prm and multi-space planning problems : how to handle many motion planning queries?
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PRM and Multi-Space Planning Problems : How to handle many motion planning queries?. Jean-Claude Latombe Computer Science Department Stanford University. (based on discussions with Tim Bretl and Kris Hauser). PRM Planning in Single Space. Applicable to robots with many dofs - PowerPoint PPT PresentationTRANSCRIPT
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PRM and Multi-Space Planning Problems:
How to handle many motion planning queries?
Jean-Claude LatombeComputer Science Department
Stanford University
(based on discussions with Tim Bretl and Kris Hauser)
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PRM Planning in Single Space
Applicable to robots with many dofs In expansive configuration spaces:
Probabilistically complete + fast convergence
But unable to detect that no solution exists Cutoff on running time
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Convergence of a PRM Planner
???What should be the cutoff time?
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Planning in Multiple Spaces
Example 1: Climbing Robot
4-contact move
3-contact move
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Climbing Robot Dilemma[Bretl, 2005]
Thousands of spaces many PRM queries Most queries have no solution Running times for feasible queries are highly variable
Large time cutoff Prohibitive time is wasted on infeasible queries Small time cutoff Critical queries might not be solved
difficult queriesor bad luck?
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Other Examples Navigation on irregular terrain [Hauser,
2008]
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Other Examples Dexterous manipulation
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Other Examples Mechanical assembly
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Other Examples Spatial re-arrangements of movable
objects
[Stillman and Kuffner, 2007]
Modular reconfigurable robotsOther Examples
[Yim]
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Other Examples Integration of task and motion planning
Change battery
Go to toolboxGrasp screwdriver
Go to old batteryUnscrew screws
Grasp old batteryUngrasp screwdriver
Remove old battery
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Basic Architecture
High-level Planner
(graph searching)
Motion Planner(PRM)
query resultMany queries are infeasible “climbing-robot” dilemma
Each query involves a distinct configuration space, with its own dimensionality, parameterization, and/or
constraints. queries cannot be processed using one single
precomputed roadmap
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Possible Approaches
Estimating query feasibility
Lazy PRM planning
High-level Planner
(graph searching)
Motion Planner(PRM)
query result
Learning Transition Feasibility[Hauser, 2008] Create a large dataset of labeled transitions
Train a classifier Q : transition {feasible, non-feasible} Use classifier to select sequences of spaces with
likely feasible transitions between them But no work yet on learning feasibility of entire
queries (that require connecting two transitions)14
4 contacts 3 contacts
Non-feasible if empty
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Possible Approaches
Estimating query feasibility
Lazy PRM planning
High-level Planner
(graph searching)
Motion Planner(PRM)
query result
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Lazy PRM Planning[Bohlin & Kavraki, 2000; Sanchez-Ante, 2001]
Observation: PRM planning wastes much time testing that sampled configurations and connections are valid (e.g., free of collision).
Idea: Perform a computation only when there is enough evidence that it may be useful.
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Lazy Collision Checking of Connections [Sanchez-Ante, 2001]
sg
X
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Lazy Collision Checking of Connections [Sanchez-Ante, 2001]
sg
Rationale Configuration spaces are rarely chaotic: so, the
connection between close valid configurations has high probability of being valid
Most of the time spent by a PRM planner is in testing connections
Most valid connections will not be part of the final solution
Testing connections is more expensive for valid connections than for invalid ones
Postpone testing a connection until the test is likely to be useful
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Extending Lazy PRM Planning
Create a bag of fine-grain computational probes:
Nodesampling
NodeConnection
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Extending Lazy PRM Planning
Sample a node and partially test if it is valid
p1 p8
p7p6p5
p4
p3p2
r d d > r+r’ p1 = 1d ≤ r+r’ p1 ~ d/r+r’
r’
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Extending Lazy PRM Planning
Create connection and partially test if it is valid
p1 p8
p7p6p5
p4
p3p2
p12
p23
p24
p45
p38
p46
p47
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Extending Lazy PRM Planning
Test further that a node is valid
p1 p12
p23
p24
p45
p38
p46
p47
p8
p7p6p5
p4’
p3p2
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Extending Lazy PRM Planning
Test further that a connection is valid
p1 p8
p7p6p5
p4’
p3p2
p12
p23
p24
p45
p38
p46
p47’
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Potential Advantages More choices opportunity for much smarter,
more efficient strategies
More flexibility in distributing computation over several spaces, e.g., focus on queries that have the highest probability of being feasible
Compatibility with probabilistic modeling of uncertainty, e.g., probabilistic distribution of obstacles
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Conclusion We will have to live with imperfect motion
planners like PRM planners Important problems require handling many
motion planning queries in distinct spaces “climbing-robot” dilemma
Possible approaches to address this dilemma:—Fast and reliable evaluation of query feasibility
(e.g., using trained classifiers)—Extended lazy PRM planning
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Narrow Passages I don’t think they are the main issue
in PRM planning. They are unlikely to occur by chance. Intentionally creating
complex narrow passages is not easy.
Alpha puzzle