Paradigms of A.I. Robotics

Paradigms of A.I. Robotics
Weiwei Pan
Department of Mathematics
Wesleyan University
Middletown, CT 06457
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Intelligent Robot
What is an Intelligent Robot
An intelligent robot is a mechanical agent operating
autonomously and flexibly in its environment.
A robot has its own goals and decision making processes
A robot is capable of extracting information from its
environment
A robot is able to achieve its goals using sensory information
about its environment
A robot can adapt to a partially unknown environment
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Intelligent Robot
Why do Robots Need A.I.
Sensory interpretation
Situation awareness
Planing and Problem Solving
Interaction with other agents
Handle unexpected events
Learning
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Outline
Robotic Paradigms
The Hierarchal Paradigm
◦ Robot Profile: SHAKEY
The Reactive Paradigm
⋄ Two Architectures of RP
◦ Robot Profile: TOTO (et METATOTO)
◦ Robot Profile: ROBOSOCCER
The Hybrid-Reactive Paradigm
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Primitive Functions of A.I. Robot
Sense
◦ Extract information from the environment
Plan
◦ Determine directives based on sensed or cognitive
information
Act
◦ Use sensed information or directive to produce
actuator commands
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The Hierarchical Paradigm
Sense Plan Act
The general method cycles through the following three steps:
Sense: take sensor reading and update the world model
Plan: determine the next set of actions based on the current world
model and goals
Act: execute actions specified by the planner
Remark. Here a world model consists of a priori representation, sensed and cognitive
information.
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Characteristics of H.P
The Hierarchical Paradigm is characterized by an explicit monolithic
world-view and a sequential ordering of the three robotic primitive.
Knowledge about the environment must be explicitly represented
The world model must contain everything that an agent needs in
order to plan its course of action
The flow of control between the three primitive robotic functions
defines a linear ordering (this is also known as horizontal
decomposition).
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Shakey the Robo
Developed in 1967-1970 at the Stanford
Research Institute
Major contributors include: Charles Rosen,
Nils Nilsson et. al.
The first mobile robot to reason about its
actions
Key components: camera, optical range
finder, bump sensors
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Pros and Cons of H.P
Advantages:
Hierarchical (top-down) structure allow for the planning module to
focus all behaviours towards a single set of goals.
Drawbacks:
(Closed world assumption) Reliance on the static world model
during the S-P-A cycle causes poor performance in dynamic
environments.
(Frame problem) Updating and maintaining a sufficiently detailed
world model can be computationally intractable.
Searching for a plan to achieve a certain goal is equally complex.
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Lessons from Biology
Ethology:
Simple animals exhibit a variety of intelligent behaviour
(Innate Release Mechanism) A specific stimuli activate a simple,
involuntary (hardwired) response
Cognitive science:
(Embodiment) Direct physical experience is the key to cognition
(Embeddedness) The environment shapes the cognitive process.
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The Reactive Paradigm
Sense
Act
A reactive robotic system decomposes functionality into behaviors,
which tightly couple perception to action without the use of intervening
abstract representations
Behaviors are implemented as circuits (hardware) or as low
computational complexity algorithms (software)
No memory required. Behaviors are pure stimulus-response
reflexes.
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Characteristics of R.P
1. Robots are situated agents operating in an ecological niche.
The robot is an integral part of the world
The robot has its own goals and intentions
The robot is capable of affecting the world
The robot is capable of sensing the world and sense information
affects its goals and actions.
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Characteristics of R.P
2. Overall behaviour is an emergent quality.
Behaviours are computationally independent and operate
concurrently
No controller that determines all behaviours for a given task
Overall behaviour is a result of interactions of independent
behaviours
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Characteristics of R.P
3. Sensing is local and behaviour-specific.
Abstract representational knowledge in perceptual processing is
avoided
Representation is expressed as robot-centric information (no world
model).
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Architectures of R.P
1. Subsumption
Developed by Rodney Brooks in 1986
Behaviours are layered with higher levels able to override
(subsume) lower ones
Behaviours operate concurrently and independently (with some
mechanism to resolve conflicts)
2. Potential Field
Developed by Ronald Arkin in ()
Basic behaviours are represented by elementary potential fields
Complex behaviours (complex fields) are the combination of
elementary ones
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The Subsumption Architecture
Definition. A behaviour in this architecture is a network of sensing and acting
modules which accomplish a task.
Definition. A module is an augmented finite state machine (a FSM with registers,
timers and enhancements to permit interface with other modules).
1. Modules are grouped into layers of competence with lower layers
capturing basic functions and higher layers creating more
goal-directed actions. Each layer can be viewed as a behaviour.
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The Subsumption Architecture
2. Behavioural layers operate concurrently. Conflicts are resolved by
having modules in a higher layer subsume output from modules
one level lower. Subsumption can occur in one of two ways:
(Inhibition) The output of the higher module is connected to the
output of the lower module. If the output of the higher is "on",
then the output of the lower module is blocked.
(Suppression) The output of both the higher and the lower
module is connected to the input of another module. If the
output of the higher module is nonzero then the output of the
higher module replaces that of the lower module.
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The Subsumption Architecture
3. Persistent internal representation of the world is avoided. The
robot should depend mostly on information coming directly from its
environment. Even when some internal state is needed for
triggering behaviours like scared or hungry such usage should be
minimized.
4. A task is accomplished by activating the appropriate layer (lower
layers are then activated by reactivity to the environment).
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Subsumption Robot
Robots built using the subsumption architecture at the MIT A.I. Robotics Laboratory:
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Following a Corridor
Suppose we have a robot with sonars pointing in different directions
and two actuators, FORWARD and TURN.
Level 0: Obstacle Avoidance
SONARD module converts sonar readings into a plot of polar
coordinates, (r, θ), centered around the robot.
FEELFORCE converts each sonar reading into a repulsive vector
and outputs their sum to RUNAWAY
RUNAWAY passes new heading to TURN
COLLIDE looks at the sonar plot and outputs "halt" to FORWARD
when nearness threshold is met.
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Following a Corridor
Level 1: Explore
WANDER module computes a random heading every n seconds
passing it to AVOID
AVOID module take output from FEELFORCE and combines it
with new heading and passes it to TURN
Remark. Here we meet our first example of subsumption, i.e. TURN takes input from
both RUNAWAY in Level 0 and AVOID in Level 1, possibly at the same time, so who
does it listen to The answer is, TURN gives preference to RUNAWAY. When the
output of RUNAWAY is nonzero it replaces the output of AVOID. This is an example of
subsumption by suppression.
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Following a Corridor
Level 2: Follow a Corridor
LOOK module examines the sonar plot an identifies a corridor and
passes the heading towards the middle of the corridor to STAY IN
MIDDLE
STAY IN MIDDLE passes the heading to AVOID (also calculates
course corrections)
INTEGRATE observes actual motion between LOOK updates and
computes deviation from intended course, passing this data to
STAY IN MIDDLE
Remark. STAY IN MIDDLE subsumes WANDER by suppression.
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Follow a Corridor
LOOK middle
STAY IN
MIDDLE
middle
off middle
INTEGRATE
WANDER
S
AVOID
polar
plot
force
modified
heading
SONAR
FEEL
FORCE
force
RUN
AWAY
S
TURN
heading
encoders
COLLIDE
halt
FORWARD
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Summary of Subsumption
Behaviours are defined as a network tightly coupling sensing and
acting
Behaviours are organized into layers (lower layers serve basic
functions and higher layers direct more goal-oriented actions)
Higher layers may override lower ones
Perception is ego-centric and distributed
No persistent internal representation of the world.
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Toto the Robo
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The Potential Field Architecture
Treat the robot as a point particle in a force field, motions of the robot
are thereby represented by paths of a particle through this field with
obstacles and goals acting appropriately on the particle via attractive
or repulsive forces.
For each behaviour the robot "feels" a force. Obstacles act as
repulsive forces and goals as attractive forces.
Complex behaviours result from applying the sum of all forces to
the robot.
The overall behaviour of a robot in an environment can be
represented by a potential field, where the vector associated to
each point represents the force the robot would feel at that point.
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Primitive Potential Field
(a) Uniform field, (b) Perpendicular field
(c) Attraction field, (d) Repulsion field, (e) Tangential field
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Obstacles and Goal
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Movement via Potential Field
The robots movements are determined by the following three cases:
1. Only the goal is perceived: the sonar returns a distance to the goal
and a vector of attraction is computed based on that data.
2. Only the obstacle is perceived: the sonar returns a distance to the
obstacle and a vector of repulsion is computed.
3. Both the goal and the obstacle are perceived: the vector of
repulsion and attraction is summed for a new forcing pushing the
robot both away from the obstacle and towards the goal.
Remark. Even though the robot’s movements through a given environment can be
visualized at once as an artificial potential field, there is no internal representation!!!
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Movement via Potential Field
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Magnitude Profile
Question: How should the robot model the force it feels from an object in its
environment as a function of distance
Answer: The robot can choose from a variety of magnitude profiles for forces being
exerted by obstacles and goals.
Definition.
The way the magnitude of vectors change in the potential field (around an obstacle or a goal) is
called the magnitude profile.
Three basic types of magnitude profiles:
Constant - the force exerted by an object is of constant magnitude with in a fixed
radius and is zero elsewhere.
Linear - the magnitude of force is inversely and linearly proportional to the distance
to the object.
Exponential - the magnitude of force is inversely and exponentially proportional to
the distance to the object.
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Magnitude Profile
(a) Linear Drop Off
(b) Exponential Drop Off
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Generating Potential Field
Definition. Given S ⊂ R 2 , a vector field on S is a function F : S → R 2 . That is, F
associates a vector to every point in S.
FACT: Every potential field is a vector field, and most potential fields are
conservative vector fields, i.e. they are (more or less) the gradient of potential
energy functions.
Remark. Think of potential energy functions as a landscape with hills and valleys and the
potential field is the vector field generated by mapping the instantaneous change in each
direction at every point in the landscape.
FACT: Magnitude profiles define potential energy functions! I.e. Given a
potential energy function, U : R 2 → R + , the potential field associated to U is
F(⃗r) = −▽U(⃗r),⃗r ∈ R 2 .
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Generating Potential Field
Let ⃗r ∈ R 2 and p(⃗r) =‖ ⃗r − ⃗r obj ‖. Choose a magnitude profile, U(⃗r), for an object.
An attractive field (standard):
then,
U att (⃗r) = 1 2 k att · p 2 (⃗r)
F att (⃗r) = −k att · (⃗r − ⃗r goal )
A repulsive field (standard):
8 “ ”
<
2
1
U rep (⃗r) =
2 k 1
rep p(⃗r) − 1 if p(⃗r) ≤ r
r 0 ,
0
:
0 if p(⃗r) > r 0 ,
then,
8 “ ”
< k 1 rep p(⃗r)
F rep (⃗r) =
− 1 1 ⃗r−⃗r goal
r 0 p 2 if p(⃗r) ≤ r
(⃗r) p(⃗r) 0 ,
: 0 if p(⃗r) > r 0 ,
where k att , k rep are constants, and r 0 is the radius of influence for the obstacle.
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Following a Corridor
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Following a Corridor
RUNAWAYpf: uses repulsive field to generate new heading. Each
sonar reading activates an instance of RUNAWAYpf, the resulting
vectors are summed and then passed to TURN.
COLLIDE: cannot be mapped as a behaviour with the PF method.
Instead, collisions trigger emergency responses outside the
potential field framework.
WANDERpf: generates a random heading and a uniform field in
the direction of that heading (the output of WANDERpf is naturally
summed with the output of RUNAWAYpf via combination of
potential fields).
FOLLOW CORRIDOR: is the potential field pictured in the
previous slide.
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Robosoccer
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PF Robot
Ron Arkin and his robots at Georgia Tech:
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Difficulties with Potential Field
Programming behaviours via potential fields encounter two common
problems:
(Local minima problem) Ideally, when the robot feels no force (i.e.
▽U(⃗r) = 0) it is at the goal position (i.e. global mininmum).
Unfortunately, given an arbitrary potential energy function U there
may be places aside from the goal position where ▽U(⃗r) = 0
(saddle points). This can be resolved by adding a small degree of
random "noise" to heading vectors.
Depending on the terrain of the environment, bad choices of
magnitude profiles can lead to disastrous behaviours along certain
paths. This can be resolved by choosing a "smarter" model for
attractive and repulsive forces.
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Comparisons Between Architecture
Subsumption
+ Modular design (each behaviour is independently testable)
- Not taskable
Potential Fields
+ Has representation that is easy to visualize over a large region
+ Any real-valued continuous function on R 2 can be used as a
potential energy function.
+ Is portable
- Local minima problem
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Summary of the Reactive Paradigm
Positive Attributes:
Reactive robots with simple behaviours can solve relatively complex
problems
The lack of internal states simplifies computation (reactive systems are
fast and inexpensive to build)
Perform well in dynamic environments
Drawbacks:
Breaking down desired behaviour into simple behaviours is an art
Hard to predict emergent behaviours
Reactive agents can only accomplish tasks that involve reflexive
behaviours (cannot perform planning or reasoning).
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The Hybrid-Reactive Paradigm
Plan
Sense
Act
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References
[1] R. R. Murphy, Introduction to AI Robotics, Cambridge,
MA: MIT Press, 2000.
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