MultiSpace Planning Problems How to handle many motion planning queries JeanClaude Latombe Computer Science Department Stanford University 1 based on discussions with Tim Bretl ID: 317036
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Slide1
PRM and Multi-Space Planning Problems: How to handle many motion planning queries?
Jean-Claude LatombeComputer Science DepartmentStanford University
1
(based on discussions with Tim
Bretl
and Kris Hauser)Slide2
PRM Planning in Single SpaceApplicable to robots with many dofsIn expansive configuration spaces:
Probabilistically complete + fast convergenceBut unable to detect that no solution exists Cutoff on running time
2Slide3
3Convergence of a PRM Planner
???What should be the cutoff time?Slide4
Planning in Multiple SpacesExample 1: Climbing Robot4
4-contact move
3-contact moveSlide5
5Climbing Robot Dilemma[Bretl, 2005]
Thousands of spaces many PRM queriesMost queries have no solutionRunning 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 queries
or bad luck?Slide6
Other ExamplesNavigation on irregular terrain [Hauser, 2008]6Slide7
Other Examples
Dexterous manipulation7Slide8
Other ExamplesMechanical assembly8Slide9
Other ExamplesSpatial re-arrangements of movable objects9
[Stillman and Kuffner, 2007]Slide10
Modular reconfigurable robots
Other Examples[Yim]Slide11
Other ExamplesIntegration of task and motion planning11
Change batteryGo to toolboxGrasp screwdriverGo to old batteryUnscrew screwsGrasp old batteryUngrasp
screwdriver
Remove old batterySlide12
Basic ArchitectureHigh-level Planner(graph searching)
Motion Planner(PRM)queryresult
Many queries are infeasible
“climbing-robot” dilemma
12
Each query involves a distinct configuration
space, with its own dimensionality, parameterization, and/or constraints
. queries cannot be processed using
one single precomputed roadmap Slide13
Possible ApproachesEstimating query feasibilityLazy PRM planning
13High-level Planner(graph searching)Motion Planner(PRM)
query
resultSlide14
Learning Transition Feasibility[Hauser, 2008]Create a large dataset of labeled
transitionsTrain 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 emptySlide15
Possible ApproachesEstimating query feasibilityLazy PRM planning
15High-level Planner(graph searching)Motion Planner(PRM)
query
resultSlide16
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.16Slide17
Lazy Collision Checking of Connections [Sanchez-Ante, 2001]17
s
g
XSlide18
Lazy Collision Checking of Connections [Sanchez-Ante, 2001]18
s
gSlide19
RationaleConfiguration spaces are rarely chaotic: so, the connection between close valid configurations has high probability of being
validMost of the time spent by a PRM planner is in testing connectionsMost valid connections will not be part of the final solutionTesting connections is more expensive for valid connections than for invalid ones Postpone
testing a connection until
the test is likely to be useful
19Slide20
Extending Lazy PRM Planning20
Create a bag of fine-grain computational probes:
Node
sampling
Node
ConnectionSlide21
Extending Lazy PRM Planning
21
Sample a node and partially test if it is valid
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d >
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= 1
d ≤
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~ d/
r+r
’
r’Slide22
Extending Lazy PRM Planning
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Create connection and partially
test if it is valid
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47Slide23
Extending Lazy PRM Planning
23
Test further that a node is valid
p
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p
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p
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’
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2Slide24
Extending Lazy PRM Planning
24
Test further that a connection is valid
p
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p
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p
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p
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p
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’
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’Slide25
Potential AdvantagesMore choices opportunity for much smarter, more efficient strategiesMore 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 obstacles25Slide26
ConclusionWe will have to live with imperfect motion planners like PRM plannersImportant 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 planning26Slide27
27Slide28
Narrow PassagesI 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.28Alpha puzzle