Fite, Shao, and Goldfarb.pdf - Vanderbilt University

620 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 20, NO. 3, JUNE 2004
Loop Shaping for Transparency and Stability
Robustness in Bilateral Telemanipulation
Kevin B. Fite, LiangShao, and Michael Goldfarb
Abstract—This paper presents and experimentally demonstrates a control
methodology that provides transparency and stability robustness in
bilateral telemanipulator systems. The approach is based upon a previously
published method that structures the human-manipulators-environment
system in a manner that enables the application of frequency-domain
loop-shaping methods. This paper reformulates the human-manipulator
interaction described in the previously published work,and experimentally
demonstrates the approach on a single degree-of-freedom telemanipulation
system. Experimental measurements indicate significant improvements
offered by the method in both the stability robustness and transparency
of the human-manipulators-environment system. Finally,experimental
results are presented that demonstrate the robustness in the transparency
to significant changes in the environment dynamics.
Index Terms—Bilateral,telemanipulation,teleoperation,transparency.
I. INTRODUCTION
A bilateral telemanipulator enables human interaction with environments
that are remote, hazardous, or otherwise inaccessible to
direct human contact. The performance of such a system is often
characterized by its ability to present the undistorted dynamics of the
environment to the human operator, a characteristic termed “transparency.”
The ability to do so is compromised by the (closed-loop)
dynamics of the master and slave manipulators, which distort the
dynamics of the environment as perceived by the human operator.
Additionally, the human, telemanipulator pair, and environment form
an interacting system that, given conditions of high environment
impedance or high loop gain, is susceptible to instability. Specifically,
though each component of the system can itself be robustly stable,
the accumulation of phase from multiple components can render
the human-manipulators-environment system unstable. A common
objective of bilateral telemanipulation is, therefore, to design a
controller that provides transparency and stability robustness of the
telemanipulator system in the presence of significant variation in
the dynamics of the environment and human operator. It should be
noted, however, that some researchers have proposed methods in
which the environment impedance is intentionally dynamically altered
to remedy the kinematic similarity issues that arise when scaling
dynamic environments [1], [2].
II. PRIOR WORK
Several researchers have investigated aspects of transparency and
stability in telemanipulation, includingHannaford [3], Yokokohji and
Yoshikawa [4], Lawrence [5], Hashstrudi-Zaad and Salcudean [6], Anderson
and Spong[7], Niemeyer and Slotine [8], Yoshikawa and Ueda
[9], and Munir and Book [10]. These and related prior works have
incorporated two-port network representations, as introduced into the
telemanipulation literature in [3], for the analysis of telemanipulator
Manuscript received February 3, 2003. This paper was recommended for publication
by Associate Editor P. Dupont and Editor I. Walker upon evaluation of
the reviewers’ comments.
K. Fite and M. Goldfarb are with the Department of Mechanical Engineering,
Vanderbilt University, Nashville, TN 37235 USA (e-mail: fitekb@vuse.vanderbilt.edu;
goldfarb@vuse.vanderbilt.edu).
L. Shao was with the Department of Mechanical Engineering, Vanderbilt University,
Nashville, TN 37235 USA.
Digital Object Identifier 10.1109/TRA.2004.825474
Fig. 1.
Two-channel bilateral telemanipulation.
transparency and the design of associated filters to provide transparent
performance. Specifically, controllers are designed to yield a two-port
telemanipulator hybrid parameter matrix that approximates the identity.
Havingaddressed the performance objective, the stability of the
two-port is addressed by incorporatingpassivity concepts. Such concepts,
however, are conservative, and as such, compromise system performance
(i.e., transparency) more than necessary.
This paper was in part motivated by the fact that prior publications
on this topic seem to uniformly incorporate network-based concepts to
address transparency and passivity-based concepts to address stability,
the former necessitatingthe latter. Rather than use hybrid two-port
network theory, the control architecture presented in this paper
addresses the performance and stability of a two-channel telemanipulation
system from a frequency-domain perspective. Specifically,
the human-manipulators-environment system is structured such
that a single loop is formed, to which standard frequency-domain
loop-shapingmethods can be applied. Lawrence et al. incorporated
similar notions in assessingthe stability and transparency of the
haptic renderingof virtual objects [11]. Such an approach enables a
less conservative control design, and therefore, better stability and
transparency properties. This approach was initially described for
purposes of bilateral telemanipulation by Fite et al. [12]. This paper
significantly alters the formulation of the method published in [12],
primarily by reformulatingthe human-manipulator interaction, and
experimentally demonstrates on a single degree-of-freedom (DOF)
telemanipulation system both the stability robustness and performance
robustness offered by the proposed method.
Finally, it should be noted that this paper does not explicitly consider
or treat the presence of time delay in the teleoperator communication
channels. Such delay is commonly present in remote teleoperation
systems, but is generally not significant in local teleoperation
systems, such as scaled teleoperation systems for dexterity enhancement
or glove-box teleoperation systems for purposes of biological or
radiological isolation.
III. FORMATION OF HUMAN-MANIPULATORS-ENVIRONMENT LOOP
Fig. 1 depicts the general notion of two-channel bilateral telemanipulation,
in which a human operator interacts with a force-controlled
master manipulator, which is in turn coupled to a position-controlled
slave manipulator interactingwith an environment. The two subsystems
are coupled through scaled motion and force communication
channels, where C 1 and C 2 represent the motion and force-scaling
gains, respectively. The motion command from the master/human
subsystem, Xh, is the combined effect of human voluntary motion and
the “feedthrough” motion from the teleoperator loop. The latter results
from a commanded motion Xh that is filtered by the slave/environment
dynamics and, in turn, generates a force at the master, Fh, which, in
turn, acts upon the human admittance and results in a component of the
commanded motion. Instability will result when the phase lagin the
teleoperator system is such that this force is 180 out of phase with the
commanded motion, and the loop gain is at least one. In order to assess
the transparency and relative stability of the loop, the teleoperator
system must be restructured so that the human voluntary input, which
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IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 20, NO. 3, JUNE 2004 621
Fig. 2.
Model of master/human dynamics.
Fig. 3. Parsing the master/human dynamics. (a) Schematic of closed-loop
force-controlled master manipulator interactingwith human. (b) Schematic of
fully parsed voluntary and feedthrough effects.
is essentially an exogenous input (i.e., not part of the feedback loop),
is parsed from the teleoperator feedback loop. Consider, for example,
a linear single-DOF master/human subsystem, which can be modeled
as shown in Fig. 2 and described in [13]. In this model, the master
manipulator is considered a simple mass-damper system (b m ;m m )
that is kinematically coupled to the human arm. The arm is modeled as
a mass-spring-damper system (m h ;b 2;k 2) with an additional stiffness
and damping (b 1 ;k 1 ) at the human/master interface (i.e., compliance
in the human grip). Human voluntary input x hv is commanded directly
into the base of the arm mass-spring-damper system, and is therefore
filtered by these dynamics before resultingin motion of the master
manipulator, a notion that is consistent with prior studies in human
motor control [14]. The iconic model clearly indicates that slave
motion command x h can result from either the voluntary human input
x hv or the feedthrough force F h . In order to express the teleoperator
system in terms of a classical loop with the human voluntary input
as an exogenous command, the multiple-input single-output (MISO)
human arm system depicted in Fig. 2 must be restructured as follows.
Assumingthat the master closed-loop force controller is described by
the transfer function C m , the master/human dynamics can be written
in the block diagram form shown in Fig. 3(a), where G 1; G 2, and G 3
are transfer function matrices given by
where
A =
G 1 = 0
G 2 = 0 0 0
b 2 s + k 2
m m
0 0
C m
m m
T
T
(1)
(2)
G 3 = C(sI 0 A) 01 (3)
0 1 0 0
0(k +k ) 0(b +b ) k b
m
m m m
0 0 0 1
k
b 0k 0(b +b )
m
m m m
C =[0k 1 0b 1 k 1 b 1] (5)
(4)
Fig. 4. Slave/environment dynamics. (a) Schematic of closed-loop
motion-controlled slave manipulator interactingwith environment impedance.
(b) Restructuringof interaction, indicatingdependence of G on Z . (c) Use
of local feedback of environment interaction force to decouple G from Z .
(d) Schematic of resultingdecoupled dynamics.
and where Y h is the admittance of the human operator, given by
Y h = sX h
F h
[m h s 2 +(b 2 + b 1)s +(k 2 + k 1)]s
=
: (6)
m h b 1s 3 +(m h k 1 + b 1b 2)s 2 +(k 1b 2 + k 2b 1)s + k 1k 2
All parameters in (1)–(6) are as defined in Fig. 2. The block diagram
of Fig. 3(a) can be rearranged until the respective paths of the
human voluntary input X hv and the feedthrough force F h contributing
to the command motion X h are separated completely, as shown in
Fig. 3(b). Specifically, the transfer function describing the force component
actingon the human admittance resultingfrom human voluntary
input is given by G hv , and the transfer function describingthe
force component actingon the human admittance resultingfrom the
feedthrough force is given by G m. Both transfer functions can be computed
from (1)–(5) and from the expressions given in Fig. 3.
The slave/environment dynamics depicted in Fig. 1 can be
represented by the equivalent schematics of Fig. 4(a) and (b),
both of which clearly indicate the dynamic couplingbetween the
slave and environment. In the figures, Z e;Y s, and C s represent
the environment impedance, slave manipulator admittance, and
position controller, respectively, and G ~ s represents the closed-loop
single-input, single-output (SISO) slave transfer function, which is
clearly a function of the environment impedance. Reconfiguring the
human-manipulators-environment system into a classical feedback
loop, as described by Figs. 3(b) and 4(b), enables application of
classical control techniques to address the transparency and stability
of the system, as initially described in [12]. The proposed control
approach incorporates two modifications to the two-channel bilateral

622 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 20, NO. 3, JUNE 2004
Fig. 5. Two-channel telemanipulation architecture. Solid arrowheads
represent signal interaction, whereas hollow ones represent physical
interaction.
structure shown in Fig. 1 to address the transparency and stability robustness
of the system. First, the closed-loop slave dynamics includes
local feedback of the interaction force between the slave manipulator
and environment, as shown in Fig. 4(c). This component effectively
compensates for the coupled slave/environment interaction, yielding
closed-loop slave dynamics G s independent of the environment, as
depicted in Fig. 4(d). Second, the control architecture includes a
loop-shapingcompensator, G c , operatingon the command motion X h
that enables frequency-domain manipulation of both the transparency
and stability robustness properties of the teleoperation loop. The
resultingteleoperator loop can be modeled as shown in Fig. 5, where
G m;G hv , and G s are transfer functions as defined by Figs. 3 and 4.
Assumingunity scalinggains and neglectingcommunication
channel time delay, the transmitted impedance, which is the
impedance of the teleoperator loop seen by the human operator, is
given by
Z t =
F m
sX h
= G cG sG mZ e: (7)
The transparency transfer function, defined as the ratio of the transmitted
impedance to the environment impedance, is written as
G t = G c G s G m : (8)
The performance-control design objective is to choose a compensator
G c that yields a transparency transfer function G t with a magnitude
of unity and phase of zero within some desired bandwidth of
operation. Note that without the previously mentioned local force feedback
around the slave manipulator, the transfer function G s would be a
function of the environment impedance, Z e , and as a result, the transparency
transfer function G t would similarly change with varying environmental
dynamics. Inclusion of the local slave force-feedback loop,
however, renders G s , and thus G t , independent of changes in the environment
dynamics (see Fig. 4).
The stability robustness of the teleoperator loop is assessed by rearranging
the loop into a Nyquist-like unity-feedback structure, enabled
by parsingthe human voluntary force from the feedthrough force, as
previously described. The resultingopen-loop transfer function governingthe
stability robustness is given by
G = 0G c G s G m Z e Y h : (9)
The stability robustness of the loop is thus easily addressed by adding
a desired amount of phase at the open-loop gain crossover frequency
with the compensator G c. The design approach is thus to use the magnitude
characteristics of G c to address the system transparency, and
use the phase characteristics to address the system stability. Though
Fig. 6. Top view of slave manipulator interacting with an environment
stiffness.
several possibilities for such compensator design exist, a reasonably
general solution is of a lead-lag compensator of the form
N i s +1
G c = kc5i=1 (10)
i i s +1
where the parameters k c ;N; i , and i are used to shape the magnitude
and phase characteristics of the compensator.
IV. IMPLEMENTATION
To verify the proposed control approach, the loop-shapingtechnique
was experimentally implemented on a single-DOF telemanipulation
system. Both the master and slave were kinematically single-DOF prismatic
manipulators, with actuation provided by a DC brushed servomotor
(PMI N12M4T) transformed to linear motion via a rack and
pinion. A rotary potentiometer (Midori CPP-45B) was used for rotor
position measurement. A rotational inertia was additionally mounted
to each servomotor to represent the inertia of a typical manipulator.
The master manipulator incorporated a handle mounted on the end of a
cantilever beam coupled to the translatingrack to provide an interface
with the human operator. Strain gauges mounted on the cantilever measured
the interaction forces occurringbetween the human operator and
the manipulator. The slave manipulator incorporated a cantilever beam
that connected its endpoint to a pair of springs supported by a shaft
mounted parallel to the linear motion. The springs imposed a bidirectional
stiffness in series with the slave motion, providinga simple yet
challenging environment with which to assess the teleoperative performance.
Similar to the master, the slave incorporated strain gauges on
the cantilever beam to measure the interaction forces between the slave
and environment. Each manipulator was capable of exertinga maximum
continuous force of approximately 45 N through a workspace
of approximately 65 cm. The slave and master manipulators are pictured
in Figs. 6 and 7, respectively. The control architecture was implemented
with the real-time interface provided by MATLAB/Simulink
(The MathWorks, Inc.) at a samplingrate of 1 kHz.
A. Master and Slave Manipulator Control
The nominal dynamics of the slave manipulator result from the rotational
inertia previously described and the (assumed) viscous friction
of the motor brushes and bearings, both transformed into translational
equivalents via the rack and pinion. The nominal (translational)

IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 20, NO. 3, JUNE 2004 623
Fig. 8. Transparency transfer function for the teleoperator system without
loop compensation, demonstratinga 63-dB transparency bandwidth of
approximately 1.4 Hz.
Fig. 7.
Side view of human operator gripping the master manipulator.
mass and dampingof the slave manipulator were experimentally determined
to be m s =4:5 kgand b s =80Ns/m, respectively. A proportional-derivative
compensator, attenuated at high frequencies with a
first-order filter, was used for the slave endpoint position control, such
that
where
C s =
k ds s + k ps
s+1
k ps =2360N 1 m
k ds = 260 Ns/m
=0:01 s:
(11)
Similar to the slave manipulator, the nominal dynamics of the master
result also from the rotational inertia and (assumed) viscous friction of
the motor, both transformed into translational equivalents via the rack
and pinion. The inertia and dampingassociated with the master manipulator
were experimentally determined to be m m = 12.25 kgand
b m = 100 Ns/m, respectively. A proportional controller with a gain of
k pm = 8 N/N was used to provide endpoint force control of the master
manipulator. Finally, the nominal environment stiffness used in the experiments
was 750 N1m.
B. Experimental Measurement of Transparency and Stability
Robustness
The transparency of the teleoperative system was assessed by
measuringthe experimental frequency response of the transparency
transfer function. Specifically, the human operator excited the
closed-loop system with a semirandom excitation. Measurements of
the motion and resultingimposed force, occurringat the interface
between the master and human operator, were made over a 30-s time
interval. The experimental frequency response was obtained from the
measured data usingthe expression
Z t;exp (j!) =
F h(j!)
sX h (j!) = 8VF(j!) (12)
8 VV(j!)
where 8 VF(j!) is the cross-power spectral density between the motion
input and the force output, and 8 VV (j!) is the power spectral
density of the motion input. The transparency transfer function was
then obtained by dividingthe experimental measure of the transmitted
impedance by the actual environment impedance.
The stability margins were experimentally obtained by breaking the
loop at the motion command to the slave and introducingsinusoidal ex-
citation to measure the open-loop (time-based) response of the system.
The gain margin of the loop was determined by measuring the sinusoidal
magnitude of the loop transfer function for excitation at the frequency
where the output human motion lagged the input by 180 . The
phase margin was found by measuring the amount of lag between the
input and output for excitation at the frequency for which the sinusoidal
magnitude of the output equals that of the input.
C. Transparency and Stability Robustness of the Uncompensated
System
A baseline experiment incorporated the structure shown in Fig. 5,
but without the loop-shapingcompensator, G c . Fig. 8 shows the experimentally
measured frequency-response plot of the transparency for
the uncompensated loop. The transparency exhibits a DC offset that
effectively attenuates the perceived magnitude of the environment. Ignoringthe
presence of the offset, the loop attains a 63-dB transparency
bandwidth of approximately 1.4 Hz. The gain and phase margins were
measured as previously described to be 6.7 dB and approximately 37 ,
respectively.
D. Transparency and Stability Robustness of the Compensated System
Usingthe previously described experimental measures of transparency
and stability robustness, a loop-shapingcompensator, G c ,as
described by (10) was designed with the following parameters:
k c =1:12
N =1
1 =0:133
1 =0:028 s:
Inclusion of the compensator as shown in Fig. 5 rectified the DC offset
exhibited by the uncompensated system and increased the transparency
bandwidth to approximately 3 Hz, as shown in Fig. 9. The compensator
additionally increased the stability robustness of the teleoperation
system, providingmeasured gain and phase margins of 10 dB and
49 , respectively. Addition of the compensator therefore increased the
transparency bandwidth by more than a factor of two, and additionally
increased the gain and phase margins by factors of 50% and 38%, respectively.
E. Performance Robustness
As previously discussed, the local feedback of the interaction force
between the slave manipulator and environment eliminates the dependence
of the transparency on the environment dynamics, and thus pro-

624 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 20, NO. 3, JUNE 2004
V. CONCLUSION
A control methodology that provides transparency and stability
robustness in bilateral telemanipulator systems was experimentally
demonstrated on a single-DOF telemanipulation system. Specifically,
the approach was shown to provide significant improvement in both
the transparency and stability robustness of the teleoperator system,
and was shown to maintain a consistent transparency bandwidth
independent of variation in the environment.
Fig. 9. Transparency transfer function for the teleoperator system with
loop compensation, demonstratinga 63-dB transparency bandwidth of
approximately 3.0 Hz.
Fig. 10. Transparency transfer function of the compensated system for an
environment stiffness 375, 750, and 2250 N1m.
vides robustness to changes in the environment impedance. Such robustness
was experimentally validated by repeatingthe transparency
measurements with the same compensator, but with a decreased environment
stiffness of 375 N1m and an increased environment stiffness of
2250 N1m, respectively. The results of these measurements are shown
in Fig. 10, which shows the transparency transfer function for the nominal,
decreased, and increased environment stiffnesses. The compensated
teleoperation system clearly maintains the nominally measured
transparency for significant changes in the impedance of the environment
with which the telemanipulator interacts.
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