Sampling and Connection Strategies for PRM Planners Jean-Claude Latombe Computer Science Department...
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![Page 1: Sampling and Connection Strategies for PRM Planners Jean-Claude Latombe Computer Science Department Stanford University Abridged and Modified Version (D.H.)](https://reader030.fdocuments.in/reader030/viewer/2022032704/56649d635503460f94a45829/html5/thumbnails/1.jpg)
Sampling and Connection Sampling and Connection StrategiesStrategies
for PRM Plannersfor PRM Planners
Jean-Claude Latombe
Computer Science DepartmentStanford University
Abridged and Modified Version (D.H.)
see JCL’s website for the full version
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The (New) IssuesThe (New) Issues
Where to sample new milestones? Sampling strategy
Which milestones to connect? Connection strategy
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ExamplesExamples
Two-stage sampling:1) Build initial roadmap with uniform sampling2) Perform additional sampling around poorly
connected milestones
Coarse Connection:1) Maintain roadmap’s connected components2) Attempt connection between 2 milestones
only if they are in two distinct components
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Multi-Query PRMMulti-Query PRM
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Single-Query PRMSingle-Query PRM
mmbb
mmgg
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Multi-Query PRMMulti-Query PRM
• Multi-stage sampling• Obstacle-sensitive sampling• Narrow-passage sampling
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Multi-Stage StrategiesMulti-Stage Strategies
Rationale:One can use intermediate sampling results to identify regions of the free space whose connectivity is more difficult to capture
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Two-Stage SamplingTwo-Stage Sampling
[Kavraki, 94]
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Two-Stage SamplingTwo-Stage Sampling
[Kavraki, 94]
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Obstacle-Sensitive StrategiesObstacle-Sensitive Strategies
Rationale:The connectivity of free space is more difficult to capture near its boundary than in wide-open area
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Obstacle-Sensitive StrategiesObstacle-Sensitive Strategies
Ray casting from samples in obstacles
Gaussian sampling
[Boor, Overmars, van der Stappen, 99]
[Amato, Overmars]
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Multi-Query PRMMulti-Query PRM
• Multi-stage sampling• Obstacle-sensitive sampling• Narrow-passage sampling
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Narrow-Passage StrategiesNarrow-Passage Strategies
Rationale:Finding the connectivity of the free space through narrow passage is the only hard problem.
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Narrow-Passage StrategiesNarrow-Passage Strategies
Medial-Axis Bias
Dilatation/contraction of the free space
Bridge test[Hsu et al, 02]
[Amato, Kavraki]
[Baginski, 96; Hsu et al, 98]
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Bridge TestBridge Test
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Comparison with Gaussian Comparison with Gaussian StrategyStrategy
Gaussian Bridge test
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Single-Query PRMSingle-Query PRM
mmbb
mmgg
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Diffusion StrategiesDiffusion Strategies
Rationale:The trees of milestones should diffuse throughout the free space to guarantee that the planner will find a path with high probability, if one exists
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Diffusion StrategiesDiffusion Strategies
Density-based strategy Associate a sampling density to each milestone in the trees Pick a milestone m at random with probability inverse to
density Expand from m
RRT strategy Pick a configuration q uniformly at random in c-space Select the milestone m the closest from q Expand from m[LaValle and Kuffner, 00]
[Hsu et al, 97]
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Adaptive-Step StrategiesAdaptive-Step Strategies
Rationale:Makes big steps in wide-open area of the free space, and smaller steps in cluttered areas.
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Adaptive-Step StrategiesAdaptive-Step Strategies
mmbb
mmgg
[Sanchez-Ante, 02]
Shrinking-window strategy
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Single-Query PRMSingle-Query PRM
mmbb
mmgg
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Coarse ConnectionsCoarse Connections
Rationale:Since connections are expensive to test, pick only those which have a good chance to test collision-free and to contribute to the roadmap connectivity.
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Coarse ConnnectionsCoarse Connnections
Methods:1. Connect only pairs of milestones that are not too far apart2. Connect each milestone to at most k other milestones3. Connect two milestones only if they are in two distinct
components of the current roadmap ( the roadmap is a collection of acyclic graph)
4. Visibility-based roadmap: Keep a new milestone m if:a) m cannot be connected to any previous milestone andb) m can be connected to 2 previous milestones belonging to
distinct components of the roadmap[Laumond and Simeon, 01]