbances. It gives a detailed evaluation <strong>of</strong> the internal mechanisms <strong>of</strong> the<br />
control system and the interaction <strong>of</strong> the control units. A kinematic analysis reveals the<br />
emerging joint trajectories and the absolute movements <strong>of</strong> the robot’s segments, allowing<br />
to conclude on gait parameters <strong>like</strong> the walking velocity or the step length. Studying the<br />
kinetic results gives insights into the necessary joint torques or the ground reaction forces<br />
occurring during a gait cycle, and allows to estimate locomotion efficiency. Comparison<br />
to both kinematic and kinetic data <strong>of</strong> human walking can expose differences as well as<br />
similarities suggesting common control strategies. Appendix B includes an image series <strong>of</strong><br />
one gait cycle <strong>of</strong> normal walking on level ground recorded in the simulation framework.<br />
8.1.1 Locomotion Modes<br />
The highest level <strong>of</strong> the biped control system is composed <strong>of</strong> the locomotion modes. During<br />
walking initiation, the interplay <strong>of</strong> these behaviors is essential to allow for a fast and<br />
smooth start <strong>of</strong> walking. This task is managed by the <strong>Walking</strong> control unit.<br />
Figure 8.1 illustrates this process by plotting the flow <strong>of</strong> activity between the involved<br />
behaviors. The Standing mode is stimulated and active by default. The stimulation <strong>of</strong> the<br />
<strong>Walking</strong> locomotion mode as initiated by the operator is marked by the dotted, vertical<br />
line. The walking mode directly stimulates the <strong>Walking</strong> Initiation mode. During this first<br />
part <strong>of</strong> walking, both the standing and the initiation behaviors are active. The compliant
138 8. Dynamic <strong>Walking</strong> Experiments<br />
Standing a<br />
Cyclic <strong>Walking</strong> a<br />
Left Foot Load<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0<br />
Time [s]<br />
2.0<br />
<strong>Walking</strong> a<br />
<strong>Walking</strong> Init. a<br />
Right Foot Load<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0 2.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 1.0<br />
Time [s]<br />
2.0<br />
Figure 8.1: Activity <strong>of</strong> the locomotion modes and normalized foot load. The dashed line marks<br />
the beginning <strong>of</strong> walking stimulation initiated by the operator.<br />
joint settings <strong>of</strong> the current standing posture are superimposed with the torque commands<br />
<strong>of</strong> the motor patterns stimulated by the initiation control unit.<br />
In a next step, the cyclic walking behavior is stimulated. Its activity is passed as inhibiting<br />
signal to the standing behavior, thus terminating its activity and giving full control to<br />
the walking behavior. At a time <strong>of</strong> 1.0sec in Figure 8.1, the flow <strong>of</strong> activity between<br />
standing and cyclic walking can be observed. It takes only about 0.6sec from stimulating<br />
the walking behavior to the activity <strong>of</strong> cyclic walking. During this first moments <strong>of</strong> cyclic<br />
walking, walking initiation is still active as some joints require different compliance during<br />
the first step compared to later steps <strong>of</strong> normal walking. Only when the first swing leg<br />
takes <strong>of</strong>f, the stimulation <strong>of</strong> the walking initiation behavior is pulled down.<br />
The actual points in time when the walking behavior changes the stimulation <strong>of</strong> its two<br />
sub-modes are determined by evaluating the load <strong>of</strong> the prospective stance and swing<br />
leg as depicted by the lower two plots <strong>of</strong> Figure 8.1. Algorithm 8.1 details this decision<br />
making. The target rating <strong>of</strong> the initiation behavior indicates its contentment as the load<br />
<strong>of</strong> the swing leg falls below the load <strong>of</strong> the stance leg and is passed as sensor information<br />
to the walking locomotion mode. The latter behavior uses this load comparison to decide<br />
when to stimulate cyclic walking and when to reduce the stimulation <strong>of</strong> walking initiation.<br />
The first switch is done as soon as the load <strong>of</strong> the swing leg is sufficiently below the one<br />
<strong>of</strong> the stance leg (t = 1.0sec in Figure 8.1). <strong>Walking</strong> initiation is fully terminated when<br />
there is no more load at all on the swing leg (t = 1.15sec).
8.1. Normal <strong>Walking</strong> 139<br />
Algorithm 8.1: Stimulation calculation <strong>of</strong> <strong>Walking</strong> Initiation and Cyclic <strong>Walking</strong><br />
1<br />
2<br />
3<br />
4<br />
5<br />
6<br />
7<br />
8<br />
9<br />
10<br />
11<br />
12<br />
13<br />
14<br />
15<br />
16<br />
17<br />
calculate value for load comparison (target rating <strong>of</strong> <strong>Walking</strong> Initiation):<br />
if load swing leg ≤ 0 then<br />
load comparison = 0<br />
end<br />
else if load stance leg ≤ 0 or load swing leg > load stance leg then<br />
load comparison = 1<br />
end<br />
else<br />
load comparison = load swing leg/load stance leg<br />
end<br />
calculate walking mode stimulation within locomotion mode <strong>Walking</strong>:<br />
if load comparison ≤ 0.8 then<br />
stimulate Cyclic <strong>Walking</strong><br />
end<br />
if Cyclic <strong>Walking</strong> stimulated and load comparison = 0 then<br />
reduce stimulation <strong>of</strong> <strong>Walking</strong> Initiation<br />
end<br />
8.1.2 Switching <strong>Walking</strong> Phases<br />
Following the walking initiation, the control system switches to cyclic locomotion. As<br />
described in Section 5.4.3, cyclic walking is composed <strong>of</strong> five consecutive motion phases.<br />
The responsible spinal pattern generator (spg) manages the phase sequence and stimulates<br />
the respective motion phase control units for the left and right body side.<br />
Figure 8.2 illustrates the sequence <strong>of</strong> phases for the first 18 seconds <strong>of</strong> normal walking<br />
by plotting the left and right states <strong>of</strong> the walking spg. The dashed, vertical line marks<br />
the beginning <strong>of</strong> activity <strong>of</strong> the Cyclic <strong>Walking</strong> control unit. As the left leg is to take the<br />
first step, the spg starts by stimulating the fourth phase <strong>of</strong> this body side. The opposite<br />
side begins with the corresponding phase one. From then on, the sequence <strong>of</strong> walking<br />
phases complies with the order prescribed by the spg. Exemplary, the figure also plots the<br />
activity <strong>of</strong> the second walking phase <strong>of</strong> the right body side. These individual behaviors<br />
are stimulated by the spg according to its current state.<br />
To further explain the mechanisms during phase transitions, Figure 8.3 enlarges seconds<br />
two and three <strong>of</strong> the previous figure. The upper plot now contains the walking phases <strong>of</strong><br />
both the left and right body side. The phase transitions are marked by the thin, vertical<br />
lines. In this representation, the bilateral synchronization <strong>of</strong> both sides can clearly be<br />
identified. This corresponds to the observations by Ivanenko et al. during their emg<br />
analysis <strong>of</strong> normal walking <strong>of</strong> human subjects.<br />
In the control system described here, this bilateral synchronization is achieved by switching<br />
the left and right motion phases on the basis <strong>of</strong> the same sensor events. Those events<br />
responsible for the phase transitions are tagged by the thick vertical lines in the lower four<br />
plots in Figure 8.3. The second and third row show the measurements <strong>of</strong> the four force<br />
sensors mounted in each foot. The solid lines represent the inner and outer toe sensors,<br />
the dashed lines those two sensors mounted in the heel. Plots four and five <strong>of</strong> the figure<br />
depict the knee angles <strong>of</strong> both legs.
140 8. Dynamic <strong>Walking</strong> Experiments<br />
Left Phase<br />
Right Phase<br />
Right Phase 2 a<br />
5<br />
4<br />
3<br />
2<br />
1<br />
5<br />
4<br />
3<br />
2<br />
1<br />
1.0<br />
0.5<br />
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0<br />
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0<br />
0.0<br />
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0<br />
Time [s]<br />
Figure 8.2: Motion phases <strong>of</strong> the left and the right body side during normal walking. The<br />
lower plot exemplifies the activity <strong>of</strong> an individual motion phase stimulated by the spg, in this<br />
case the right <strong>Walking</strong> Phase 2.<br />
The transition from phase one to phase two <strong>of</strong> the stance leg and from phase four to five<br />
<strong>of</strong> the swing leg is triggered by the lock knee event. It is based on the knee angle <strong>of</strong> the<br />
swing leg. During the swing motion, the knee passively bends due to mass inertia and then<br />
extends again as the hip joint decelerates. As soon as the leg is stretched, the heel strike<br />
is expected, and the spg switches to the next phase. Three <strong>of</strong> these events are marked in<br />
the knee angle plots <strong>of</strong> the figure.<br />
The next phase transition takes place after the heel strike is finished and the foot has made<br />
full contact with the ground. This fact can be extracted from the force measurements<br />
by the four sensors attached in the corners <strong>of</strong> each foot. As shown in the figure, first the<br />
heel sensors represented by the dashed lines detect contact with the ground. As soon as<br />
the toe sensors depicted as solid lines also touch down, the phase transition is triggered.<br />
The small gap between the actual full contact shown in the plot and the phase switch can<br />
be explained by two facts: First, a certain threshold must be exceeded before contact is<br />
confirmed. Secondly, the control system’s cycle time <strong>of</strong> 25ms results in a sampling rate <strong>of</strong><br />
40Hz clearly being visible in the zoom level <strong>of</strong> this figure.<br />
The final phase transition event is also based on the force sensors <strong>of</strong> the feet. Phase four<br />
starts as soon as the load on the prospective swing leg falls below a threshold <strong>of</strong> about<br />
150N. The force plots in the figure illustrate the fact that first the heel <strong>of</strong> the foot leaves<br />
the ground. The Leg Propel motor pattern generates the plantarflexion <strong>of</strong> the foot, thus<br />
pushing the toe sensors towards the ground to support the forward motion <strong>of</strong> the robot.
8.1. Normal <strong>Walking</strong> 141<br />
<strong>Walking</strong> Phases<br />
Left Foot Forces [N]<br />
Right Foot Forces [N]<br />
Left Knee Angle [ ◦ ]<br />
Right Knee Angle [ ◦ ]<br />
5<br />
4<br />
3<br />
2<br />
1<br />
400<br />
200<br />
0<br />
400<br />
200<br />
0<br />
60<br />
40<br />
20<br />
right<br />
left<br />
2.0 2.5 3.0 3.5 4.0<br />
2.0 2.5 3.0 3.5 4.0<br />
2.0 2.5 3.0 3.5 4.0<br />
0<br />
2.0 2.5 3.0 3.5 4.0<br />
60<br />
40<br />
20<br />
0<br />
2.0 2.5 3.0<br />
Time [s]<br />
3.5 4.0<br />
Figure 8.3: Transitions <strong>of</strong> motion phases are triggered by three events toe <strong>of</strong>f, full contact, and<br />
locked knee. Thick vertical lines mark the decisive events in the respective plots. Solid lines in<br />
foot force plots represent the inner and outer toe forces, dashed lines those <strong>of</strong> the heel sensors.
142 8. Dynamic <strong>Walking</strong> Experiments<br />
When this torque pattern subsides and the Active Hip Swing motor pattern indirectly<br />
initiates the knee bending, the load is taken from the toe sensors and the phase transition<br />
will take place.<br />
8.1.3 Behavioral Activity<br />
With each state transition <strong>of</strong> the walking spg, the stimulation proceeds from one motion<br />
phase to the next. Each motion phase in then responsible for stimulating those reflexes<br />
and motor patterns that should be active during this part <strong>of</strong> the walking cycle. This<br />
section illustrates the flow <strong>of</strong> stimulation and activity to clarify the behavioral interaction.<br />
8.1.3.1 Motor Pattern Activity<br />
Motor patterns act as the feed-forward control units <strong>of</strong> the control system. Therefore their<br />
activity only depends on their activation ι and not on any sensor information. Figure 8.4<br />
shows the activation and the activity <strong>of</strong> all participating motor patterns during the same<br />
run <strong>of</strong> normal walking as used in the previous plots. The first row <strong>of</strong> the figure depicts<br />
the walking phases <strong>of</strong> the selected 2.5sec interval, the thin vertical lines mark the phase<br />
transitions. The shaded plots in the remaining rows represent the behavior activation ι, the<br />
solid lines stand for their activity a. Motion phases always fully stimulate the respective<br />
motor patterns by a value <strong>of</strong> s = 1.<br />
The Arm Swing motor patterns are stimulated in phases three and four to correspond to<br />
the leg swing. Since the pattern generates a backward torque impulse <strong>of</strong> the ipsilateral<br />
and a forward impulse for the contralateral arm, the left pattern is activated during the<br />
left leg swing and vice versa. As soon as the control unit is activated, it starts its activity<br />
corresponding to equation 6.3 as discussed in Section 6.2.2. The behavior is stimulated<br />
long enough for the pattern to finish, and no inhibition interrupts is progress.<br />
The Initiate Swing motor pattern is stimulated from phase three onwards. Hence its<br />
pattern generation is started as soon as the foot load is low enough. Otherwise the high<br />
friction between the foot and the ground would not allow the foot to lift, and the hip<br />
torque would induce a rotation <strong>of</strong> the robot about the z-axis as well as a forward bending<br />
<strong>of</strong> the hip and the upper body. Due to the inhibition <strong>of</strong> the motor pattern by the activity<br />
<strong>of</strong> the Lock Hip reflex, the activation ι = s·(1−i) <strong>of</strong> the behavior can be reduced despite<br />
the fact that it is still stimulated by the motion phase. The step-<strong>like</strong> progress <strong>of</strong> the<br />
activation plots in the figure must be accounted for by the control cycle frequency <strong>of</strong> 40Hz.<br />
As the activity <strong>of</strong> a behavior must not exceed its activation, the motor pattern generation<br />
is suppressed.<br />
During motion phases two and three, the Leg Propel motor pattern is stimulated. As no<br />
inhibition signal is connected to the behavior, its activation lasts until the stimulation is<br />
terminated. Similar to the Initiate Swing control unit, the pattern is suppressed if the<br />
activation decreases before the pattern is completed. This behavior makes perfect sense as<br />
the control unit should not continue the plantarflexion after lift-<strong>of</strong>f, but should still propel<br />
the body forward in case the stance phase is prolonged.<br />
Finally, the Weight Acceptance motor pattern shows an exception in its activity calculation.<br />
As it needs full influence on the knee angle just before and during heel strike, the activity<br />
is set to the full value <strong>of</strong> activation. In doing so, the knee can be bent right before heel
8.1. Normal <strong>Walking</strong> 143<br />
<strong>Walking</strong><br />
Phases<br />
Left Arm<br />
Swing ι, a<br />
Right Arm<br />
Swing ι, a<br />
Left Init.<br />
Swing ι, a<br />
Right Init.<br />
Swing ι, a<br />
Left Leg<br />
Propel ι, a<br />
Right Leg<br />
Propel ι, a<br />
Left Weight<br />
Accept. ι, a<br />
Right Weight<br />
Accept. ι, a<br />
5<br />
4<br />
3<br />
2<br />
1<br />
right<br />
left<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0 2.5 3.0 3.5 4.0 4.5<br />
Time [s]<br />
Figure 8.4: Activation ι and activity a <strong>of</strong> the motor patterns during normal walking. The<br />
shaded plots represent the activation <strong>of</strong> the behaviors.
144 8. Dynamic <strong>Walking</strong> Experiments<br />
strike to reduce the impact, and its angle can be controlled during the first part <strong>of</strong> the<br />
stance phase to achieve the semi-flat walking gait. The actual torques generated during<br />
this phase will be discussed below.<br />
8.1.3.2 Reflex Activity<br />
Un<strong>like</strong> motor patterns, reflexes are feedback control units. Consequently, their activity<br />
raises due to sensor information. But <strong>like</strong> all iB2C behaviors, they must be stimulated to<br />
enable any activity. Figure 8.5 shows the activation and activity <strong>of</strong> relevant local reflexes<br />
during normal walking. Again, the figure is based on the same data as the previous plots.<br />
The Lock Knee reflex has been omitted as it only shows minor activity at the end <strong>of</strong> phase<br />
four to dampen the knee swing. Otherwise, it mainly serves as sensor pre-processor for<br />
the walking spg as its target rating indicates when the knee is stretched again at the end<br />
<strong>of</strong> the swing phase.<br />
The Lock Hip reflex is responsible for controlling the hip joint at the end <strong>of</strong> the leg swing.<br />
Its activity rises as the hip angle about the y-axis approaches its target position. With<br />
increasing activity, the dampening force is applied to the joint to slow down the leg swing.<br />
Then the hip position is retained by passing the target angle to the position control. The<br />
high activity value provides for the necessary joint stiffness. During heel strike, the reflex<br />
is still stimulated and continues to be active. Thereby the upper body is stabilized against<br />
its forward momentum during foot impact.<br />
To keep the pelvis from rotating about the hip joint’s x-axis, the Stabilize Pelvis reflex<br />
is stimulated during phases one and two, i.e. during the part <strong>of</strong> the stance phase when<br />
most <strong>of</strong> the body weight is supported. The reflex’s activity is based on the foot load <strong>of</strong> the<br />
supporting leg. As can be seen in Figure 8.5, the activity mostly parallels the activation <strong>of</strong><br />
the behavior. Only towards the end <strong>of</strong> phase two, the activity declines with the load <strong>of</strong> the<br />
support foot due to the touchdown <strong>of</strong> the contralateral foot. Small notches in the activity<br />
can appear when some amount <strong>of</strong> the body weight is supported by the contralateral leg,<br />
e.g. caused by a dragging <strong>of</strong> the foot or excessive leg propulsion. The figure also illustrates<br />
how the left and right sided instances <strong>of</strong> the reflex alternate in stabilizing the pelvis.<br />
The activity <strong>of</strong> the local reflex Heel Strike is based in the force information <strong>of</strong> the two<br />
load sensors mounted at the back <strong>of</strong> each foot. As soon as heel contact is measured, the<br />
reflex activity increases and a dampening force is applied to the ankle joint based on its<br />
rotational velocity. This action prevents the foot from slapping down at impact in case the<br />
mechanical damping is not sufficient. The activity declines together with the stimulation<br />
<strong>of</strong> the reflex at the end <strong>of</strong> phase five.<br />
The Cutaneous Reflex is stimulated during the swing phase <strong>of</strong> the leg. In normal walking<br />
on level terrain it should show only minor activity. While the left sided reflex remains<br />
nearly fully inactive during the interval shown in the figure, the right sided reflex displays<br />
at least a small peak <strong>of</strong> activity. This peak is caused by a remaining ground contact <strong>of</strong> the<br />
toes during the begin <strong>of</strong> the swing phase. The reflex makes sure that the foot completely<br />
loses contact to the ground by a short torque impulse in the ankle and the knee joint.<br />
It is interesting to note that relevant activity <strong>of</strong> some reflexes is necessary during normal<br />
walking while other reflexes mainly handle disturbances. Similar observations can be<br />
made on the reflex action in human walking. This phenomenon can also be noticed in the<br />
activity <strong>of</strong> postural reflexes as illustrated by Figure 8.6. In contrast to the local reflexes,
8.1. Normal <strong>Walking</strong> 145<br />
<strong>Walking</strong><br />
Phases<br />
Left Lock<br />
Hip ι, a<br />
Right Lock<br />
Hip ι, a<br />
L. Stabilize<br />
Pelvis ι, a<br />
R. Stabilize<br />
Pelvis ι, a<br />
Left Heel<br />
Strike ι, a<br />
Right Heel<br />
Strike ι, a<br />
L. Cutaneous<br />
Reflex ι, a<br />
R. Cutaneous<br />
Reflex ι, a<br />
5<br />
4<br />
3<br />
2<br />
1<br />
right<br />
left<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0 2.5 3.0 3.5 4.0 4.5<br />
Time [s]<br />
Figure 8.5: Activation ι and activity a <strong>of</strong> the local reflexes during normal walking. The shaded<br />
plots represent the activation <strong>of</strong> the behaviors. The Lock Knee reflex has been omitted.
146 8. Dynamic <strong>Walking</strong> Experiments<br />
here those control units responsible for compensating disturbances predominate, but also<br />
show substantial activity during normal walking.<br />
The postural reflex Upright Trunk is stimulated throughout all phases <strong>of</strong> cyclic walking<br />
to achieve maximum stability <strong>of</strong> the upper body. But as the reflex cannot and should<br />
not influence the hip joint in case the leg <strong>of</strong> the considered body side has no ground<br />
contact, the activity function includes the normalized foot load as factor. Thereby the<br />
reflex suspends its activity during the leg swing in phase four and the beginning <strong>of</strong> phase<br />
five. As soon as the leg has regained ground contact, the reflex resumes its task. Figure 8.6<br />
also illustrates the fact that during double support around phase three both the left and<br />
the right Upright Trunk control units are active. This allows an even better stabilization<br />
<strong>of</strong> the upper body as the action <strong>of</strong> both reflexes work in concert. Furthermore, it can<br />
be observed that the behavior shows significant activity even during normal walking in<br />
even terrain. This is caused by the considerable mass inertia <strong>of</strong> the upper body keeping it<br />
moving forward while the pelvis decelerates at heel strike, and vice versa during propulsion.<br />
Likewise, the torque generated by the Initiate Swing motor pattern not only causes the<br />
leg to swing but also effects in a bending <strong>of</strong> the trunk. These self-induced disturbances are<br />
partly compensated by anticipatory torque impulses produced by the responsible motor<br />
patterns, but must additionally be balanced by the Upright Trunk reflexes. Accordingly,<br />
the highest activity <strong>of</strong> these behaviors can be observed right after heel strike.<br />
The Forward Velocity control unit is stimulated by walking phase one. During this part <strong>of</strong><br />
the walking cycle, the foot has full ground contact and the postural reflex can influence<br />
the forward velocity by applying a correcting torque to the ankle joint. Again, relevant<br />
activity can be observed even during normal walking, however not as strong as in the<br />
previously discussed reflex. Movements <strong>of</strong> the upper body and the swinging extremities<br />
can cause variations in the forward velocity, or more precisely in the estimated position<br />
<strong>of</strong> the extrapolated center <strong>of</strong> mass (xcom). These disturbances are then compensated by<br />
the reflex. Also, it cannot be avoided that the xcom estimation is inaccurate, resulting in<br />
slight reflex action that would not have been necessary otherwise. Nevertheless, the xcom<br />
calculations are sufficient for stabilizing the forward velocity.<br />
The same considerations hold true for the Lateral Balance Ankle behavior. It is also<br />
stimulated during walking phase one as it balances the robot by exerting torques via the<br />
ankle joint. Even on level ground as in the run presented in Figure 8.6, considerable<br />
activity can be observed. This behavior can be explained by the fact that the reflex<br />
can only fine-tune the posture due to the short sidewards leverage <strong>of</strong> the feet, so the<br />
maximum activity is already reached at minor disturbances. Combined with appropriate<br />
foot placement, this reflex action contributes to the lateral stability.<br />
Concluding the discussion on behavioral activity, the Lateral Foot Placement control<br />
unit shows a different activity signature than the other postural reflexes. As it controls<br />
the adduction and abduction <strong>of</strong> the leg by passing a target angle and a low compliance<br />
value to the position control <strong>of</strong> the hip joint about the x-axis, the behavior must be<br />
active throughout the swing phase. Its activity is again based on the normalized foot<br />
load because influencing the foot position is only possible during ground clearance. The<br />
activity value is used directly as stiffness demand for the position controller as described<br />
in Section 6.1.2. Thus, the behavior activity cannot serve as indication on the amount <strong>of</strong><br />
lateral foot placement correction. Rather, the behavior’s target rating should be consulted<br />
for that information. Being stimulated during phases four and five, the reflex can start its
8.1. Normal <strong>Walking</strong> 147<br />
<strong>Walking</strong><br />
Phases<br />
L. Upright<br />
Trunk ι, a<br />
R. Upright<br />
Trunk ι, a<br />
L. Forward<br />
Velocity ι, a<br />
R. Forward<br />
Velocity ι, a<br />
L. Lat. Bal.<br />
Ankle ι, a<br />
R. Lat. Bal.<br />
Ankle ι, a<br />
L. Lat. Foot<br />
Placem. ι, a<br />
R. Lat. Foot<br />
Placem. ι, a<br />
5<br />
4<br />
3<br />
2<br />
1<br />
right<br />
left<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0<br />
1<br />
2.5 3.0 3.5 4.0 4.5<br />
0<br />
2.0 2.5 3.0 3.5 4.0 4.5<br />
Figure 8.6: Activation ι and activity a <strong>of</strong> the postural reflexes during normal walking. The<br />
shaded plots represent the activation <strong>of</strong> the behaviors.
148 8. Dynamic <strong>Walking</strong> Experiments<br />
task as soon as the foot leaves the ground and can continue to correct the foot position<br />
right up to the point when the foot touches down.<br />
In summary, three different types <strong>of</strong> behavioral activity can be observed in the low-level<br />
control units: motor patterns show a predefined progression <strong>of</strong> activity, only depending on<br />
the starting point when the pattern is triggered. Some reflexes <strong>like</strong> the Lock Hip reflex<br />
are an essential part <strong>of</strong> the walking cycle, showing high activity at certain kinematic or<br />
kinetic events to contribute to normal walking. Finally, the remainder <strong>of</strong> reflexes work<br />
towards stabilizing the robot. They display more or less activity depending on internal or<br />
external disturbances.<br />
8.1.4 Kinematic Analysis<br />
The kinematic analysis <strong>of</strong> gait handles joint angles trajectories and the translation and<br />
rotation <strong>of</strong> body segments relative to a fixed coordinate system. This kind <strong>of</strong> evaluation<br />
allows to gain a better understanding <strong>of</strong> the resulting motions by considering angle ranges,<br />
variations in trajectories, or locomotion velocity. Furthermore, the results can be compared<br />
to human walking. Other than in clinical gait studies, in the experiments presented here<br />
the relevant data can directly be extracted from the simulation environment.<br />
8.1.4.1 Joint Angles<br />
Figure 8.7 presents the angle trajectories <strong>of</strong> all joints over the course <strong>of</strong> one gait cycle. To<br />
this end, 30 consecutive steps <strong>of</strong> walking on level ground are averaged by manually tagging<br />
the intervals from one heel strike to the next. Each interval is then normalized in length,<br />
and the mean, minimum, and maximum values are calculated. The 15 left and the 15 right<br />
data sets are combined while taking sign conversions into account due to the mirroring<br />
along the sagittal plane. Positive values express a joint flexion, abduction, or dorsiflexion,<br />
while negative values signify extension, adduction, or plantarflexion, respectively. This<br />
complies to the standards in biomechanical analysis and facilitates the comparison <strong>of</strong> the<br />
trajectories to human data. The average duration <strong>of</strong> the gait cycles is 1.27sec, with the<br />
shortest duration being 1.20sec and the longest duration amounting to 1.30sec. In the<br />
figure, the mean values are represented by the solid lines, the minimum and maximum<br />
values are indicated by the dashed lines. The vertical dashed line at 69% marks the mean<br />
location <strong>of</strong> the transition from stance to swing. The left column <strong>of</strong> plots depicts the joints<br />
in the sagittal plane, i.e. revolving about the y-axis, while the right column presents the<br />
remaining joints.<br />
The spine joint remains within a small angle range throughout the walking cycle since it is<br />
set to a fixed position at relatively low compliance. The joint trajectory about the y-axis<br />
exhibits a pattern that is repeated after half the cycle, once for each leg. For the x- and<br />
z-axis, a similar behavior can be observed, but the pattern swaps its sign from one side to<br />
the next. This can be explained by the fact that the forward motion <strong>of</strong> the upper body is<br />
symmetrical for each leg and runs at twice the frequency <strong>of</strong> the gait cycle. The lateral<br />
movement <strong>of</strong> the trunk is in phase with the cycle and is mirrored for each leg. Especially<br />
the rotation about the x-axis illustrates the robot’s sway from left to right during one gait<br />
cycle, as the inertia <strong>of</strong> the upper body causes a deflection about the spine joint.<br />
The sine-<strong>like</strong> motion <strong>of</strong> the shoulder joint about the y-axis was already discussed in<br />
Chapter 5. It results from torque impulses generated by the Arm Swing motor patterns
8.1. Normal <strong>Walking</strong> 149<br />
Spine Y [ ◦ ]<br />
Shoulder Y [ ◦ ]<br />
Elbow Y [ ◦ ]<br />
Hip Y [ ◦ ]<br />
Knee Y [ ◦ ]<br />
Ankle Y [ ◦ ]<br />
2<br />
0<br />
−2<br />
40<br />
20<br />
0<br />
−20<br />
0 25 50 75 100<br />
−40<br />
0 25 50 75 100<br />
15<br />
10<br />
5<br />
0<br />
40<br />
20<br />
0<br />
−20<br />
60<br />
40<br />
20<br />
−20<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
0<br />
0 25 50 75 100<br />
20<br />
0<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Spine X [ ◦ ]<br />
Spine Z [ ◦ ]<br />
Shoulder X [ ◦ ]<br />
Hip X [ ◦ ]<br />
Hip Z [ ◦ ]<br />
Ankle X [ ◦ ]<br />
2<br />
0<br />
−2<br />
5<br />
0<br />
0 25 50 75 100<br />
−5<br />
0 25 50 75 100<br />
2<br />
0<br />
−2<br />
5<br />
0<br />
0 25 50 75 100<br />
−5<br />
0 25 50 75 100<br />
4<br />
2<br />
0<br />
−2<br />
2<br />
0<br />
0 25 50 75 100<br />
−2<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 8.7: Joint angles over the course <strong>of</strong> one gait cycle. The solid lines represent the mean<br />
values over 30 steps <strong>of</strong> normal walking on even ground. The dashed lines mark the minimum<br />
and maximum values. The vertical dashed line indicates the transition from stance to swing.
150 8. Dynamic <strong>Walking</strong> Experiments<br />
and is out-<strong>of</strong>-phase with the hip trajectory. Shoulder rotation in the x-axis is restricted<br />
by a high stiffness value keeping the arm aligned to the trunk. Still, some compliance<br />
remains and the arm mass inertia combined with the body sway from left to right create a<br />
deflection <strong>of</strong> about ±1 ◦ .<br />
The elbow joint is set to low compliance throughout the walking cycle. It rests at its<br />
extension limit while the arm swings forward due to mass inertia. As the shoulder joints<br />
change direction, the elbow passively bends up to an angle <strong>of</strong> about 15 ◦ . Due to the<br />
relatively low mass <strong>of</strong> the lower arm segment, its movement has little influence on the<br />
walking process.<br />
The action <strong>of</strong> the hip, knee, and ankle joint about the y-axis has the most significant<br />
influence on forward walking. The hip joints mainly reflects the leg swing. At heel strike,<br />
the hip is flexed to its maximum and then extends during the stance phase as the body<br />
travels over the stance leg. This trajectory is not predefined, rather it emerges from the<br />
pendulum motion <strong>of</strong> the body and the work <strong>of</strong> the postural reflex Upright Trunk keeping<br />
the pelvis and the upper body in an upright orientation. As the motor pattern initiating<br />
the leg swing starts its activity, the hip joint moves forward until its position is controlled<br />
by the Lock Hip reflex. During this last part <strong>of</strong> the gait cycle, the variation in angle is<br />
nearly disappearing as the swing leg’s angle <strong>of</strong> attack is set by a position control with low<br />
compliance.<br />
Bending <strong>of</strong> the knee joint starts even before heel strike as the responsible motor pattern<br />
initiates this action at the beginning <strong>of</strong> walking phase five. The knee then flexes up to<br />
the defined angle during weight acceptance before stretching again in anticipation <strong>of</strong> the<br />
swing phase. As the hip initiates the leg swing, the knee begins to bend passively due to<br />
the mass inertia <strong>of</strong> the lower leg. Still without active control, it then extends again as<br />
the hip decelerates towards the end <strong>of</strong> the walking cycle. The trajectory <strong>of</strong> the passive<br />
knee flexion shows considerable variation caused by different starting points, varying robot<br />
velocity, and diverging stride lengths. Similar to the hip joint, the bending <strong>of</strong> the knee<br />
starts well before the swing foot leaves the ground.<br />
The onset <strong>of</strong> the ankle trajectory about the y-axis reflects the fact that the foot planarflexes<br />
as it moves from only heel contact to full ground contact. During the stance phase, the<br />
body passively swings over the foot, only influenced by the passive elasticity <strong>of</strong> the joint<br />
and the Forward Velocity reflex. As soon as the leg propulsion starts at the end <strong>of</strong> the<br />
stance phase, the ankle dorsiflexes to push the robot forward. At lift-<strong>of</strong>f, the foot travels<br />
back to minor plantarflexion set by the respective motion phase with low compliance to<br />
facilitate ground clearance during the swing phase.<br />
Similar to the spine joint, the hip joint’s z-axis reveals the small rotation <strong>of</strong> the pelvis<br />
during walking. The hip joint’s x-axis is used for stabilizing the pelvis during stance phase<br />
and adjusting the lateral foot placement during swing phase. At the beginning <strong>of</strong> the cycle<br />
the weight <strong>of</strong> the robot shifts from one leg to another, resulting in a small indulge <strong>of</strong> the<br />
pelvis before it is steady again. The sway <strong>of</strong> the upper body to the new stance leg at the<br />
middle <strong>of</strong> the gait cycle results in adduction <strong>of</strong> the hip joint by a few degrees. During<br />
the swing phase, the postural reflex Lateral Foot Placement moves the leg to the left or<br />
right depending on the com estimation. This explains the relatively large variation in<br />
joint angle. The robot sheers in the lateral direction, resulting in an <strong>of</strong>fset <strong>of</strong> the hip angle<br />
throughout the gait cycle.
8.1. Normal <strong>Walking</strong> 151<br />
Joint Minimum [ ◦ ] Maximum [ ◦ ] Joint Limits [ ◦ ]<br />
Spine X -1.1 1.2 -57 – 57<br />
Spine Y -1.9 0.9 -57 – 57<br />
Spine Z -3.2 3.2 -57 – 57<br />
Shoulder X 0.7 1.5 0 – 115<br />
Shoulder Y -33.8 33.9 -57 – 57<br />
Elbow Y -0.1 15.1 0 – 115<br />
Hip X -0.5 3.4 -57 – 57<br />
Hip Y -18.9 35.8 -10 – 49<br />
Hip Z -1.9 2.7 -57 – 57<br />
Knee Y 4.3 60.2 0 – 115<br />
Ankle X -0.3 2.4 -29 – 29<br />
Ankle Y -24.6 23.8 -29 – 29<br />
Table 8.1: Minimum and maximum values <strong>of</strong> the mean joint angle trajectories over 20 steps<br />
during normal walking on level ground.<br />
For equal reasons, a similar <strong>of</strong>fset can be observed in the ankle joint’s x-axis. During the<br />
stance phase, the robot leans to the side <strong>of</strong> the stance leg, resulting in an increasing angle.<br />
Before the swing phase, the robot sways back towards the sagittal plane. During leg swing,<br />
the ankle remains passive except for the parallel spring pulling it back to neutral position.<br />
At touchdown, the ankle adapts to the ground surface, thus, given a level ground plane,<br />
the angle only depends on the robot orientation.<br />
Itshouldbenotedagainthattheangletrajectoriesjustpresentedresultfromtheinteraction<br />
<strong>of</strong> passive dynamics including parallel and series springs, torque impulses by the motor<br />
patterns, and local reflex action. Except for a small part <strong>of</strong> the knee trajectory during<br />
weight acceptance, no joint position trajectories are predefined. The position control is<br />
only used with constant equilibrium points and compliance settings throughout a motion<br />
phase.<br />
The minimum and maximum values <strong>of</strong> the mean joint angle trajectories occurring during<br />
the presented experiment are summarized in Table 8.1. Furthermore, the joint limits are<br />
listed for comparison. It can be seen that the joints stay well below their limits that have<br />
been chosen while keeping a development <strong>of</strong> a real robot in mind. Only the hip joint<br />
shows an over-extension in its y-axis. This demonstrates that the joint limits are not<br />
implemented as fixed mechanical stops, but rather as elastic limits generating increasing<br />
torque as the joint exceeds its boundaries.<br />
8.1.4.2 Segment Translation and Rotation<br />
While the above discussion on joint angles considers relative coordinates, kinematic analysis<br />
also handles absolute poses <strong>of</strong> segments. Figure 8.8 illustrates the trajectories <strong>of</strong> the robot’s<br />
head and pelvis relative to a fixed coordinate system. The head is plotted as solid line,<br />
the pelvis is represented by the dashed line. The figure shows the first 22 seconds <strong>of</strong> the<br />
same run <strong>of</strong> normal walking used in the previous plots.<br />
The progression <strong>of</strong> both the head and the pelvis in x-direction displays a very steady<br />
velocity after the initial acceleration during walking initiation. The resulting walking
152 8. Dynamic <strong>Walking</strong> Experiments<br />
Head/Pelvis<br />
Position X [m]<br />
Head/Pelvis<br />
Position Y [m]<br />
Head/Pelvis<br />
Position Z [m]<br />
30<br />
20<br />
10<br />
0<br />
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0<br />
1<br />
0<br />
−1<br />
2<br />
1<br />
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0<br />
0<br />
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0<br />
Time [s]<br />
Figure 8.8: Head (solid line) and pelvis (dashed line) position during normal walking. Caused<br />
by slip and joint compliance, the robot shows slight derivation from straightforward direction.<br />
Left Foot<br />
Position Z [m]<br />
Right Foot<br />
Position Z [m]<br />
0.4<br />
0.2<br />
0.0<br />
0.4<br />
0.2<br />
0.0<br />
toe<br />
heel<br />
ankle<br />
walking dir.<br />
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0<br />
0.76m 0.75m<br />
3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0<br />
Position X [m]<br />
Figure 8.9: Movement <strong>of</strong> the foot in the sagittal plane during a stride. The plots mark the<br />
trajectories <strong>of</strong> the center <strong>of</strong> the left toe, the ankle, and left heel segment the foot is composed <strong>of</strong>.
8.1. Normal <strong>Walking</strong> 153<br />
velocity in this run amounts to 1.2 m/s or 4.3 km/h. This velocity corresponds to relaxed<br />
walking <strong>of</strong> human subjects.<br />
Two characteristics can be observed in the trajectories in the lateral direction. On the one<br />
hand, head and pelvis sway slightly to the left and to the right during a walking cycle.<br />
The oscillation <strong>of</strong> the head amounts to about ±4cm, the one <strong>of</strong> the pelvis to ±3cm. On<br />
the other hand, the robot does not stay on a straight line while walking forward. Rather,<br />
it tends to show minor rotations which vary from run to run. These rotations are caused<br />
by a slip <strong>of</strong> the feet on the ground and by the compliance <strong>of</strong> the joints about the z-axis.<br />
The head and pelvis trajectories in z-direction illustrate the semi-flat walking gait already<br />
mentioned in previous chapters. During each stance phase, the body travels over the<br />
stance leg and is first lifted and than lowered again during this process. The amplitude <strong>of</strong><br />
this oscillation is reduced by the bending <strong>of</strong> the leg initiated by the Weight Acceptance<br />
motor pattern. Due to additional sway <strong>of</strong> the upper body in the sagittal plane, the head’s<br />
amplitude is slightly higher than the one <strong>of</strong> the pelvis, coming to approximately 5cm.<br />
The movement <strong>of</strong> the feet is detailed in Figure 8.9. Three trajectories in the sagittal<br />
plane for both feet are given, namely those <strong>of</strong> the inner toe, the ankle, and the inner heel<br />
segments. As the plots represent the position <strong>of</strong> the segment centers, the z-position <strong>of</strong> toe<br />
and heel does not reach zero but stays 3cm above the ground, corresponding to the radius<br />
<strong>of</strong> the two segments. To provide a reference to the progress <strong>of</strong> time, the plots are drawn<br />
with markers at a time interval <strong>of</strong> 25ms.<br />
The foot location during the stance phase can easily be identified by the clustering <strong>of</strong> plot<br />
markers. During leg propulsion, the heel lifts from the ground and the toes are pushed<br />
towards the ground by plantarflexion <strong>of</strong> the foot to increase the robots forward velocity.<br />
The toes lift <strong>of</strong>f the ground as soon as the swing phase begins and the foot rotates to a<br />
neutral ankle position. During this first part <strong>of</strong> the swing phase, the toes are the foot<br />
segment closest to the ground and determine the ground clearance <strong>of</strong> 5–6cm. In the second<br />
half <strong>of</strong> the swing phase, the knee joint extends. This causes the foot to rotate as the ankle<br />
joint stays passive and does not significantly change its angle. Thus, the toe segment<br />
moves upwards and the height <strong>of</strong> the heel segment is reduced. During this part <strong>of</strong> the<br />
swing phase, the heel is located closest to the floor and the ground clearance is reduced to<br />
only 2cm at the lowest point. Just before heel strike, this distance increases again as the<br />
knee reaches its full extension.<br />
Figure 8.9 also illustrates the step length during normal walking. Measuring the distance<br />
between the successive heel strikes <strong>of</strong> the left and the right leg amounts to 0.76m and<br />
0.75m. This length varies only slightly among the steps <strong>of</strong> the presented run. The mean<br />
step length results in 0.78m, with a minimum value <strong>of</strong> 0.73m, and a maximum value <strong>of</strong><br />
0.81m. The standard deviation <strong>of</strong> the step length amounts to 0.02m.<br />
The foot placement is further visualized by Figure 8.10, showing 28 foot points <strong>of</strong> the<br />
considered run. The consistent step length is illustrated as well as the fact that the robot<br />
does not manage to remain on a straight line, but instead displays small displacements<br />
and rotation due to slip and joint compliance. As in human walking, additional external<br />
sensor systems <strong>like</strong> vision would be necessary to correct the walking direction.<br />
The figure also allows to identify the step width. Analysis <strong>of</strong> the underlying data reveals a<br />
mean step width <strong>of</strong> 0.16m at a standard deviation <strong>of</strong> 0.03m. The minimum value <strong>of</strong> the<br />
run amounts to 0.10m, the maximum value comes to 0.22m. The higher variation <strong>of</strong> the
154 8. Dynamic <strong>Walking</strong> Experiments<br />
Foot Points<br />
Position Y [m]<br />
2.0 walking dir.<br />
0.0<br />
−2.0<br />
2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0<br />
Position X [m]<br />
Figure 8.10: Foot points on the horizontal plane during 28 steps <strong>of</strong> normal walking. The dotted<br />
line marks the trajectory <strong>of</strong> the pelvis.<br />
step width compared to the step length can be explained by the difficulty to stabilize the<br />
robot in the lateral direction due to its narrow foot placement and the high center <strong>of</strong> mass.<br />
This results in considerable activity <strong>of</strong> the postural reflex Lateral Foot Placement and thus<br />
in stronger scattering <strong>of</strong> the step width.<br />
Figure 8.11 illustrates the orientation <strong>of</strong> the head and the pelvis segment during the<br />
walking cycle. The rotation about the x-axis indicates the raise <strong>of</strong> the pelvis during the<br />
stance phase by the Stabilize Pelvis reflex. The trunk and head show even stronger sway<br />
from left to right due to the rotation about the spine joint and the considerable mass <strong>of</strong><br />
the upper body.<br />
The upper body oscillation in the sagittal plane explains the orientation <strong>of</strong> head and pelvis<br />
about the y-axis. It appears with twice the frequency <strong>of</strong> the stride, as the trunk leans<br />
forward after each heel strike. The Upright Trunk postural reflex cannot fully compensate<br />
for the mass inertia pushing the upper body forward after impact. A pelvis rotation <strong>of</strong> up<br />
to 8 ◦ remains. Again, the head displays the higher amplitude as the spine flexion is added<br />
to the pelvis rotation.<br />
The rotation <strong>of</strong> the pelvis about the z-axis mainly emerges from the compliance <strong>of</strong> the<br />
hip joint about the same axis. As the swing leg moves forward, a torque is induced to the<br />
pelvis that increases with the step length. Here, the rotation <strong>of</strong> the head and trunk is<br />
reduced by the flexibility <strong>of</strong> the spine and the compensating swing <strong>of</strong> the arms.<br />
8.1.4.3 Variation <strong>of</strong> <strong>Walking</strong> Velocity<br />
The figures so far have been based on a run <strong>of</strong> normal walking with the velocity modulation<br />
factor set to 0.8. This modulation signal influences several reflexes and motor patterns by<br />
adapting target values or scaling the amplitude <strong>of</strong> torque impulses. All these adjustments<br />
are obtained by simply multiplying the relevant values by the velocity factor. No other<br />
elaboratefunctionsareused. Bychangingthismodulationvalue, differentwalkingvelocities<br />
can be achieved. Figure 8.12 illustrates this relation by plotting the forward progression <strong>of</strong><br />
the pelvis for five different velocity factors.<br />
By varying the velocity modulation factor, walking velocities ranging from 1.1 m/s to<br />
1.4 m/s can be reached. At higher velocities, the steps lengthen and the oscillation <strong>of</strong> the<br />
upper body increases due to the stronger impact at heel strike. Slow walking reduces<br />
this oscillation in the sagittal plane, but lateral sway is still prominent. The lower torque<br />
impulse <strong>of</strong> the hip joint initiating the leg swing lessens the passive flexion angle <strong>of</strong> the
8.1. Normal <strong>Walking</strong> 155<br />
Pelvis X [ ◦ ]<br />
Pelvis Y [ ◦ ]<br />
Pelvis Z [ ◦ ]<br />
2<br />
0<br />
−2<br />
10<br />
5<br />
0<br />
10<br />
0<br />
−10<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Head X [ ◦ ]<br />
Head Y [ ◦ ]<br />
Head Z [ ◦ ]<br />
2<br />
0<br />
−2<br />
10<br />
5<br />
0<br />
10<br />
0<br />
−10<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 8.11: Orientation <strong>of</strong> head and pelvis over the course <strong>of</strong> one gait cycle. The solid lines<br />
represent the mean values over 30 steps <strong>of</strong> normal walking, the dashed lines mark the minimum<br />
and maximum values. The vertical dashed line indicates the transition from stance to swing.<br />
Pelvis Position X [m]<br />
10<br />
8<br />
6<br />
4<br />
2<br />
0<br />
0.0 1.0 2.0 3.0 4.0<br />
Time [s]<br />
5.0 6.0 7.0 8.0<br />
velocity resulting<br />
factor: velocity:<br />
0.75 1.13m/s 0.80 1.21m/s 0.85 1.27m/s 0.90 1.34m/s 0.95 1.38m/s Figure 8.12: Pelvis progression at different walking velocities. Only the walking velocity<br />
modulation value is changed, no other parameters are adapted.
156 8. Dynamic <strong>Walking</strong> Experiments<br />
knee. This decreases the ground clearance distance and raises the probability <strong>of</strong> the robot<br />
to stumble. Table 8.2 summarizes the resulting mean velocities and step lengths during<br />
walking with different velocity modulation factors.<br />
Velocity Factor <strong>Walking</strong> Velocity Step Length Max. Ankle Torque<br />
[ m/s] [m] [N]<br />
0.75 1.13 0.68 52<br />
0.80 1.21 0.76 56<br />
0.85 1.27 0.84 60<br />
0.90 1.34 0.88 65<br />
0.95 1.38 0.92 69<br />
Table 8.2: Variation <strong>of</strong> walking velocity, stride length, and maximum ankle torque during leg<br />
propulsion <strong>of</strong> walking with different velocity modulation values.<br />
The described variations <strong>of</strong> velocity are achieved without adapting any parameter <strong>of</strong> the<br />
control units involved. Further reducing or increasing the factor causes instabilities mainly<br />
due to stumbling during leg swing or tilting in the lateral direction. By manually tuning<br />
the parameters <strong>of</strong> some control units, faster or slower walking is possible, but no extensive<br />
gain <strong>of</strong> velocity can be obtained. For very slow and deliberate walking, the fundamental<br />
form <strong>of</strong> locomotion would have to be adapted. This gait transition can also be observed in<br />
human subjects. Likewise, to further increase the speed, the locomotion form should be<br />
changed to a running gait.<br />
8.1.4.4 Comparison to human data<br />
As human morphology and motion control serves as basis for this thesis, it stands to reason<br />
to compare the results from simulation to those from human gait analysis. In 1998, the<br />
Vicon company 1 , a manufacturer <strong>of</strong> systems for biomechanical gait analysis, provided a<br />
kinematic and kinetc data set <strong>of</strong> human walking that is used as basis <strong>of</strong> the following<br />
comparisons.<br />
Figure 8.13 presents the differences and similarities <strong>of</strong> four joint angle trajectories. The<br />
solid lines represent the results from simulation, the dashed lines are taken from the Vicon<br />
data set. The first plot illustrates that humans show stronger pelvis lift during the stance<br />
phase by additional hip abduction. Still, both curves have two elevations <strong>of</strong> hip abduction<br />
in common, one occurring during stance and one during the swing phase. However, humans<br />
keep the swing leg closer to the stance leg during the swing phase.<br />
More similarities can be found in the trajectories <strong>of</strong> the hip joint’s y-axis. Both curves<br />
have the same characteristic progress. The main difference is the additional hip extension<br />
<strong>of</strong> the simulated biped towards the end <strong>of</strong> the stance phase.<br />
The knee trajectories also show a similar behavior. Here, it must be admitted that the<br />
knee angle during weight acceptance is loosely modeled after the human example, as a<br />
semi-flat walking gait is aimed for. As such, the resemblance is to be expected. However,<br />
both in human and in the bipedal robot’s walking, the knee angle during the swing phase<br />
1 http://www.vicon.com/
8.1. Normal <strong>Walking</strong> 157<br />
Hip X [ ◦ ]<br />
Knee Y [ ◦ ]<br />
10<br />
0<br />
−10<br />
60<br />
40<br />
20<br />
0<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Hip Y [ ◦ ]<br />
Ankle Y [ ◦ ]<br />
40<br />
20<br />
0<br />
−20<br />
20<br />
0<br />
−20<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 8.13: Comparing joint angles in human walking (dashed lines) to those <strong>of</strong> the simulated<br />
biped (solid lines). <strong>Human</strong> data is taken from a data set provided by the Vicon company in 1998.<br />
emerges by passive dynamics and comparable trajectories arise. Generally, the peak angle<br />
<strong>of</strong> the simulated robot during this phase is slightly smaller and the duration <strong>of</strong> the knee<br />
bending is shorter. Furthermore, a small delay just before the leg swing can be observed.<br />
This is caused by the fact that, compared to human subjects, the robot lacks a small<br />
amount <strong>of</strong> forward velocity giving it more time between leg extension and touchdown <strong>of</strong><br />
the contralateral leg. In this point, the human gait clearly shows a superior optimization.<br />
As last example, the comparison <strong>of</strong> the ankle movements again reveals strong similarities.<br />
The robot tends to stronger plantarflexion after heel strike, whereas humans longer role<br />
over the heel. During this phase <strong>of</strong> point contact, no torques can be induced by ankle<br />
flexion. Again, the optimization <strong>of</strong> human walking allows this sacrifice <strong>of</strong> potential control<br />
in favor <strong>of</strong> a more efficient gait. Another difference can be found in additional plantarflexion<br />
during leg propulsion and in stronger dorsiflexion during the swing phase.<br />
Similar to the joint angle trajectories, resemblance <strong>of</strong> the absolute movements <strong>of</strong> body<br />
segments in humans and in the simulated robot can be observed. Figure 8.14 illustrates<br />
this fact using the position <strong>of</strong> the toe segment as an example. The vertical displacement <strong>of</strong><br />
the toe is plotted over the progress <strong>of</strong> one stride. The experimental data <strong>of</strong> the biped robot<br />
is averaged over 30 steps <strong>of</strong> normal walking on level terrain. As the position <strong>of</strong> the center<br />
<strong>of</strong> the inner toe segment is shown, there remains an <strong>of</strong>fset <strong>of</strong> 3cm to the ground plane.<br />
Both curves show the same distinctive course and similar amplitude. After heel strike, the<br />
toes are lowered to the ground where they stay throughout the stance phase and during<br />
leg propulsion. At the onset <strong>of</strong> the swing phase, the toes lift from the ground as the foot<br />
dorsiflexes to a neutral angle. During the leg swing, the toes first come closer to the ground<br />
as the leg traverses under the trunk. As soon as the knee extends towards the end <strong>of</strong> the<br />
swing, the foot rotates and the toes point upwards, resulting in the maximum distance to<br />
the ground.<br />
In summary, the joint angle and segment position trajectories <strong>of</strong> human subjects and the<br />
simulated robot show remarkable resemblance. The reason for this can be found in several
158 8. Dynamic <strong>Walking</strong> Experiments<br />
(a)<br />
Toe Position Z [m]<br />
0.2<br />
0.1<br />
0.0<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 8.14: Comparing the vertical toe displacement <strong>of</strong> human subjects (a) to those <strong>of</strong> the<br />
simulated biped (b), averaged over 30 steps. <strong>Human</strong> data plot taken from [Winter 92], p47.<br />
facts. First, both control strategies rely on the exploitation <strong>of</strong> passive dynamics. As the<br />
masses and lengths <strong>of</strong> the robot’s body segments have been modeled based on human<br />
data, one expects that similar motions emerge. Furthermore, the active part <strong>of</strong> the control<br />
system is designed following insights from neuroscience and biomechanics. Several <strong>of</strong> the<br />
relevant control concepts have been transferred, and indeed <strong>like</strong>wise locomotion patterns<br />
originate. Finally, many parameters <strong>of</strong> the control units might be unconsciously tuned<br />
to achieve a human-<strong>like</strong> gait <strong>of</strong> the simulated biped because <strong>of</strong> repeated consultation <strong>of</strong><br />
biomechanical data and observation <strong>of</strong> the supremacy <strong>of</strong> human walking during the design<br />
and development <strong>of</strong> the suggested control system.<br />
8.1.5 Kinetic Analysis<br />
Kinetic analysis considers the acting <strong>of</strong> internal as well as external forces and torques.<br />
This gives a deeper insight into the inner workings <strong>of</strong> the control system and allows to<br />
draw conclusions regarding the feasibility <strong>of</strong> the approach on a real robot. Furthermore,<br />
preliminary statements on the efficiency <strong>of</strong> the emerging gait are possible.<br />
8.1.5.1 Ground Reaction Forces<br />
During undisturbed walking, external forces are only induced by ground contact. The<br />
robot is equipped with several sensors to measure these forces: A three axis load cell<br />
connects the foot with the ankle joint. In addition, four one-dimensional force sensors<br />
are mounted in the corners <strong>of</strong> each feet, and referred to as inner toe, outer toe, inner<br />
heel, and outer heel sensor. Figure 8.15 visualizes the measurements <strong>of</strong> these sensors.<br />
Again, the data is normalized to one gait cycle and averaged over 30 successive steps <strong>of</strong><br />
walking on level ground. The solid lines represent the mean values, the dashed lines show<br />
the minimum and maximum values. The vertical dashed line marks the stance-to-swing<br />
transition. To ease orientation, the angle trajectory <strong>of</strong> the ankle joint is included in the<br />
upper right corner.<br />
The force in z-direction perceived by the load cell summarizes the load the foot has to bear.<br />
Adding up the forces measured by the individual foot sensors results in the same trajectory.<br />
During initial weight acceptance, the foot load surpasses the amount <strong>of</strong> gravitational force<br />
generated by the body weight due to the impact. However, this overshoot is only marginal<br />
(b)
8.1. Normal <strong>Walking</strong> 159<br />
LC Force Z [N]<br />
LC Torque X [Nm]<br />
Inner Toe [N]<br />
Outer Toe [N]<br />
900<br />
600<br />
300<br />
0<br />
20<br />
0<br />
0 25 50 75 100<br />
−20<br />
0 25 50 75 100<br />
400<br />
200<br />
0<br />
400<br />
200<br />
0<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Ankle Y [ ◦ ]<br />
LC Torque Y [Nm]<br />
Inner Heel [N]<br />
Outer Heel [N]<br />
20<br />
0<br />
−20<br />
60<br />
30<br />
0<br />
0 25 50 75 100<br />
−30<br />
0 25 50 75 100<br />
400<br />
200<br />
0<br />
400<br />
200<br />
0<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 8.15: Forces and torques measured by the foot sensors over one gait cycle. The solid<br />
lines represent the mean values over 30 steps <strong>of</strong> normal walking on even ground. The dashed<br />
lines mark the minimum and maximum values. The vertical dashed line indicates the transition<br />
from stance to swing.<br />
thanks to the preventive leg bending before heel strike by the Weight Acceptance motor<br />
pattern. Also, some <strong>of</strong> the impact is absorbed by damping in the ankle joint as the foot<br />
rotates from heel strike to full contact during the first ten percent <strong>of</strong> the gait cycle. The<br />
short decline in foot load right after full contact can be explained by the activity <strong>of</strong> the<br />
leg propulsion motor pattern that pushes the robot forward via the contralateral ankle<br />
joint. This action shifts some <strong>of</strong> the body weight back to the other leg. As the swing <strong>of</strong><br />
the contralateral leg sets in after about 20 percent <strong>of</strong> the cycle, the body weight is fully<br />
supported by the stance leg. A short peak in vertical force can be observed during leg<br />
propulsion, then the force drops to zero at lift-<strong>of</strong>f. During the swing phase, only small<br />
deviations from zero appear due to the weight <strong>of</strong> the foot pulling at the load cell.<br />
The torques measured by the load cell give a first indication on the progress <strong>of</strong> the center<br />
<strong>of</strong> pressure (cop). During the stance phase, the torque about the x-axis oscillates about
160 8. Dynamic <strong>Walking</strong> Experiments<br />
Medial Lateral<br />
Center <strong>of</strong> Pressure<br />
outer heel outer toe<br />
inner heel inner toe<br />
Posterior Anterior<br />
Ant.<br />
CoP X<br />
Post.<br />
Lat.<br />
CoP Y<br />
Med.<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
% <strong>of</strong> Gait Cycle<br />
Figure 8.16: Center <strong>of</strong> pressure trajectories calculated from the four force sensors in each foot.<br />
The values present an average over 30 steps <strong>of</strong> normal walking on even terrain.<br />
zero due to the action <strong>of</strong> the Lateral Balance Ankle reflex. The dashed minimum and<br />
maximum values show considerable variation in the trajectory, underlining the reactive<br />
character <strong>of</strong> the responsible motor pattern. The torque value remains within ±10Nm,<br />
considering the short leverage <strong>of</strong> the foot in the lateral direction. Higher torques would<br />
cause the foot to turn onto its edge.<br />
The torque about the y-axis illustrates that the cop travels from heel to toe. At heel-strike,<br />
the foot pushes the robot forward by the torque <strong>of</strong> the passive ankle spring and the activity<br />
<strong>of</strong> the Forward Velocity reflex. Due to the action <strong>of</strong> the leg propulsion motor pattern, a<br />
strong torque peak <strong>of</strong> more than 60Nm can be observed. Both torque values disappear<br />
during the swing phase since no more external forces act on the foot.<br />
The measurements <strong>of</strong> the individual toe and heel sensors provide further details on the<br />
ground reaction forces. At touchdown, only the heel sensors detect the impact, with an<br />
emphasis on the outer side <strong>of</strong> the foot. The ankle joint then rotates to full foot contact<br />
and the toe sensors also measure a force, with the peak value showing strong variations<br />
due to deviations in the robot’s forward velocity. Already after 50 percent <strong>of</strong> the gait<br />
cycle, i.e. well before the swing phase, the heel loses contact with the ground and leg<br />
propulsion pushes the toes downwards. Here, a maximum force <strong>of</strong> over 400N can occur.<br />
Not surprisingly, the foot sensors do not measure relevant forces during the swing phase.<br />
The four force sensors mounted in the foot corners also allow to estimate the trajectory <strong>of</strong><br />
the cop. Computing the ratio between the inner and outer sensors, or the toe and heel<br />
sensors, respectively, yields<br />
CoPX =<br />
CoPY =<br />
Finner toe +Fouter toe<br />
Finner toe +Fouter toe +Finner heel +Fouter heel<br />
Fouter toe +Fouter heel<br />
Finner toe +Fouter toe +Finner heel +Fouter heel<br />
(8.1)<br />
(8.2)
8.1. Normal <strong>Walking</strong> 161<br />
Figure 8.16 shows the progress <strong>of</strong> the cop values over the progress <strong>of</strong> one gait cycle on<br />
the right side, and the trajectory <strong>of</strong> the cop in the horizontal plane on the left side. Both<br />
visualizations illustrate the characteristics <strong>of</strong> the cop trajectory. At heel strike, the cop<br />
is located at the posterior end <strong>of</strong> the foot and quickly moves towards the center. During<br />
the middle part <strong>of</strong> the stance phase, the cop stays around the center <strong>of</strong> the foot while the<br />
postural reflexes generate correcting ankle torques to stabilize the robot. Towards the end<br />
<strong>of</strong> the stance phase, the cop travels to the anterior end and to the medial side <strong>of</strong> the foot<br />
as the leg propulsion accelerates the robot forward by plantarflexion <strong>of</strong> the foot. Since<br />
the upper body moves in the direction <strong>of</strong> the next stance leg, the main propulsion force is<br />
raised by the inner toe segment.<br />
Disregarding the influence <strong>of</strong> the postural reflexes, the cop trajectory travels smoothly<br />
from heel to toes during the stance phase. In y-direction, it remains well within the center<br />
<strong>of</strong> the foot with a small bias to the lateral side since the robot leans towards the side <strong>of</strong><br />
the stance leg. The distance to the stability margin stays large throughout the walking<br />
cycle, indicating that there is still ample reserve concerning the machine’s stability and<br />
there is no immediate risk for the robot to tumble.<br />
8.1.5.2 Joint Torques<br />
Analysis <strong>of</strong> the torques occurring in the joints during walking provides additional information<br />
on the working <strong>of</strong> the control system and allows to assess its application on a real<br />
robot. Figure 8.17 displays the effective torques as solid lines. The torque value <strong>of</strong> the<br />
simulated torque controller are given as dotted lines. These values do not include the<br />
effects <strong>of</strong> the parallel spring and the joint damping. All plots are again based on the same<br />
run as the previous figures and represent the mean values <strong>of</strong> 30 consecutive steps. The<br />
dashed lines illustrate the minimum and maximum values, the vertical dashed line marks<br />
the transition from stance to swing.<br />
The torque acting on the y-axis <strong>of</strong> the spine joint is mainly generated by the position control<br />
working at low compliance and constant target angle. High torque values <strong>of</strong> −100Nm can<br />
be observed after each heel strike. They compensate the mass inertia <strong>of</strong> the trunk swaying<br />
forward. The further progress <strong>of</strong> the torque trajectory reflects the continuous stabilization<br />
<strong>of</strong> the upper body. Similar behavior can be seen in the other axis <strong>of</strong> the spine joint. The<br />
z-axis in particular shows lower joint stiffness in the smooth motor torque values.<br />
The shoulder joint exhibits the motor torque impulses generated by the Arm Swing motor<br />
pattern. Depending on the current joint angle and velocity, damping and a weak parallel<br />
elasticity partly work against the requested arm swing. The ad- and abduction <strong>of</strong> the arm<br />
are restricted by the torque produced by the compliant position controller. The elbow<br />
joint is set to zero stiffness and the motor only shows activity when the joint reaches its<br />
limits in the fully extended position.<br />
The y-axis <strong>of</strong> the hip joint exhibits the highest torque peak <strong>of</strong> all joints. As the corresponding<br />
spine joint, it has to decelerate the upper body after heel strike, but due to the longer<br />
leverage and the additional weight <strong>of</strong> the pelvis segment, the torque values are even higher<br />
and reach nearly 200Nm. A second peak occurs during the acceleration <strong>of</strong> the hip joint<br />
for initiating the leg swing. At higher walking velocities, a short swing phase is necessary<br />
to move the leg to its anterior position in time for the next heel strike. As already realized<br />
by J. Pratt, the maximum velocity and torque <strong>of</strong> the hip joint limits the robot’s walking
162 8. Dynamic <strong>Walking</strong> Experiments<br />
Spine Y [Nm]<br />
Shoulder Y [Nm]<br />
Elbow Y [Nm]<br />
Hip Y [Nm]<br />
Knee Y [Nm]<br />
Ankle Y [Nm]<br />
100<br />
0<br />
−100<br />
10<br />
0<br />
−10<br />
5<br />
0<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
−5<br />
0 25 50 75 100<br />
100<br />
0<br />
−100<br />
−200<br />
0 25 50 75 100<br />
50<br />
0<br />
−50<br />
−100<br />
0 25 50 75 100<br />
30<br />
0<br />
−30<br />
−60<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Spine X [Nm]<br />
Spine Z [Nm]<br />
Shoulder X [Nm]<br />
Hip X [Nm]<br />
Hip Z [Nm]<br />
Ankle X [Nm]<br />
50<br />
0<br />
−50<br />
0 25 50 75 100<br />
20<br />
0<br />
−20<br />
10<br />
0<br />
−10<br />
50<br />
0<br />
−50<br />
−100<br />
20<br />
0<br />
−20<br />
20<br />
0<br />
−20<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 8.17: Average joint torques acting during one gait cycle. The solid line represents the<br />
mean values over 30 steps <strong>of</strong> normal walking on level ground. The dashed lines mark the minimum<br />
and maximum values. Torques generated by the motor without the influence <strong>of</strong> damping and<br />
parallel springs are shown by the dotted line.
8.1. Normal <strong>Walking</strong> 163<br />
velocity [Pratt 00]. At the end <strong>of</strong> the swing phase, the torque is reduced to the amount<br />
necessary to lock the hip angle and to control the legs angle <strong>of</strong> attack.<br />
During the stance phase, the hip joint also shows high torque values about its x-axis.<br />
This torque is used to stabilize the pelvis against the weight <strong>of</strong> the upper body while the<br />
contralateral leg is swinging. As soon as the double support phase starts after 50 percent<br />
<strong>of</strong> the gait cycle, the load is distributed and the torque is reduced. During the legs swing<br />
phase, some torque is necessary to adjust the lateral foot placement. The torque about<br />
the hip joint’s z-axis is produced due to the compliant joint action and is proportional to<br />
the current joint angle.<br />
The main strain on the knee joint also occurs during the stance phase. The minor flexion<br />
<strong>of</strong> the knee implicates that the joint has to support the body weight while it is not fully<br />
stretched. With the onset <strong>of</strong> the swing phase, the knee joint is set to passive action at<br />
maximum compliance, and the motor does not have to produce any torque.<br />
At heel strike, the ankle joint slows down the plantarflexion <strong>of</strong> the foot by a passive torque<br />
resulting from damping and the parallel spring. The joint’s motor remains mainly inactive<br />
except for the corrections <strong>of</strong> the Forward Velocity reflex until the leg propulsion motor<br />
pattern sets in. Then considerable torque is produced to accelerate the robot forward.<br />
During the swing phase, the foot is kept in minor dorsiflexion and the motor has to<br />
compensate for the torque generated by the parallel spring due to the deflection from its<br />
equilibrium position. The torques produced in the x-axis <strong>of</strong> the ankle joint result from the<br />
action <strong>of</strong> the Lateral Balance Ankle postural reflex.<br />
While the peak torque values, in particular those <strong>of</strong> the hip joint, appear to be relatively<br />
large, they are still far below the capabilities <strong>of</strong> humans or state-<strong>of</strong>-the-art bipedal robots.<br />
For instance, the robot LOLA <strong>of</strong> the University <strong>of</strong> Munich can generate a peak torque <strong>of</strong><br />
370Nm in the y-axis <strong>of</strong> its hip joint, at a total robot weight <strong>of</strong> 55kg and a similar number<br />
<strong>of</strong> degrees <strong>of</strong> freedom. Thus it should be possible to develop joint actuators meeting at least<br />
the torque demands. There still remains the problem <strong>of</strong> achieving adjustable compliance<br />
and sufficiently low joint friction.<br />
8.1.5.3 Joint Power<br />
In knowing the joint angles and torques, it is possible to calculate the mechanical work<br />
done by the joints as well as their mechanical power. Rotational work W is defined as<br />
W = τθ, (8.3)<br />
with τ being the torque and θ the joint revolution this torque is applied through. Power<br />
is the rate at which this work is performed. Using the data set <strong>of</strong> the run presented<br />
throughout this chapter, the mechanical power Pj for each joint j is calculated as<br />
Pj(t) =<br />
1<br />
2 [τj(t+∆T)−τj(t−∆T)]·θj(t+∆T)−θj(t−∆T)<br />
, (8.4)<br />
2·∆T<br />
with ∆T = 25msec. The resulting power trajectories are again averaged over 30 steps <strong>of</strong><br />
normal walking, and the mean, minimum, and maximum values are shown in Figure 8.18.<br />
The solid lines represent the power based on the effective torque values, while the dotted<br />
lines depict the mechanical motor power.
164 8. Dynamic <strong>Walking</strong> Experiments<br />
Spine Y [W]<br />
Shoulder Y [W]<br />
Elbow Y [W]<br />
Hip Y [W]<br />
Knee Y [W]<br />
Ankle Y [W]<br />
50<br />
0<br />
−50<br />
0 25 50 75 100<br />
20<br />
10<br />
0<br />
−10<br />
0 25 50 75 100<br />
0<br />
−1<br />
−2<br />
−3<br />
800<br />
400<br />
0<br />
100<br />
0<br />
−100<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
−200<br />
0 25 50 75 100<br />
500<br />
250<br />
0<br />
−250<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Spine X [W]<br />
Spine Z [W]<br />
Shoulder X [W]<br />
Hip X [W]<br />
Hip Z [W]<br />
Ankle X [W]<br />
0<br />
−5<br />
−10<br />
5<br />
0<br />
−5<br />
0 25 50 75 100<br />
−10<br />
0 25 50 75 100<br />
1<br />
0<br />
−1<br />
−2<br />
0 25 50 75 100<br />
60<br />
30<br />
0<br />
5<br />
0<br />
−5<br />
−10<br />
5<br />
0<br />
−5<br />
0 25 50 75 100<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 8.18: Average approximated joint power arising during one gait cycle. The solid line<br />
represents the mean values over 30 steps <strong>of</strong> normal walking on level ground. The dashed lines<br />
mark the minimum and maximum values. Power generated by the motor without the influence<br />
<strong>of</strong> damping and parallel springs is shown by the dotted line.
8.1. Normal <strong>Walking</strong> 165<br />
Peak Peak Motor Maximum Max. Motor<br />
�<br />
Motor<br />
Joint Torque [Nm] Torque [Nm] Power [W] Power [W] Power [W]<br />
Spine X 29.0 13.4 0.5 1.5 0.3<br />
Spine Y 111.1 103.8 20.3 21.4 3.2<br />
Spine Z 16.3 9.5 1.6 1.9 0.5<br />
Shoulder X 7.4 6.9 0.2 0.3
166 8. Dynamic <strong>Walking</strong> Experiments<br />
�<br />
ΣPj =<br />
max(0,Pj(t))dt (8.5)<br />
Totalizing these values gives a mechanical power consumption <strong>of</strong> the biped during walking<br />
<strong>of</strong> 318.8W, with the two hip joints alone contributing nearly two thirds <strong>of</strong> this sum. As the<br />
control units were designed without any concern about energy consumption, it is highly<br />
probable that this number could be reduced after appropriate optimization.<br />
In an article on passive walkers, Collins et al. propose to use the dimensionless mechanical<br />
cost <strong>of</strong> transport cmt = (energy used)/(weight×distance traveled) to compare the walking<br />
efficiency <strong>of</strong> different robots and humans [Collins 05]. They give an estimate <strong>of</strong> cmt = 0.05<br />
for human walking and <strong>of</strong> cmt = 1.6 for the robot Asimo by Honda. With a weight <strong>of</strong><br />
76kg and an approximate walking velocity <strong>of</strong> 1.2 m/s during the analyzed run, the cost <strong>of</strong><br />
transport for the presented biped amounts to<br />
cmt = 318.8W<br />
760N·1.2 m/s<br />
= 0.35 (8.6)<br />
While this value is still well above the one <strong>of</strong> human walking, it attributes the presented<br />
bipedal robot to be nearly five times more efficient than Asimo using a technical control<br />
approachbasedonjointanglecontrol. Andasnotedbefore,thesystemstillhasthepotential<br />
to be optimized regarding its energy consumption. Of course, the simulation environment<br />
does not model all aspects <strong>of</strong> a real robot. Therefore, this result can only indicate the<br />
walking efficiency <strong>of</strong> the suggested methodology by exploiting inherent dynamics and<br />
making use <strong>of</strong> elastic energy storage.<br />
8.1.5.4 Active and Passive Joint Action<br />
To conclude the kinetic analysis, Table 8.4 lists which joints are actively controlled and<br />
which joints are passive during each walking phase. Only the spine joints and the joints <strong>of</strong><br />
the left body half are given. The number states the stiffness factor defining the compliance<br />
<strong>of</strong> each joint for the constant equilibrium point. A stiffness factor <strong>of</strong> 1.0 results in minimum<br />
compliance, a factor <strong>of</strong> 0.0 in a freely rotating joint with only the damping acting. The<br />
letters ‘M’ and ‘R’ indicate that a motor pattern or a reflex is influencing the joint during<br />
that phase. Reflexes put in parentheses only act due to disturbances and remain mostly<br />
inactive during normal walking.<br />
Including both the left and the right sided joints in the calculation results in the following<br />
totals: during stimulation <strong>of</strong> phases one and three, 8 joint are actively controlled and 13<br />
joints act passively. In phase combination one and four, 10 joints are active and 11 joints<br />
are passive. And during phases two and five, again 8 joints are active and 13 joints are<br />
passive. In total, no more than half <strong>of</strong> the joints are simultaneously actively controlled<br />
throughout the walking cycle, reducing the overall complexity <strong>of</strong> the control system. In<br />
fact, only 1–4 <strong>of</strong> the 21 degrees <strong>of</strong> freedom must be controlled by motor patterns for<br />
directing the passive system dynamics towards a walking gait.<br />
Furthermore, some passive joints remain at the same compliance setting during all phases <strong>of</strong><br />
walking. These joints could be replaced by fixed springs and would not need an additional<br />
actuator. However, a closer look reveals that this situation would change when starting to<br />
walk on intense slopes, or when including curved walking. Then, the spine joints would be
8.1. Normal <strong>Walking</strong> 167<br />
Joint Phase 1 Phase 2 Phase 3 Phase 4 Phase 5<br />
Spine X 0.9 0.9 0.9 0.9 0.9<br />
Spine Y 1.0 1.0 1.0 1.0 1.0<br />
Spine Z 0.2 0.2 0.2 0.2 0.2<br />
Shoulder X 0.3 0.3 0.3 0.3 0.3<br />
Shoulder Y 0.0 0.0 0.0 M 0.0 M 0.0<br />
Elbow Y 0.0 0.0 0.0 0.0 0.0<br />
Hip X 0.1 R 0.1 R 0.1 0.1 R 0.1 R<br />
Hip Y 0.0 R 0.0 R 0.0 M,R 0.0 M,R 0.0 R<br />
Hip Z 0.5 0.5 0.5 0.5 0.5<br />
Knee Y 0.0 M 0.3 0.0 0.0 (R) 0.0 M<br />
Ankle X 0.4 R 0.0 R 0.1 0.1 0.1<br />
Ankle Y 0.0 R 0.0 R 0.0 M 0.1 (R) 0.1 (R)<br />
Active 5 4 3 5 4<br />
Passive 7 8 9 7 8<br />
Table 8.4: Passive and active joints during each walking phase for the left sided joints. The<br />
numbers give the joint stiffness, M and R mark the active control by a motor pattern or reflex.<br />
necessary to compensate the inclination, and the hip’s z-axis would be used to control the<br />
walking direction. Still, the passive joint action suffices during walking on minor slopes or<br />
small steps as will be shown below.<br />
8.1.5.5 Comparison to human data<br />
As done for the kinematic data, some results from the kinetic analysis are compared to<br />
human walking. Figure 8.19 shows the effective torque <strong>of</strong> four joints for both human<br />
walking and the presented biped. <strong>Human</strong> data is again taken from the data set provided by<br />
Vicon and is plotted as dashed line. The torque values are given in Nm/kg, normalizing the<br />
torque by the body weight as commonly done in biomechanics to make results comparable.<br />
The torque trajectories <strong>of</strong> the hip joint show strong similarities. Besides the additional<br />
oscillation occurring in the robot data, the shape <strong>of</strong> the curves match. The torque about<br />
the hip’s x-axis even resembles in amplitude. In contrast, the robot’s torque values <strong>of</strong> the<br />
y-axis are up to three times higher than in human subjects. During the stance phase, this<br />
can be explained by stronger sway <strong>of</strong> the upper body that must be compensated. Here,<br />
suitable anticipatory motor patterns could reduce the necessary torque.<br />
The knee joint shows a different characteristic during weight acceptance in the first part<br />
<strong>of</strong> the stance phase. <strong>Human</strong> subjects actively flex the knee before and during heel strike.<br />
Then the body weight is decelerated by a torque working against excessive bending <strong>of</strong> the<br />
knee. The robot also actively bends the knee. But then the plantarflexion <strong>of</strong> the foot on<br />
the contralateral side accepts some <strong>of</strong> the body weight, and the flexion <strong>of</strong> the knee must<br />
actually be supported. During leg swing, in both human and robot, minor torques appear<br />
due to elasticities and damping.<br />
The ankle torque trajectories again show notable resemblance. The main difference is the<br />
shift <strong>of</strong> the onset <strong>of</strong> the push-<strong>of</strong>f motor pattern that occurs earlier in human subjects and<br />
is <strong>of</strong> higher amplitude.
168 8. Dynamic <strong>Walking</strong> Experiments<br />
Ext 2<br />
Hip X<br />
[ Nm/kg]<br />
1<br />
0<br />
Flex −1<br />
Ext 2<br />
Knee Y<br />
[ Nm/kg]<br />
1<br />
0<br />
Flex −1<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Ext 2<br />
Hip Y<br />
[ Nm/kg]<br />
1<br />
0<br />
Flex −1<br />
Ext 2<br />
Ankle Y<br />
[ Nm/kg]<br />
1<br />
0<br />
Flex −1<br />
0 25 50 75 100<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 8.19: Comparing joint moments in human walking (dashed lines) to those <strong>of</strong> the<br />
simulated biped (solid lines). Torque values are normalized by body weight. <strong>Human</strong> data is<br />
again taken from the data set provided by Vicon.<br />
Figure 8.20 presents a similar comparison <strong>of</strong> joint power trajectories. Unfortunately, the<br />
Vicon data set does not include any information on the power <strong>of</strong> hip ab- and adduction,<br />
so only three joint axes are compared. As expected after the analysis <strong>of</strong> the torque output,<br />
the hip joint’s power consumption is considerable higher in the presented robot than in<br />
human subjects. In particular during the initiation <strong>of</strong> the leg swing, a strong power peak<br />
can be observed. As already argued above, this might originate from the relatively strong<br />
damping.<br />
The knee joint again produces a very similar power progression. Both human subjects and<br />
the robot exhibit two small peaks <strong>of</strong> power absorption during the leg swing. Those <strong>of</strong> the<br />
robot are located closer to one another as the knee flexion is <strong>of</strong> shorter duration. The<br />
power trajectories <strong>of</strong> the ankle joint also show strong resemblance. However, the robot<br />
absorbs more energy during the ankle rotation at heel strike. During leg propulsion, the<br />
robot produces slightly more power output.<br />
In summary, the kinetic comparison renders a similar picture as the kinematic comparison.<br />
The torque as well as the power trajectories during human and robot walking mostly<br />
resemble each other. The main differences can be found in the flexion and extension <strong>of</strong> the<br />
hip joint. Here, the robot produces considerably more torque and power output. Thus,<br />
any optimization towards reducing the energy consumption should begin by considering<br />
the control units affecting this joint.<br />
8.2 <strong>Walking</strong> under Disturbances<br />
The first part <strong>of</strong> this chapter illustrated that the proposed control approach is well able<br />
to achieve efficient, dynamic walking <strong>of</strong> a bipedal robot. Already in the normal walking
8.2. <strong>Walking</strong> under Disturbances 169<br />
Prod 4<br />
Knee Y<br />
[ W/kg]<br />
2<br />
0<br />
Abs −2<br />
Prod 4<br />
Hip Y<br />
[ W/kg]<br />
Abs −2<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
2<br />
0<br />
0 25 50 75 100<br />
Prod 4<br />
Ankle Y<br />
[ W/kg]<br />
2<br />
0<br />
Abs −2<br />
0 25 50<br />
% <strong>of</strong> Gait Cycle<br />
75 100<br />
Figure 8.20: Comparing joint power in human walking (dashed lines) to those <strong>of</strong> the simulated<br />
biped (solid lines). Power values are normalized by body weight. <strong>Human</strong> data is taken from the<br />
Vicon data set.<br />
described there, local and postural reflexes help to stabilize the robot against self-induced<br />
disturbances and against the impacts occurring at each foot contact. It is one conjecture <strong>of</strong><br />
this thesis that the distributed and purely reactive action <strong>of</strong> these independent control units<br />
enables walking under the influence <strong>of</strong> additional external and unforeseen disturbances.<br />
This section will evaluate the performance <strong>of</strong> the reflex network during perturbed walking<br />
by examining three different kinds <strong>of</strong> disturbances as shown in Figure 8.21: walking on<br />
sloped terrain, walking over steps, and walking while external forces are applied to the<br />
trunk <strong>of</strong> the robot. It should be noted again that all experiments are performed with<br />
the same set <strong>of</strong> model and control unit parameters. Only a different walking velocity<br />
modulation factor is used in some runs to vary the amount <strong>of</strong> energy put into the system<br />
by the motor patterns.<br />
8.2.1 Sloped Terrain<br />
In a first experiment, the robot is placed on sloped terrain <strong>of</strong> different angles. The robot<br />
is dropped from a small height on the ground and the standing control is balancing the<br />
robot. Then walking is initiated and the biped has to start and to continue to walk on the<br />
sloped surface. Downhill and uphill walking is examined as well as locomotion on terrain<br />
inclined to the side.<br />
Figure 8.22 compares the walking on level ground with walking on a surface inclined<br />
upwards by one degree and inclined downward by two and four degrees. The pelvis height<br />
is included to illustrate the progression <strong>of</strong> the slope and to show that the robot manages<br />
to maintain a smooth and steady gait. On the left, the figure plots both the effective as<br />
well as the pure motor torques <strong>of</strong> the ankle joint about the y-axis. The trajectories are
170 8. Dynamic <strong>Walking</strong> Experiments<br />
(a) (b) (c)<br />
Figure 8.21: Experiments on walking under disturbances: (a) walking on a downhill slope, (b)<br />
stepping up a platform, (c) walking with an external force acting at the torso.<br />
averaged over the steps <strong>of</strong> the respective run. The first eight seconds <strong>of</strong> the activity <strong>of</strong> the<br />
left (green) and right (red) Forward Velocity postural reflexes are depicted on the lower<br />
right. During the runs on level and downhill ground, the walking velocity factor is set to<br />
0.8, during the uphill run the factor is set to 0.95 as will be explained below. The resulting<br />
effective walking velocity amount to approximately 1.2 m/s, differing slightly depending on<br />
the ground inclination.<br />
Regarding the action <strong>of</strong> the postural reflex, it can be noted that only when walking downhill<br />
at 4 ◦ considerably more activity can be observed. In the other terrains, the required<br />
postural correction is indeed different in its characteristic but similar in strength. Only at<br />
steep inclinations, higher reflex intensity becomes necessary.<br />
The results <strong>of</strong> the reflex action can best be observed in the ankle torque during the first<br />
half <strong>of</strong> the gait cycle. After about 5% <strong>of</strong> the cycle, the foot has full ground contact and the<br />
Forward Velocity control units influence the ankle torque until the heel lifts <strong>of</strong>f at about<br />
45%. In Figure 8.22, this interval is marked by the light red box. During this phase, foot<br />
dorsiflexion, i.e. positive ankle torque values, push the heel to the ground and accelerate<br />
the robot. In contrast, plantarflexion represented by negative torque values, decelerate the<br />
robot. During uphill walking, dorsiflexion <strong>of</strong> the foot slightly predominates, but no distinct<br />
difference to walking on level ground can be observed. The situation is more obvious as<br />
the ground inclines forward. Already at two degrees, prominent foot plantarflexion can be<br />
noted. This effect intensifies with increasing slope. At four degrees, a peak motor torque<br />
<strong>of</strong> nearly −40Nm occurs.<br />
Another distinction in ankle torque can be noticed during the subsequent leg propulsion.<br />
As the body mass has traveled in front <strong>of</strong> the stance leg, the situation reverses and foot<br />
plantarflexion now results in accelerating the robot. From downhill to uphill walking, a<br />
considerable increase in leg propulsion from −40Nm to nearly −80Nm can be observed.<br />
This behavior stabilizes the robot since the gain or reduction in potential energy caused by<br />
the slope must be compensated. The reason for the change in ankle torque can be found<br />
in two facts: during uphill walking, the parallel spring mounted in the ankle is extended
8.2. <strong>Walking</strong> under Disturbances 171<br />
Uphill Slope 1 ◦<br />
Level Ground<br />
Downhill Slope 2 ◦<br />
Downhill Slope 4 ◦<br />
Ankle Torque Y [Nm]<br />
Ankle Torque Y [Nm]<br />
Ankle Torque Y [Nm]<br />
Ankle Torque Y [Nm]<br />
40<br />
0<br />
−40<br />
−80<br />
40<br />
0<br />
−40<br />
−80<br />
40<br />
0<br />
−40<br />
−80<br />
40<br />
0<br />
−40<br />
−80<br />
0 25 50 75 100<br />
% <strong>of</strong> Gait Cycle<br />
0 25 50 75 100<br />
% <strong>of</strong> Gait Cycle<br />
0 25 50 75 100<br />
% <strong>of</strong> Gait Cycle<br />
0 25 50 75 100<br />
% <strong>of</strong> Gait Cycle<br />
Pelvis Z [m]<br />
Forw. Vel. a<br />
Pelvis Z [m]<br />
Forw. Vel. a<br />
Pelvis Z [m]<br />
Forw. Vel. a<br />
Pelvis Z [m]<br />
Forw. Vel. a<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0 8.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0 8.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0 8.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0 8.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0 8.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0 8.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0 8.0<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0<br />
Time [s]<br />
6.0 8.0<br />
Figure 8.22: Comparison <strong>of</strong> the ankle torque, the pelvis height, and the activity <strong>of</strong> the Forward<br />
Velocity postural reflex at different ground slopes.
172 8. Dynamic <strong>Walking</strong> Experiments<br />
further towards the end <strong>of</strong> the stance phase and thus induces more torque during leg<br />
propulsion. Similarly, ankle torque is reduced while walking downhill. This effect occurs<br />
without any control and illustrates the self-stabilizing properties <strong>of</strong> elastic elements. The<br />
second reason for the change in ankle torque lies in the Leg Propulsion motor pattern.<br />
The amplitude <strong>of</strong> its torque impulse is influenced by two modulation factors. On the one<br />
hand, the ankle’s angle at the onset <strong>of</strong> the pattern increases or decreases the amplitude,<br />
resulting in a behavior similar to the one <strong>of</strong> the parallel spring. On the other hand, the<br />
control unit receives the same modulation factor as the Forward Velocity reflex based on<br />
the trajectory <strong>of</strong> the estimated com position. By this means, the leg propulsion effect is<br />
reinforced in case the estimated velocity is too low, and vice versa.<br />
By repeating the experiment on different slopes, the limits <strong>of</strong> the postural control system<br />
can be determined. At downhill inclinations <strong>of</strong> more than 5 ◦ , the robot does not manage<br />
to maintain stability for a long time. The step length increases too much, resulting in<br />
stronger oscillation <strong>of</strong> the trunk, but also in reduced lateral stability as changes in foot<br />
placement and ankle torque have less influence. Uphill walking shows to be more difficult.<br />
Already at minor slopes, two problems can be observed: the robot’s forward velocity<br />
decreases at each step as additional potential energy must be raised; and due to the small<br />
ground clearance during foot swing, the robot tends to stumble. To a certain degree, both<br />
difficulties can be solved by increasing the walking velocity modulation factor. That way,<br />
more energy is added to the system, and the higher torque in the hip joint during swing<br />
initiation results in a slightly larger ground clearance. Still, starting at uphill slopes <strong>of</strong><br />
about two 2 ◦ , the robot cannot maintain walking for more than a few steps.<br />
Stability during up- and downhill walking could be increased by adapting the parameters<br />
<strong>of</strong> some control units and by introducing additional postural reflexes. Tuning <strong>of</strong> the step<br />
length, the propulsion forces, or the correcting ankle torques would slightly improve the<br />
walking abilities. To achieve a more substantial enhancement <strong>of</strong> stability, a postural reflex<br />
adapting the orientation <strong>of</strong> the upper body seems more promising. As it can be observed<br />
in humans, leaning backwards during downhill and bending forward during uphill walking<br />
generates the desired effect. Such a control unit would either require an estimation <strong>of</strong> the<br />
ground inclination based on the inertial measurement unit, or could observe the activity<br />
and the target rating <strong>of</strong> the postural behaviors as indication on the need to change the<br />
upper body pose. As already validated in preliminary test, the ground clearance can be<br />
increased by introducing an additional motor pattern being stimulated during leg swing<br />
and creating auxiliary torque impulses in the knee and hip joint.<br />
<strong>Walking</strong> on a slope directed orthogonally to the walking direction serves as evaluation <strong>of</strong><br />
the lateral stabilization capabilities. The setup is the same as in the previously described<br />
experimental runs, only the inclination <strong>of</strong> the ground points to the side <strong>of</strong> the robot.<br />
Figure 8.23 illustrates the differences between walking on level terrain and walking on a<br />
surface inclined to the right by 1.5 ◦ .<br />
The most obvious distinction can be observed in the action <strong>of</strong> the Lateral Foot Placement<br />
postural reflex. The inclination pushes the robot to the right with every step it takes,<br />
resulting also in a rotation <strong>of</strong> the whole machine around the x-axis. The reflex reacts to this<br />
disturbances by placing the feet further to the right than in normal walking. As illustrated<br />
by the foot point diagrams, the left foot shown as green circle is placed practically in front<br />
<strong>of</strong> the last stance foot, whereas the right foot is positioned up to 60cm to the right. As a
8.2. <strong>Walking</strong> under Disturbances 173<br />
Slope Down to Right 1.5 ◦<br />
Level Ground<br />
Foot Points<br />
Position Y [m]<br />
Lat. Balance<br />
Ankle a<br />
Foot Points<br />
Position Y [m]<br />
Lat. Balance<br />
Ankle a<br />
−1<br />
−2<br />
0 walking dir.<br />
−3<br />
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0<br />
Position X [m]<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0<br />
Time [s]<br />
8.0 10.0 12.0<br />
1 walking dir.<br />
0<br />
−1<br />
3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0<br />
Position X [m]<br />
1.0<br />
0.5<br />
0.0<br />
0.0 2.0 4.0 6.0<br />
Time [s]<br />
8.0 10.0 12.0<br />
Figure 8.23: Comparison <strong>of</strong> lateral foot placement and the activity <strong>of</strong> the Lateral Balance<br />
Ankle postural reflex on level terrain and ground sloped to the right.<br />
result, the robot is walking sidewards down the slope, whereas on level ground, the minor<br />
foot placement corrections do not deflect the robot distinctly from its path.<br />
In addition, the Lateral Balance Ankle reflex also exhibits plainly increased activity. It<br />
works against the robot tilting in the direction <strong>of</strong> the inclination by raising the ankle<br />
torque about the x-axis. Since only a small leverage is available in the foot, the reflex<br />
already reaches its saturation at some points. Due to this reflex action, the cop is located<br />
further to the margin <strong>of</strong> the foot, thus increasing the risk <strong>of</strong> rolling over the edge <strong>of</strong> the<br />
foot while at the same time pushing the robot to a more stable, upright position.<br />
It shows that the robot cannot maintain stability during walking at sidewards slopes <strong>of</strong> 2 ◦<br />
or more. The main reason for this is that the robot is expecting level ground at heel strike<br />
but instead the foot must be lowered even further. Since the hip is kept rigid during this<br />
phase, the robot has to tilt to the side to reach the ground. Again, an additional control
174 8. Dynamic <strong>Walking</strong> Experiments<br />
Pelvis<br />
Position Z [m]<br />
Foot Points<br />
Position Y [m]<br />
Forward<br />
Velocity a<br />
1.2<br />
1.0<br />
0.8<br />
1.0<br />
0.0<br />
−1.0<br />
1.0<br />
0.5<br />
0.0<br />
walking dir.<br />
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0<br />
1.0 2.0 3.0 4.0 5.0<br />
Position X [m]<br />
6.0 7.0 8.0 9.0<br />
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5<br />
Time [s]<br />
Figure 8.24: Pelvis height, foot points, and activity <strong>of</strong> the Forward Velocity postural reflex<br />
during walking up and down a platform <strong>of</strong> 3cm in height. The gray box marks the position <strong>of</strong><br />
the platform.<br />
unit could solve this problem. By rotation the hip towards the ground inclination, and<br />
at the same time bending the spine joint to lean the trunk in the opposite direction, the<br />
disturbance just described could be reduced.<br />
8.2.2 <strong>Walking</strong> over Steps<br />
Similar to the experiments on walking up- and downhill, traversing steps mainly poses<br />
demands on the postural reflexes controlling the forward velocity. But in contrast to slope<br />
walking, steps produce short peaks <strong>of</strong> disturbances and present a discontinuity to the<br />
control system. The main difficulties lie in sudden accelerations and stumbling over the<br />
steps.<br />
Figure 8.24 presents the results <strong>of</strong> walking over a platform <strong>of</strong> 3cm in height and 4m in<br />
length. The robot first has to step upon the platform, walk along it, and then step down<br />
again. The platform is visualized by the gray box. The time scale <strong>of</strong> the reflex activity in<br />
the lower plot is scaled to approximately fit to the translational progression shown in the<br />
upper two plots.<br />
The side view <strong>of</strong> the pelvis trajectory illustrates how the robot gains height during walking<br />
on the platform. Additionally, it reveals two variations from its normal trajectory, as
8.2. <strong>Walking</strong> under Disturbances 175<br />
marked by the arrows in the plot. Directly after stepping on the platform, the pelvis<br />
stays higher at its lowest point, whereas after stepping down, it descends a bit more. The<br />
lowest point <strong>of</strong> this trajectory is reached after heel strike before the upper body again is<br />
raised by the stance leg, thus indicating a change in step length. More precisely, the step<br />
length is reduced when stepping up and lengthened when stepping down. This behavior<br />
compensates the loss respectively the gain <strong>of</strong> potential energy and results from the change<br />
in walking velocity. The variance in step length can also be observed in the foot placement<br />
plot. Furthermore it shows that the robot slightly walks to the left after stepping down the<br />
platform. This arises from the lateral acceleration while stepping down with the left foot.<br />
The lowest plot <strong>of</strong> Figure 8.24 depicts the activity <strong>of</strong> the Forward Velocity postural reflexes.<br />
The green plot represents the left reflex and the red plot the right reflex. They correspond<br />
to the left and right foot points shown in the plot above. It can be observed that the reflex<br />
activity increases right after stepping on and stepping <strong>of</strong>f the platform. After these events,<br />
the activity drops back to normal level. The postural reflex tries to correct the deviations<br />
in walking velocity by foot dorsi- or plantarflexion in a similar way as it was described<br />
during walking on slopes.<br />
The maximum platform height the robot can step upon is mainly restricted by the feet’s<br />
ground clearance during the swing phase. As shown in Figure 8.9, for the major part<br />
<strong>of</strong> the swing phase, the distance <strong>of</strong> the heel or toe segment to the ground is below 5cm.<br />
Already for the experiment just described, the platform had to be placed at the appropriate<br />
distance to the robot so it would manage to step upon it. Again, an additional motor<br />
pattern adding torque impulses in the knee and the hip would increase ground clearance<br />
and would allow to walk over higher steps.<br />
<strong>Walking</strong> down the platform works up to a height <strong>of</strong> 5cm. Above this height, the robot<br />
gains too much velocity and does not manage to finish the subsequent step in time, i.e.<br />
the robot stumbles during the swing phase. Additional hip torque would be needed to<br />
accelerate the swing phase. Furthermore, higher steps cause additional lateral disturbances<br />
that the robot cannot always compensate by correcting the foot placement.<br />
8.2.3 Constant External Forces<br />
In a final series <strong>of</strong> experiments, a constant external force is applied to the robot’s trunk<br />
pushing it forward or pulling it backwards. Other than during walking on a slope, the<br />
robot does not risk to stumble on a rising inclination or to excessively lengthening its<br />
steps. But the external force constrains the trunk movements and thus disturbs the passive<br />
dynamics <strong>of</strong> the system.<br />
Figure 8.25 illustrates the ankle’s power output and the activity <strong>of</strong> the Forward Velocity<br />
postural reflex at no external force and during both a pushing and a pulling force <strong>of</strong> 10N.<br />
As expected, additional reflex activity can be observed in both cases <strong>of</strong> external forces.<br />
The ankle power trajectories show only small but distinctive variations. Right after heel<br />
strike, marked by the left arrow in the plots, negative work is done while the foot is rotated<br />
to full ground contact. The amount <strong>of</strong> work increases while pushing the robot, resulting<br />
in a dissipation <strong>of</strong> the additional energy. In case the robot is restricted by the force, the<br />
negative work is reduced.<br />
The opposite situation can be seen during leg propulsion as marked by the right arrow in<br />
the ankle power plots. Here additional energy is put into the system when the robot is
176 8. Dynamic <strong>Walking</strong> Experiments<br />
Push Torso 10N<br />
Undisturbed<br />
Pull Torso 10N<br />
Ankle Power Y [W]<br />
Ankle Power Y [W]<br />
Ankle Power Y [W]<br />
400<br />
200<br />
0<br />
−200<br />
0 25 50 75 100<br />
% <strong>of</strong> Gait Cycle<br />
400<br />
200<br />
0<br />
−200<br />
0 25 50 75 100<br />
% <strong>of</strong> Gait Cycle<br />
400<br />
200<br />
0<br />
−200<br />
0 25 50 75 100<br />
% <strong>of</strong> Gait Cycle<br />
Forw. Vel. a<br />
Forw. Vel. a<br />
Forw. Vel. a<br />
1.0<br />
0.5<br />
0.0<br />
2.0 4.0 6.0<br />
Time [s]<br />
8.0 10.0<br />
1.0<br />
0.5<br />
0.0<br />
2.0 4.0 6.0<br />
Time [s]<br />
8.0 10.0<br />
1.0<br />
0.5<br />
0.0<br />
2.0 4.0 6.0<br />
Time [s]<br />
8.0 10.0<br />
Figure 8.25: Comparison <strong>of</strong> the ankle power and the activity <strong>of</strong> the Forward Velocity postural<br />
reflex at different constant external forces.<br />
pulled backwards, and less work is performed in case the robot is pushed forwards. Since<br />
the power output <strong>of</strong> the motor remains more or less the same during the indicated phases,<br />
the variations in effective power must result from the parallel spring and from damping.<br />
Again, passive action by an elastic element shows a self-stabilizing effect.<br />
Similar results are achieved by forces acting from different directions. For instance, a torso<br />
force directed to the front and the left generates activity <strong>of</strong> the reflexes acting both in<br />
the frontal and the sagittal plane, and the robot takes sidewards steps to the left. Forces<br />
acting in walking direction should not exceed 15N, lateral forces should remain below 8N,<br />
otherwise the robot will stumble.<br />
In summary, the postural control system works satisfactorily when confronted with different<br />
and unforeseen disturbances and manages to maintain stability at small to medium<br />
perturbations. The suggested combination <strong>of</strong> local reflexes, postural reflexes, and elastic<br />
elements can achieve robust dynamic walking. This is the case despite the fact that the<br />
control system has not yet being optimized for locomotion stability. Additional control<br />
units targeted at certain classes <strong>of</strong> disturbances could increase the robustness even further.
9. Conclusion and Outlook<br />
This thesis approached the task <strong>of</strong> designing a locomotion control methodology for twolegged<br />
robots. The presented concept is based on findings from the study <strong>of</strong> human motion<br />
control and can achieve dynamic, efficient, and robust walking <strong>of</strong> three-dimensional and<br />
fully articulated bipeds. The key characteristics <strong>of</strong> the suggested control system are:<br />
� Designed above the neuron level, the control is structured as a hierarchical network <strong>of</strong><br />
feedback and feed-forward control units, allowing gradual stimulation and inhibition.<br />
Neither a monolithic dynamic model nor pre-calculated trajectories are used.<br />
� Stimulation and synchronization <strong>of</strong> control units originates from spinal pattern<br />
generators; state transitions are triggered by kinetic and kinematic events.<br />
� Passive dynamics and self-stabilizing effects <strong>of</strong> elasticities are exploited by relying<br />
mainly on local torque commands instead <strong>of</strong> whole body joint angle control.<br />
� Postural control is based on reflexes <strong>of</strong> varying complexity. High-level postural<br />
reflexes apply simplified local dynamic models. Reflex action is phase-dependent.<br />
� The computational demands <strong>of</strong> the control system are comparatively low since<br />
cooperating local control units are used instead <strong>of</strong> a full-featured dynamic model.<br />
With the aid <strong>of</strong> a dynamic simulation environment, the control approach has been applied<br />
to an anthropomorphic biped model with 21 degrees <strong>of</strong> freedom and human-<strong>like</strong> morphology<br />
and actuation. This validation yielded the following main results:<br />
� The control system can achieve both dynamic walking and balanced standing; it can<br />
cope with the high complexity and the mechanical elasticities <strong>of</strong> the modeled biped.<br />
� The kinematic and kinetic analysis <strong>of</strong> the emerging, naturally looking walking gait<br />
reveals remarkable similarities to human walking.<br />
� Only a subset <strong>of</strong> the available degrees <strong>of</strong> freedom must be actively controlled in each<br />
phase <strong>of</strong> walking to direct the passive system dynamics towards a walking gait.
178 9. Conclusion and Outlook<br />
� The achieved velocity <strong>of</strong> up to 5 km/h with a robot <strong>of</strong> human-<strong>like</strong> size and weight<br />
surpasses the walking speed <strong>of</strong> most state-<strong>of</strong>-the-art bipeds. At the same time,<br />
locomotion is considerably more energy efficient than in joint angle controlled robots.<br />
� <strong>Walking</strong> and standing are robust against unknown and unexpected disturbances <strong>of</strong><br />
small to medium intensity <strong>like</strong> inclined ground, steps, or external forces.<br />
� The presented results and the analysis <strong>of</strong> biological motion control suggest that<br />
human-<strong>like</strong> morphology and actuation is a necessary prerequisite to achieve human<strong>like</strong><br />
walking skills.<br />
In conclusion, this thesis has shown that a control system based on concepts <strong>of</strong> human<br />
locomotion control applied to an anthropomorphic biped can in fact result in walking<br />
properties comparable to those observed in humans. The main drawback <strong>of</strong> the suggested<br />
approach remains the necessity to adjust a multitude <strong>of</strong> control unit parameters. Some<br />
possible solutions to this problem are discussed in the outlook succeeding the detailed<br />
summary presented in the next section.<br />
9.1 Summary<br />
The thesis started with an assessment <strong>of</strong> state-<strong>of</strong>-the-art biped control systems based on an<br />
extensive analysis <strong>of</strong> related work. It was argued that despite several decades <strong>of</strong> research,<br />
today’s robots are still far behind the locomotion capabilities <strong>of</strong> humans. The majority <strong>of</strong><br />
biped control systems rely on analytical approaches based on multibody dynamic modelling<br />
and pre-calculated joint angle trajectories. <strong>Walking</strong> stability is ensured using Zero-Moment<br />
Point constraints or similar considerations. While these methods are mathematically sound<br />
and allow for exact and purposeful motions, they show several drawbacks <strong>like</strong> strong model<br />
dependency, high energetic and computational costs, or low robustness to unforeseen<br />
disturbances. In contrast, the elegant motions observed in humans are highly robust, fast,<br />
energy efficient, and do not rely on a central model but rather emerge from a distributed<br />
control network and the inherent system dynamics in interaction with the environment.<br />
These facts gave rise to the main hypothesis <strong>of</strong> this thesis, namely that a control system<br />
based on concepts <strong>of</strong> human motion control can yield human-<strong>like</strong> locomotion capabilities<br />
in bipedal robots.<br />
Features <strong>of</strong> the <strong>Control</strong> Concept<br />
To verify the hypothesis mentioned above, literature on biomechanics and neuroscience<br />
was reviewed to find structural and functional features <strong>of</strong> human motion control that can<br />
be transferred to technical control systems. The following key aspects were identified:<br />
human walking relies on functional morphology and leaves some <strong>of</strong> the control burden<br />
to its“intelligent mechanics”. Inherent dynamics and self-stabilizing properties <strong>of</strong> elastic<br />
elements are exploited to further reduce the control effort and the energy consumption.<br />
The active control system is organized as a hierarchical network. Spinal control units issue<br />
coordinated feed-forward patterns <strong>of</strong> muscle activity. Feedback exists on various levels <strong>of</strong><br />
complexity, ranging from monosynaptic reflexes to postural control. Reflex action differs<br />
depending on the current phase <strong>of</strong> motion. emg analysis suggests that walking is divided
9.1. Summary 179<br />
in five phases being stimulated in bilateral synchronization. Postural control is supraspinal,<br />
i.e. it requires more than local sensor information.<br />
Based on these insights, the suggested control concept was designed. As passive dynamics<br />
should be exploited, no whole body joint trajectories are calculated. Rather, as in biological<br />
systems, the motions emerge from a hierarchical network <strong>of</strong> control units. Being based<br />
on ideas from behavioral robot control architectures, these units already have a semantic<br />
interpretation and thus are located above the level <strong>of</strong> individual neurons found in biological<br />
control systems. Six classes <strong>of</strong> control units were derived: locomotion modes are located at<br />
the highest level <strong>of</strong> control and represent a form <strong>of</strong> locomotion <strong>like</strong> walking or standing.<br />
They stimulate spinal pattern generators, state machine-<strong>like</strong> units that stimulate motion<br />
phases based on kinetic and kinematic events instead <strong>of</strong> oscillators with fixed timing.<br />
The motion phases then provide for synchronized stimulation <strong>of</strong> feed-forward control<br />
commands and activate the appropriate feedback units. Feed-forward control is issued by<br />
motor patterns in the form <strong>of</strong> local torque impulses directed at only one or a few adjacent<br />
joints. They shape the passive system dynamics to create the desired motion. Feedback is<br />
implemented by local and postural reflexes: local reflexes only affect spatially related joints<br />
based on data <strong>of</strong> adjacent sensors and introduce a tight sensor-actor coupling. Postural<br />
reflexes require whole body sensor information and can use simplified dynamic models<br />
to calculate their reaction. Arranged in a hierarchical network based on stimulation and<br />
inhibition, instances <strong>of</strong> these control unit classes generate the system behavior. Modulation<br />
signals <strong>like</strong> the desired walking velocity can influence the output <strong>of</strong> control units.<br />
Results from gait analysis and neuroscientific research helped to identify the necessary<br />
feed-forward and feedback control units. To simplify the design <strong>of</strong> motor patterns, a<br />
common sigmoid function has been suggested to represent all feed-forward joint commands.<br />
The spinal pattern generator (spg) for walking and the corresponding walking phases have<br />
been derived from findings based on emg analysis <strong>of</strong> human walking. The spg manages<br />
five motion phases, namely weight acceptance, leg propulsion, trunk stabilization, leg<br />
swing, and heel strike. On the basis <strong>of</strong> biomechanical gait analysis, motor patterns have<br />
been identified for each <strong>of</strong> these phases to achieve a walking gait. Reflexes similar to those<br />
working in human walking have been inserted.<br />
<strong>Control</strong> <strong>of</strong> stability during walking is based on several postural reflexes. They control<br />
the forward velocity, lateral stability, and the pose <strong>of</strong> the upper body by adjusting joint<br />
torque or changing foot placement. Most <strong>of</strong> these reflexes derive their reaction from an<br />
estimation <strong>of</strong> the robot’s center <strong>of</strong> mass based on a simplified dynamical model. The<br />
normal trajectories <strong>of</strong> the center <strong>of</strong> mass projection or an extrapolated version including<br />
its velocity are approximated. Deviation from these trajectories serve as indication for the<br />
reaction <strong>of</strong> the postural reflexes.<br />
The suggested control concept requires certain characteristics <strong>of</strong> the underlying mechatronic<br />
system. For instance, beneficial effects <strong>of</strong> the passive system dynamics cannot be exploited<br />
if the robot’s joints are self-locking or have overly high friction. Similarly, self-stabilizing<br />
properties <strong>of</strong> elastic elements can only be used if such elastic elements are present. This<br />
supports the statement <strong>of</strong> some biomechanics researchers claiming that biomimetic robots<br />
should be based on functional morphology. Consequentially, the presented control was<br />
applied to a suitable robotic system featuring an actuator with parallel springs, low friction,<br />
and adjustable series compliance.
180 9. Conclusion and Outlook<br />
Experimental Validation<br />
Since no real robot fullfilling the requirements mentioned above was available, a validation<br />
framework based on dynamical simulation has been developed. It features rigid body<br />
mechanics, customizable inertia tensors for each segment, a penalty-based contact model<br />
including coulomb-<strong>like</strong> friction calculation, and access to internal variables <strong>like</strong> forces and<br />
torques acting on bodies and joints. Thus, the framework is well suited to assess the<br />
feasibility <strong>of</strong> the suggested control concept and to analyze its performance. On top <strong>of</strong> the<br />
simulation’s constraint mechanism for defining joints, a model <strong>of</strong> the joint itself and its<br />
control system has been designed. It includes a parallel spring with constant rate and<br />
equilibrium point, damping, and a combined position and torque control allowing to adjust<br />
the series compliance. Within this framework, a bipedal robot with 6 degrees <strong>of</strong> freedom<br />
in each leg, a 3 d<strong>of</strong> spine joint, and 3 d<strong>of</strong> arms has been modeled. The mass distribution,<br />
the total weight, and the segment lengths were chosen to resemble typical human subjects.<br />
Flexible layout <strong>of</strong> the simulated environment allows to easily design different experimental<br />
setups.<br />
Experiments in the validation framework demonstrated that the presented control concept<br />
is indeed capable <strong>of</strong> achieving three-dimensional dynamic walking <strong>of</strong> an anthropomorphic<br />
bipedal robot, including the transition from balanced standing to walking. The naturally<br />
looking gait emerges from the combined control output <strong>of</strong> the phase-dependent stimulated<br />
reflexes and motor patterns, the inherent system dynamics, and the interaction <strong>of</strong> the<br />
robot with the environment. In fact, it shows that only about half <strong>of</strong> the 21 degrees <strong>of</strong><br />
freedom need to be actively controlled simultaneously during each phase <strong>of</strong> walking. The<br />
remaining joints act passively at different degrees <strong>of</strong> compliance. Even more, the control<br />
<strong>of</strong> only 1–4 d<strong>of</strong> by motor patterns is sufficient to direct the passive dynamics towards a<br />
walking gait.<br />
The presented approach is also capable to achieve stabilized standing. The control for<br />
balanced standing is mainly based on joint compliance to adapt to the ground, and on<br />
high joint stiffness to stabilize against external disturbances. Similar strategies can be<br />
observed in balancing human subjects. To evaluate this so called ankle strategy, the robot<br />
was confronted with different ground geometries and disturbances. The robot can stabilize<br />
its posture on ground inclination <strong>of</strong> up to 30 ◦ and withstand short force impulses <strong>of</strong> 1000N<br />
or movements <strong>of</strong> the supporting platform <strong>of</strong> up to 2.5 m/s. After stabilizing, the control<br />
system optimizes the robot’s posture by locally minimizing joint torques. This has been<br />
demonstrated by gradually inclining the surface the robot is standing on, or by changing<br />
the weight <strong>of</strong> a virtual backpack up to the weight <strong>of</strong> the robot itself.<br />
Analysis <strong>of</strong> the Resulting Gait<br />
An extensive behavioral, kinematic, and kinetic analysis <strong>of</strong> normal walking on level ground<br />
provided detailed information on the emerging gait and the interaction <strong>of</strong> the control<br />
units. It was illustrated that only a few kinetc and kinematic events are sufficient to<br />
trigger the state transitions <strong>of</strong> the walking spg in bilateral synchronization. It was shown<br />
that the behavior-based architecture iB2C with its stimulation and fusion mechanisms<br />
is an appropriate foundation <strong>of</strong> a biologically inspired control system. No elaborated<br />
stimulation strategies are necessary, thus simplifying the network design. The behavior<br />
signals allow to inspect the control unit activity throughout the walking phases to gain
9.1. Summary 181<br />
a solid understanding <strong>of</strong> the internal processes <strong>of</strong> the control network. Three different<br />
activity characteristics can be observed in the low-level control units: motor patterns<br />
follow a predefined activity progression; some reflexes always contribute an essential part<br />
to normal walking and show high activity at certain events <strong>of</strong> the gait cycle; finally, other<br />
reflexes working towards stabilization are more or less active depending on internal or<br />
external disturbances.<br />
Both kinematic and kinetic results show remarkable resemblance to human walking. Joint<br />
angle trajectories show the same characteristics and even similar amplitude. The same is<br />
true for the absolute position <strong>of</strong> body segments, joint torques, and power values. This can<br />
be observed despite the fact that no joint angle control based on human data has been<br />
applied. Reasons for this similarity can be found in the <strong>like</strong>wise exploitation <strong>of</strong> passive<br />
system dynamics at comparable segment masses and lengths, and in the fact that indeed a<br />
control system close to the human motion control has been found. These results might even<br />
serve as indication that some assumptions <strong>of</strong> neuroscientists on the function <strong>of</strong> locomotion<br />
control in humans that were used in this work are pointing in the right direction.<br />
<strong>Walking</strong> Velocity, Efficiency, and Robustness<br />
Inspection <strong>of</strong> the segment translation reveals the walking velocity <strong>of</strong> the robot. Varying<br />
the velocity modulation factor allows to change the walking velocity between 1.1 m/s and<br />
1.4 m/s. This shows that the mechanism <strong>of</strong> passing modulation signals to control units to<br />
scale their control output is working. Similarly, modulation <strong>of</strong> the walking direction or<br />
the step height could be implemented. The maximum velocity <strong>of</strong> about 5 km/h for a robot<br />
<strong>of</strong> human-<strong>like</strong> weight and height surpasses the walking speed <strong>of</strong> most <strong>of</strong> today’s bipeds.<br />
To compare the walking velocity <strong>of</strong> legged animals and robots, Alexander suggested to<br />
use the dimensionless Froude number defined as Fr = v2 /gl, where v is the velocity, g<br />
the gravitational acceleration, and l the leg length [Alexander 84]. For the presented<br />
biped, this number amounts to Fr = 0.21. At the time <strong>of</strong> writing, the fastest walking<br />
fully articulated biped is the robot Asimo, walking at a speed <strong>of</strong> 4 km/h, and running even<br />
faster [Takenaka 09a]. This results in a similar Froude number <strong>of</strong> Fr = 0.19, whereas<br />
KHR-4 comes to Fr = 0.02, Johnnie to 0.05, or HRP-2 to Fr = 0.07. <strong>Robots</strong> with a<br />
biologically motivated control or actuation system generally achieve high values, e.g. the<br />
robots Spring Flamingo and Rabbid both have a Froude number <strong>of</strong> Fr = 0.18, and the<br />
23cm small RunBot even reaches Fr = 0.28. The last three robots are supported by a<br />
rotating beam and only walk in the sagittal plane, so it still has to be shown whether<br />
their control approaches scale to three-dimensional walking. For comparison, fast human<br />
walking yields a Froude number <strong>of</strong> about Fr = 0.5.<br />
To assess the efficiency <strong>of</strong> the resulting walking gait, an estimation <strong>of</strong> the joint work<br />
and power output based on the torque and rotational displacement has been done. The<br />
overall mechanical power consumption during walking adds up to a bit more than 300W.<br />
Normalizingthisvaluetotherobot’sweightandthewalkingvelocitygivesanapproximation<br />
<strong>of</strong>thecosts<strong>of</strong>transport. Comparingthisresulttoasimilarestimation<strong>of</strong>therobotAsimo as<br />
a typical representative for joint angle controlled machines yields an efficiency improvement<br />
by a factor <strong>of</strong> five. Still, the energy consumption is not as low as in humans or actuated<br />
passive walkers. It should be noted that the control system has not yet been optimized<br />
towards low energy consumption at all. Of course, simulation can only provide a rough<br />
guess on the necessary power when applying the control concept to a real robot, but
182 9. Conclusion and Outlook<br />
nevertheless a considerable energetic benefit is to be expected. The necessary requirements<br />
for the peak values <strong>of</strong> joint angles, torques, or power can easily be met by today’s hardware.<br />
Still, the design <strong>of</strong> an actuator featuring the characteristics assumed in this work is a<br />
matter <strong>of</strong> ongoing research. First efforts in this direction made in the scope <strong>of</strong> this thesis<br />
have been introduced.<br />
Finally, the experiments on walking under external disturbances attribute a considerable<br />
robustness to the control system. <strong>Walking</strong> on uphill and downhill slopes as well as over<br />
steps <strong>of</strong> up to 5cm demonstated the capabilities <strong>of</strong> postural reflexes to regulate the forward<br />
velocity by varying step length and ankle torque. With the ground plane inclined to the<br />
side, lateral stabilization by foot placement adaptation and correcting ankle torque could<br />
be illustrated. Also, constant external forces acting on the trunk could be compensated by<br />
the postural reflexes. In all cases, self-stabilizing effects <strong>of</strong> the elastic elements could be<br />
observed to some degree. The analyzed disturbances were <strong>of</strong> small to medium intensity<br />
and a priori unknown to the control system. No external sensor systems <strong>like</strong> cameras or<br />
range finders captured the ground geometry. Considering that the design <strong>of</strong> a postural<br />
control system was not the main focus <strong>of</strong> this thesis, the resulting walking robustness is<br />
more than satisfactory. It shows that a combination <strong>of</strong> local reflexes, independent postural<br />
reflexes using simplified dynamical models, and parallel mechanical elasticity can yield<br />
a capable stability control. It was pointed out that tuning <strong>of</strong> the existing control units<br />
and adding further postural reflexes could increase the robustness <strong>of</strong> the robot against<br />
disturbances.<br />
9.2 Future Work<br />
Several refinements and extensions <strong>of</strong> the presented control system are conceivable. One<br />
potential improvement <strong>of</strong> the existing control units is the reduction <strong>of</strong> the energy consumption.<br />
As already mentioned in the previous chapter, the major part <strong>of</strong> the mechanical<br />
work is currently done by the hip joint during trunk stabilization and leg swing initiation.<br />
Improved timing and slower accelerations could already reduce the necessary energy. Furthermore,<br />
introducing an anticipatory motor pattern for deceleration the upper body at<br />
heel strike could lead to further enhancements.<br />
Possible ways to increase postural stability have been proposed at the end <strong>of</strong> the previous<br />
chapter. Optimizing the existing postural reflexes and the estimation <strong>of</strong> the extrapolated<br />
center <strong>of</strong> mass trajectory would already enhance stability. To further increase walking<br />
robustness, additional control units would have to be introduced. For instance, based on<br />
an estimation <strong>of</strong> the inclination <strong>of</strong> the ground plane, adjustments <strong>of</strong> the upper trunk and<br />
pelvis orientation would facilitate walking on sloped ground. Observation <strong>of</strong> the activity as<br />
well as the target rating <strong>of</strong> reflexes can indicate the necessity to change modulation factors<br />
<strong>like</strong> the walking velocity, or to stimulate additional control units, e.g. for generating higher<br />
leg swings to increase ground clearance.<br />
Such a control unit responsible for raising the foot during the leg swing could be implemented<br />
by an additional motor pattern being superimposed on the action <strong>of</strong> the already<br />
existing control units during the swing phase. Ivanenko et al. have shown that the emg<br />
activity observed during lifting a leg while standing can again be found when human<br />
subjects are ask to lift their legs higher during walking. This suggests a reuse <strong>of</strong> a muscle<br />
stimulation pattern that could be transferred as motor pattern unit acting on the knee
9.2. Future Work 183<br />
learning<br />
mode<br />
global<br />
rating<br />
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Figure 9.1: Connecting a reinforcement learning module to the control signals <strong>of</strong> an iB2C<br />
behavior. From [Steiner 09], p41.<br />
and hip joint. Making use <strong>of</strong> the behavior-based weighted sum fusion method applied<br />
during the fusion <strong>of</strong> torque commands allows a simple insertion <strong>of</strong> such a control unit to<br />
the existing network. Preliminary tests in this direction have already yielded successful<br />
results.<br />
In combination with an additional modulation signal, a similar approach could be used to<br />
include curve walking. A motor pattern adding a torque impulse to the z-axis <strong>of</strong> the hip<br />
joint during the stance phase would initiate the necessary body rotation. Depending on<br />
the resulting self-induced disturbances, the postural reflexes would have to be modulated<br />
by the walking direction signal. With additional external sensors <strong>like</strong> a vision system,<br />
walking towards a target or directional corrections during straight walking would become<br />
possible.<br />
Of course it is desirable to add further locomotion skills to the control system. A first step<br />
would be the inclusion <strong>of</strong> walking termination. In preliminary experiments, it appeared<br />
to be sufficient to reduce the walking velocity, shorten the step length, and switch back<br />
to standing mode after the heel contact <strong>of</strong> the last step. This procedure will then be<br />
implemented by a gait transition control unit similar to the locomotion mode for walking<br />
initiation. Neuroscientists assume that the same five emg components that explain muscle<br />
activity during walking are also deployed during running. They only differ in timing and<br />
amplitude. It would be interesting to see whether a running gait could also be achieved by<br />
a similar reuse <strong>of</strong> motor patterns for the presented biped.<br />
Up to this point, the suggested future improvements do not require any change <strong>of</strong> the<br />
control concept presented in this thesis. However, the existing drawback <strong>of</strong> having to<br />
manually tune the parameters <strong>of</strong> the control units and <strong>of</strong> the biped model persists. While<br />
it helps that the units have a semantic interpretation and some parameters can be deduced<br />
from their physical meaning, there still remains a set <strong>of</strong> parameters that are difficult to<br />
optimize empirically. One possibility to support the refinement <strong>of</strong> control parameters<br />
could be the inclusion <strong>of</strong> machine learning algorithms. In a first study, the integration<br />
<strong>of</strong> reinforcement learning into the behavior-based robot control architecture iB2C was<br />
investigated [Steiner 09]. As shown in Figure 9.1, a generalized learning module was
184 9. Conclusion and Outlook<br />
inserted behind each behavior module that should be tuned. Based on Q- or Q(λ)-learning<br />
and the iB2C target rating signal used as reward, the activity signal and the control<br />
signals <strong>of</strong> the behavior can be modified by a learned factor or <strong>of</strong>fset. It was shown that<br />
the determination <strong>of</strong> a purely local reward will not be sufficient for the application <strong>of</strong><br />
Q-learning to a complex and interleaved problem <strong>like</strong> bipedal walking. However, the<br />
definition <strong>of</strong> a global reward suitable for reinforcement learning algorithms is far from<br />
being straight-forward.<br />
Another possible approach would be the integration <strong>of</strong> optimization techniques. As<br />
already mentioned, first steps in this direction have been done during the development<br />
on the monopod prototype [Luksch 07]. The applied method based on multiple shooting<br />
optimization techniques required a special representation <strong>of</strong> a complete dynamics model<br />
<strong>of</strong> the robot and its environment. It allows to optimize mechanical parameters as well<br />
as to find an optimal control based on joint torque commands. One idea would be to<br />
include the biologically motivated control system as additional layer and find optimal<br />
parameters instead <strong>of</strong> directly searching for torque trajectories. To this purpose, a suitable<br />
representation <strong>of</strong> the control system that can be used by the optimization tools or an<br />
integration <strong>of</strong> the optimization algorithms in the presented framework would have to<br />
be designed. Alternative optimization algorithms could be considered. In any case, the<br />
problem <strong>of</strong> finding an appropriate target functional remains.<br />
Finally, still no solution exists to the problem <strong>of</strong> finding a joint actuator featuring the<br />
characteristics required by some parts <strong>of</strong> the presented control concept. Several groups are<br />
working on a design for a robotic actuation system with adjustable compliance. Examples<br />
are the series elastic actuators used in the robot Spring Flamingo, the maccepa concept<br />
based on a spring and two actuators for changing the stiffness and the equilibrium point,<br />
amasc working with large leaf springs, and pneumatic muscles [Pratt 95a, Ham 06b,<br />
Hurst 08, Vanderborght 06]. All these approaches have individual drawbacks and do not<br />
fulfill all requirements stated in Chapter 8. First efforts <strong>of</strong> the author and others towards<br />
the development <strong>of</strong> an actuator have been briefly introduced in this work. Initial results<br />
on the combination <strong>of</strong> electrical motors, parallel elastic elements, and compliance control<br />
seem promising [Wahl 09, Blank 09a, Blank 09b]. Further ideas deal with the introduction<br />
<strong>of</strong> an additional series elasticity and the use <strong>of</strong> a different motor and gearbox.<br />
The application <strong>of</strong> the suggested control concept to a real robot should be possible without<br />
major changes except for the adaptation <strong>of</strong> parameters. The dynamics simulation might<br />
not include all effects found in a real machine, but it features at least all major physical<br />
characteristics relevant during walking, thus giving the insights <strong>of</strong> this thesis significant<br />
validity. Since the control concept is based on reactive units and does not depend on<br />
an exact model <strong>of</strong> the robot and its environment, additional discrepancy introduced by<br />
the mechanical or electronic components will be inherently compensated up to a certain<br />
degree.<br />
In conclusion, this thesis has shown that a control methodology based on the transfer <strong>of</strong><br />
concepts found in human motion control can yield remarkable locomotion skills in bipedal<br />
robot. Already now, the presented robot can compete with today’s most advanced bipeds<br />
regarding walking velocity, efficiency, and robustness. Thanks to the flexible, modular<br />
design and the behavior-based architecture, the control network remains easily extensible,<br />
thus allowing to smoothly implement the suggested future work and to advance the control<br />
system’s capabilities even further.
A. Biomechanical and Anatomical<br />
Terms<br />
Throughout this thesis, biomechanical terms are used as they unambiguous describe<br />
processes during bipedal walking. While most terms are be explained at first appearance,<br />
this appendix again summarizes those expressions that can be more easily apprehended<br />
figuratively. Therefore, the upper part <strong>of</strong> Figure A.1 illustrates anatomical directions.<br />
Commonly, these are given relative to the center <strong>of</strong> the body located in the abdomen. The<br />
lower part <strong>of</strong> the figure depicts the horizontal and vertical planes as well as the axes used<br />
to define a coordinate system <strong>of</strong> the human body. Again, these planes and lines all go<br />
through the center <strong>of</strong> the body.<br />
Figure A.2 explains the terms used in biomechanics to describe the direction <strong>of</strong> joint<br />
rotations. These expressions are extensively used in Chapter 3 during the discussion <strong>of</strong><br />
biomechanical gait studies, but are also adopted during the presentation <strong>of</strong> control unit<br />
functions and the analysis <strong>of</strong> the robot’s walking gait. The figure is confined to the flexions,<br />
extensions, ab- and adductions, and rotations <strong>of</strong> those joints that have major influence<br />
during the emergence <strong>of</strong> walking.<br />
At several points <strong>of</strong> this text, the anatomical names <strong>of</strong> human bones are used to avoid<br />
ambiguity. Figure A.3 thus presents a labeled diagram <strong>of</strong> the human skeleton in anterior<br />
and posterior view to indicate the location <strong>of</strong> these bones.<br />
During the design <strong>of</strong> motor patterns and reflexes, data on muscle activity was consulted<br />
repeatedly in form <strong>of</strong> emg analysis. To transfer these biomechanical and neuroscientific<br />
results to technical control units, the location and the function <strong>of</strong> the respective muscles<br />
must be known. To this end, Table A.1 lists the muscles involved in human walking along<br />
with their established abbreviation and the joint action resulting from their contraction.<br />
Biarticular muscle span two joint and thus yield the movement <strong>of</strong> more than only one joint.<br />
Finally, Figure A.4 shows a diagram <strong>of</strong> most <strong>of</strong> the major skeletal muscles to indicate their<br />
location and insertion point.
186 A. Biomechanical and Anatomical Terms<br />
Figure A.1: Anatomical directions and body planes. From [Hamill 03], p15,p22.
Figure A.2: Directions <strong>of</strong> joint flexion, extension, abduction, adduction, and rotation.<br />
From [Hamill 03], pp16–19.<br />
187
188 A. Biomechanical and Anatomical Terms<br />
Abbrev. Muscle Action<br />
Shoulder Complex<br />
BIC Biceps brachii Arm abduction<br />
DELT Deltoid Arm abduction, flexion, horiz. flexion & extension<br />
LD Latissimus dorsi Arm internal rotation, adduction, extension<br />
TRAP Trapezius Shoulder girdle upw. rot., elevation, retract.; arm abd.<br />
Forearm<br />
BIC Biceps brachii Forearm flexion, supination<br />
TRIC Triceps brachii Forearm extension<br />
Hip Joint<br />
ADDL Adductor longus Thigh adduction, internal rotation<br />
ADDM Adductor magnus Thigh adduction, internal rotation<br />
BF Biceps femoris Thigh extension; shank flexion, external rotation<br />
GM Gluteus maximus Thigh extension, external rotation<br />
GMed Gluteus medius Thigh abduction, internal rotation<br />
RF Rectus femoris Thigh flexion; leg extension<br />
SART Sartorius Thigh flexion, external rot.; leg flexion, internal rot.<br />
ST Semitendinosus Thigh extension, internal rot.; leg flexion, intern. rot.<br />
TFL Tensor fascia latae Thigh flexion, abduction, internal rotation<br />
Knee Joint<br />
LG Gastrocnemius lateralis Leg flexion; foot plantarflexion<br />
MG Gastrocnemius medialis Leg flexion; foot plantarflexion<br />
RF Rectus femoris Thigh flexion; leg extension<br />
SART Sartorius Thigh flexion, external rot.; leg flexion, internal rot.<br />
VLat Vastus lateralis Leg extension<br />
VMed Vastus medialis Leg extension<br />
Ankle and Foot<br />
EDL Extensor digitorium brevis Toe extension<br />
FDB Flexor digitorium brevis Toe flexion<br />
LG Gastrocnemius lateralis Leg flexion; foot plantarflexion<br />
MG Gastrocnemius medialis Leg flexion; foot plantarflexion<br />
PERB Peroneus brevis Foot eversion, plantarflexion<br />
PERL Peroneus longus Foot eversion, plantarflexion; forefoot abduction<br />
SOL Soleus Foot plantarflexion<br />
TA Tibialis anterior Foot dorsiflexion, inversion<br />
TP Tibialis posterior Foot inversion, plantarflexion<br />
Vertebral Column<br />
ES Erector spinae Trunk extension<br />
ILIO Iliopsoas Thigh flexion; trunk flexion<br />
OE External oblique Trunk flexion, lateral flexion, rotation to opposite side<br />
OI Internal oblique Trunk flexion, lateral flexion, rotation to same side<br />
RAM Rectus abdominis middle Trunk flexion<br />
RAS Rectus abdominis superior Trunk flexion<br />
STER Sternocleidomastoid Head, cervical flexion, lateral flex., rot. to same side<br />
Table A.1: Skeletal muscles involved during human walking. Muscle actions from [Hamill 03].
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Figure A.3: Diagram <strong>of</strong> major human body bones (Source: Wikimedia Commons, public<br />
domain).
190 A. Biomechanical and Anatomical Terms<br />
Figure A.4: Diagram <strong>of</strong> the skeletal muscles <strong>of</strong> the human body (Source: Wikimedia Commons,<br />
public domain).
B. Dynamics Simulation Framework<br />
As already motivated in the main part <strong>of</strong> this thesis, a suitable simulation environment<br />
is inevitable for the validation <strong>of</strong> the suggested control concept. Building a real robot<br />
possessing all biologically motivated features necessary for the control system unfortunately<br />
is out <strong>of</strong> question in the scope <strong>of</strong> this work. Consequently, the existing simulation and<br />
visualization framework SimVis3D has been extended by the capability to simulate the<br />
dynamics <strong>of</strong> rigid bodies by embedding a physics engine. The selected physics simulation<br />
tool features rigid body mechanics, customizable inertia tensors for each segment, a<br />
penalty-based contact model including coulomb-<strong>like</strong> friction calculation, and access to<br />
internal variables <strong>like</strong> forces and torques acting on bodies and and joint Thus, it provides<br />
a sufficiently details simulation frameworm to evaluate the feasibility <strong>of</strong> the suggested<br />
control concept and to analyze its performance. Flexible mechanisms to design different<br />
environment allow to test the control system in various setups. This appendix gives<br />
additional information on these topics and provide the scene description file used for the<br />
experiments <strong>of</strong> this thesis. A few details on the graphical tools are provided and the<br />
walking gait is visualized in form <strong>of</strong> an image sequence extracted from the simulation<br />
framework.<br />
B.1 MCA2 and SimVis3D<br />
SimVis3D 1 has been and is being developed at the Robotics Research Lab for simulating<br />
robots and their environments [Braun 07]. Being part <strong>of</strong> robotics control framework mca2 2 ,<br />
it can directly be connected to the robot control system substituting an actual robot.<br />
SimVis3D is built on top <strong>of</strong> the rendering library Coin3D 3 , an implementation <strong>of</strong> the<br />
OpenInventor standard by sgi. It manages a tree-<strong>like</strong> scene graph containing the graphical<br />
elements, geometrical transformations, and additional annotation. This graph can then be<br />
rendered by OpenGL for visualization within the mca2 user interface.<br />
Theinitialscenedescriptionisprovidedinform<strong>of</strong>axmlfileastheoneshowninListingB.1.<br />
Three types <strong>of</strong> entries can be added to the scene: parts, elements, and sensors.<br />
1 http://rrlib.cs.uni-kl.de/simvis3d/<br />
2 http://rrlib.cs.uni-kl.de/mca2-kl/<br />
3 http://www.coin3d.org
192 B. Dynamics Simulation Framework<br />
Listing B.1: Sample scene description file <strong>of</strong> SimVis3D.<br />
1 <br />
3 <br />
5
B.2. Embedding <strong>of</strong> the Physics Engine 193<br />
1 <br />
Listing B.2: Sample <strong>of</strong> a collision geometry file.<br />
2 <br />
5 <br />
B.2 Embedding <strong>of</strong> the Physics Engine<br />
The mechanism <strong>of</strong> adding new element types is used to embed the physics engine into<br />
SimVis3D. As rigid body dynamics calculation package, the Newton Game Dynamics<br />
library 4 is applied. Three new element types are defined to modify the scene graph and pass<br />
information to the physics library: physics static, physics object, and physics joint.<br />
Elements <strong>of</strong> the type physics static describe the stationary environment. As illustrated<br />
in line 8 <strong>of</strong> Listing B.1, only a collision geometry needs to be provided. Additionally, the<br />
object’s material can be passed, otherwise it falls back to the default material.<br />
In contrast to static objects, physics object entries as those added in line 9 and line 10<br />
define the movable rigid bodies <strong>of</strong> the simulation scene. Besides the collision geometry<br />
and the material, a mass value is assigned to these objects. The inertia tensor <strong>of</strong> the<br />
object is calculated with the assumption that this mass is distributed evenly within the<br />
given collision body. In addition, an initial linear and rotatory velocity <strong>of</strong> the object can<br />
be set by the velocity and omega parameters. If omitted, these values are set to zero.<br />
Each physics object entry inserts a transformation matrix node to the scene graph at<br />
the given insertion point and exports its values as SimVis3D parameters. After every<br />
simulation cycle, the physics engine will set the current pose <strong>of</strong> each object by accessing<br />
the corresponding matrix entries within the mca2 blackboard containing the SimVis3D<br />
parameters.<br />
Entries <strong>of</strong> the type physics joint define constraints acting between two physical objects.<br />
Chapter 6 already introduced the joint mechanism <strong>of</strong> the Newton library. The necessary<br />
parameters are set within the xml entries as shown in line 11 <strong>of</strong> the listing. The parent<br />
and child parameters indicate which objects are affected by the joint. Leaving the parent<br />
object empty attaches the child object to the static world. The joint_type parameter<br />
determines which kind <strong>of</strong> constraints are added to the objects. Possible joint types include<br />
fixed joints, hinges, sliders, ball joints, or force and torque sensors. Some joint types<br />
<strong>of</strong>fer different actuation methods, e.g. mechanical stops, position control, springs, or the<br />
biological motivated actuator used in this thesis. The actuator can be specified by passing<br />
further parameters such as min, max, motor, or spring. The joint location is defined by<br />
giving the pivot point about which the joint revolves. Its orientation respectively its<br />
translational movement axis is set by the direction parameter. Joint elements do not<br />
modify the scene graph but only pass information to the physics engine.<br />
4 http://www.newtondynamics.com
194 B. Dynamics Simulation Framework<br />
1 <br />
Listing B.3: Sample <strong>of</strong> a material interaction file.<br />
2 <br />
3 <br />
4 <br />
5 <br />
7 <br />
8 <br />
Joint entries as well as physical object entries can extend the interface <strong>of</strong> the mca2 module<br />
encapsulating the physics engine. This is done by adding controller input and sensor<br />
output edges to the module that can then be accessed by the control system. A joint will<br />
normally insert controller input edges to set target values <strong>of</strong> the joint controller. Sensor<br />
information passed to the control system can include data on the current joint position or<br />
the acting torque. An inertial measurement unit provides the forces and torques necessary<br />
to sustain the object constraints. By adding the sensors or controls parameters to the<br />
xml entry <strong>of</strong> physical objects, the current pose <strong>of</strong> the object can be provided or an external<br />
force can be applied to it via controller input edges.<br />
The collision geometry necessary for static and dynamic physical objects is described by an<br />
xml file as the one shown in Listing B.2. Collision geometries can either be composed <strong>of</strong> a<br />
list <strong>of</strong> object primitives or <strong>of</strong> a mesh <strong>of</strong> triangles. The meshes are passed as an additional<br />
file containing a list <strong>of</strong> triangles defined by three points each. Triangle meshes are only<br />
allowed for static objects to reduce the complexity <strong>of</strong> collision checks. Possible geometrical<br />
primitives available to approximate the object shape include spheres, cubes, and cylinders.<br />
Each shape is positioned by six pose values in object local coordinates and parameters<br />
defining the expansions <strong>of</strong> the primitive. The optional color parameters can be evaluated<br />
by a script which can convert collision geometry files to the OpenInventor format. These<br />
visualizations can directly be used in SimVis3D part entries or can help to compare the<br />
collision geometry to an existing more elaborated visualization object.<br />
In case <strong>of</strong> two objects colliding, their materials are evaluated to determine the collision<br />
behavior. Listing B.3 shows a sample file containing the pairwise definitions <strong>of</strong> material<br />
interaction. For every two materials a s<strong>of</strong>tness and elasticity values can be set specifying the<br />
behavior <strong>of</strong> the joints that are created in case <strong>of</strong> a collision. The static and kinetic friction<br />
can also be defined. Additionally, collisions can be discarded by setting the collidable<br />
option to zero. Should an even more sophisticated collision behavior be necessary, a<br />
different callback routine can be specified.
B.3. Interface to <strong>Control</strong> System and Simulation 195<br />
Figure B.1: Graphical user interfacemcagui for accessing the control system and the simulation.<br />
B.3 Interface to <strong>Control</strong> System and Simulation<br />
The robotics control framework mca2 comes with a set <strong>of</strong> graphical tools to access the<br />
control system and the simulation framework during runtime. Figure B.1 shows a section<br />
<strong>of</strong> the graphical user interface mcagui with the configuration used during the development<br />
and validation <strong>of</strong> the presented control system.<br />
A 3D visualization <strong>of</strong> the simulated scene allows to directly observe the effects <strong>of</strong> the control<br />
system (1). Several cameras can be defined and moved freely. The physics simulation can<br />
be resetted, interrupted, or executed stepwise by a control panel (2). As the simulation runs<br />
only a few times slower than realtime, it is possible to interactively control disturbances<br />
or start predefined experiments (3). Arbitrary forces can be applied to robot segments<br />
and experimental results can be recorded. The walking velocity modulation factor can<br />
also be set in the user interface (4). Several graphical widgets can be connected to sensor<br />
information provided by the simulation framework or the control system (5). Finally, the<br />
iB2C behavior signals activation, activity, and target rating <strong>of</strong> all units <strong>of</strong> the control<br />
network can be inspected (6). This provides a quick and clear glimpse on the current<br />
control processes.<br />
A more detailed view on the activity and interaction <strong>of</strong> control units is provided by the<br />
mcabrowser. This graphical tool connects to the control system at runtime and allows to<br />
navigate through the module hierarchy as well as to adapt the parameters <strong>of</strong> all control<br />
units. Figure B.2 depicts screenshots <strong>of</strong> three control groups. The first image shows the
196 B. Dynamics Simulation Framework<br />
(a) (b)<br />
(c)<br />
Figure B.2: Visualization <strong>of</strong> the control system using mcabrowser. (a) Connection <strong>of</strong> the brain,<br />
the spinal cord, and the joint groups. (b) Locomotion modes inside the brain group. (c) <strong>Control</strong><br />
units <strong>of</strong> a leg group during walking phase 1.<br />
highest level <strong>of</strong> the control system. It visualizes the main hierarchy composed <strong>of</strong> the brain<br />
group, the spinal cord group, and the four joint groups representing the upper and lower<br />
body and the two legs. Figure B.2b and c show the brain and one <strong>of</strong> the leg groups in<br />
iB2C visualization mode. The yellow, green, and red horizontal bars in the module boxes<br />
indicate the behavior’s current activation, activity, and target rating. Green and blue<br />
connecting edges mark the transfer <strong>of</strong> stimulation or derived signals. Red connections<br />
signalize inhibition. This view allows to easily grasp the activity <strong>of</strong> control units during<br />
individual motion phases and to debug possible implementation errors.<br />
Finally, Figure B.3 illustrates one cycle <strong>of</strong> the normal walking gait on even ground by<br />
giving a sequence <strong>of</strong> images recorded by the simulation visualization plug-in in the mcagui.<br />
The time interval between two pictures amounts to 75ms.
B.3. Interface to <strong>Control</strong> System and Simulation 197<br />
Figure B.3: Image sequence <strong>of</strong> one gait cycle <strong>of</strong> normal walking on even ground.
198 B. Dynamics Simulation Framework<br />
B.4 Simulation Scenario for Biped Experiments<br />
The scenario used for most experiments described in this thesis is given by the scene<br />
description file printed in the listing below. The right-hand occurrences <strong>of</strong> all segments<br />
existing for both the left and the right side <strong>of</strong> the robot have been omitted for brevity.<br />
The environment features a large plane for the robot to walk on, a movable and rotatable<br />
plate used for the stable standing experiments, a small movable ball to apply arbitrary<br />
disturbances, and to force plates to measure ground reaction forces. The masses <strong>of</strong> all<br />
robot segments can be found in the section on the physical objects starting in line 35. All<br />
joints employed in the robot model are built <strong>of</strong> the type torquepos spring implementing<br />
the actuation described in Chapter 6. The three parameters passed by the motor keyword<br />
represent the maximum motor torque and the proportional factors for the position and<br />
velocity control loop. The parallel spring is described by the three spring parameters,<br />
namely the equilibrium position, the spring rate, and the damper constant.<br />
1 <br />
2 <br />
3<br />
Listing B.4: Scene description file used for most <strong>of</strong> the experiments.<br />
4 <br />
5 <br />
6 <br />
8 <br />
9 <br />
10 <br />
12<br />
13 <br />
15 <br />
17 <br />
19 <br />
21 <br />
23 <br />
25
B.4. Simulation Scenario for Biped Experiments 199<br />
27 <br />
29 <br />
31 <br />
33 <br />
35<br />
36 <br />
37 <br />
39 <br />
40 <br />
41 <br />
42 <br />
43 <br />
44<br />
45 <br />
46 <br />
47 <br />
48 <br />
51 <br />
52 <br />
53 <br />
54 <br />
55
200 B. Dynamics Simulation Framework<br />
auto_freeze="0" attached_to="RADIUS_LEFT" /><br />
56 <br />
57 <br />
58 <br />
59 <br />
60 <br />
61 <br />
62 <br />
63 <br />
65 <br />
67<br />
68 <br />
69 <br />
71
B.4. Simulation Scenario for Biped Experiments 201<br />
max="0.0" pivot="0 0 0" direction="0 1 0" motor="40.0 100.0 30.0" spring="-0.1 '<br />
5.0 2.0" attached_to="RADIUS_LEFT" /><br />
79 <br />
80 <br />
81 <br />
82 <br />
83 <br />
84 <br />
85 <br />
98<br />
99 <br />
101 <br />
103
202 B. Dynamics Simulation Framework
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