sampling and connection strategies for prm planners jean-claude latombe computer science department...
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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
The (New) IssuesThe (New) Issues
Where to sample new milestones? Sampling strategy
Which milestones to connect? Connection strategy
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
Multi-Query PRMMulti-Query PRM
Single-Query PRMSingle-Query PRM
mmbb
mmgg
Multi-Query PRMMulti-Query PRM
• Multi-stage sampling• Obstacle-sensitive sampling• Narrow-passage sampling
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
Two-Stage SamplingTwo-Stage Sampling
[Kavraki, 94]
Two-Stage SamplingTwo-Stage Sampling
[Kavraki, 94]
Obstacle-Sensitive StrategiesObstacle-Sensitive Strategies
Rationale:The connectivity of free space is more difficult to capture near its boundary than in wide-open area
Obstacle-Sensitive StrategiesObstacle-Sensitive Strategies
Ray casting from samples in obstacles
Gaussian sampling
[Boor, Overmars, van der Stappen, 99]
[Amato, Overmars]
Multi-Query PRMMulti-Query PRM
• Multi-stage sampling• Obstacle-sensitive sampling• Narrow-passage sampling
Narrow-Passage StrategiesNarrow-Passage Strategies
Rationale:Finding the connectivity of the free space through narrow passage is the only hard problem.
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]
Bridge TestBridge Test
Comparison with Gaussian Comparison with Gaussian StrategyStrategy
Gaussian Bridge test
Single-Query PRMSingle-Query PRM
mmbb
mmgg
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
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]
Adaptive-Step StrategiesAdaptive-Step Strategies
Rationale:Makes big steps in wide-open area of the free space, and smaller steps in cluttered areas.
Adaptive-Step StrategiesAdaptive-Step Strategies
mmbb
mmgg
[Sanchez-Ante, 02]
Shrinking-window strategy
Single-Query PRMSingle-Query PRM
mmbb
mmgg
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.
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]