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Approaches to Robot Motion Planning and Control
2.166Fall 2008
Approaches to desigining robot control software:
Traditional model-based approach vs.
Subsumption Architecture
Historical Context
• Early robots, such as Shakey and Hilare, employed a “traditional”decomposition of intelligence
• Separate modules for:–Perception –Mapping/World Modeling–Decision Making–Motion Planning–Control
Shakey: 1960’s
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1970’s: Stanford Cart (Moravec) Early 1980’s: Hilare (France)
Geometric Motion Planning Hilare in Action (1981)
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Model-based Control (Conventional Approach)
Illustration courtesy of Siegwart and Nourbakhsh
Traditional Decomposition
perception
modeling
planning
task execution
motor control
sensors actuators
a.
Figures copyright Rodney A. Brooks, MIT
avoid hitting things
locomote
explore
build maps
manipulate the world
actuatorsensors
b.
An Alternative Approach: Decomposition by Functionality in the World/
Layers of increasing complexity
Figures copyright Rodney A. Brooks, MIT
An Early Subsumption Robot
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Behavior-based Control of the Roomba (2004)
Video courtesy of David Moore
Example: Roomba
Moore et al., Sensys 2004
Contrast with Roomba
Data from Moore et al., Sensys 2004
0 50 100 150 200
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
20 Localized pathTrue path
Distance (cm)
Robot path over timeGenghis Walking Robot (1988)
Figures copyright Rodney A. Brooks, MIT
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Genghis control architecture
for/backpitch
alphacollide
betapos
legdown
up legtrigger
betaforce
betabalance
s
i
i
IRsensors
walk
steer
s
d
alphaadvance
alphabalance s alpha
pos
prowl feelers
Figures copyright Rodney A. Brooks, MIT
Genghis Walking Robot (1988)
Figures copyright Rodney A. Brooks, MIT
Genghis Walking Robot (1988) Origins of Subsumption: circa 1989, MIT• Example: The Collection Machine,
Connell and Brooks
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Traditional Approaches to Robot Motion Planning
For an excellent source of information, see the book “Planning Algorithms” by Steve Lavalle, ©2005
Available for free at:
• http://msl.cs.uiuc.edu/planning/
Approaches to Robot Motion Planning
• “bug” algorithms
• Configuration Space
• Cell decomposition methods
• Roadmap methods
• Potential field methods
• Sampling based methods
Bug Algorithms • Assumptions:
– “point” robot – limited local sensing (e.g., tactile)– perfect navigation– static environment
Illustration: Choset et al., MIT Press 2005
Algorithm “Bug1”(Lumelsky and Stepanov, 1987)
Algorithm: Choset et al., MIT Press 2005
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Algorithm “Bug1”(Lumelsky and Stepanov, 1987)
Illustration: Choset et al., MIT Press 2005
Algorithm “Bug1”(Lumelsky and Stepanov, 1987)
Illustration: Choset et al., MIT Press 2005
Algorithm “Bug2”(Lumelsky and Stepanov, 1987)
Algorithm: Choset et al., MIT Press 2005
Algorithm “Bug2”(Lumelsky and Stepanov, 1987)
Illustration: Choset et al., MIT Press 2005
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Q: Does Bug2 always do better than Bug1?
Illustration: Choset et al., MIT Press 2005
Approaches to Robot Motion Planning
• “bug” algorithms
• Configuration Space
• Cell decomposition methods
• Roadmap methods
• Potential field methods
Configuration Space
start
goalgoal
start
• Shrink robot to a point• Expand obstacles to include any positions
where the robot and the obstacle positions would intersect
• Q: How does this simplify the problem?
Illustration: R. Brooks
Example: 2-Joint Robot Arm
Source: Russell and Norvig, AIMA, Chapter 25
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Example: 2-Joint Robot Arm
Source: Russell and Norvig, AIMA, Chapter 25
Robot Arm Configuration Space
Example: Robot Arm
Source: Russell and Norvig, AIMA, Chapter 25
Approaches to Robot Motion Planning
• “bug” algorithms
• Configuration Space
• Cell decomposition methods
• Roadmap methods
• Potential field methods
Cell Decomposition Methods
Source: AIMA, Chapter 25
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Cell Decomposition Methods
Illustration: R. Brooks
• Basic idea: transform a continuous problem into a (discrete) graph search
Approaches to Robot Motion Planning
• “bug” algorithms
• Configuration Space
• Cell decomposition methods
• Roadmap methods
• Potential field methods
Example: Ski Trail Map (Aspen) Roadmap Methods
Source: Russell and Norvig, AIMA
Voronoi Diagram Probabilistic Roadmap
Need methods to search the graph as well as how to get on and off the roadmap (on-ramps/off-ramps on “highways”)
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Approaches to Robot Motion Planning
• “bug” algorithms
• Configuration Space
• Cell decomposition methods
• Roadmap methods
• Potential field methods
Potential Field Methods
• Define a vector field• The robot is a “particle” in this field• Goal generates an attractive force• Obstacles generate repulsive forces• Let the particle follow the field to get to the goal• E.g., fluid flow or gravity analogy
Right: H. J. Feder, 1998Left: http://astron.berkeley.edu/~jrg/ay202/img1680.gif
2-D Robot Example Again
Source: Russell and Norvig, AIMA
2-D Robot Example Again
Source: Russell and Norvig, AIMA
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Sampling Based Methods
From: Lavalle, Planning Algorithms, 2006
From: Lavalle, Planning Algorithms, 2006
RRT Motion Planning
From: Lavalle, Planning Algorithms, 2006
Sampling-Based Motion PlanningRRT with obstacles