Sampling Strategies for Probabilistic Roadmaps

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• Sampling Strategies forProbabilistic Roadmaps

Issue Where to sample new roadmap
nodes? Goals Minimize roadmap size Answer
queries correctly
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Types of Strategies

• Single- vs. Multi-queries
• Workspace-based
• Filtering
• Adaptive
• Deformation

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Workspace-Guided Strategies

• Main idea
• Most narrow passages in configuration space
  derive from narrow passages in the workspace
• Methods
• Detect narrow passages in the workspace
• Sample more densely configurations that place
  selected robot points in workspaces narrow
  passages

Workspace-guided sampling Kurniawati and Hsu,
2004
Uniform sampling
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Filtering Strategies

• Basic Idea
• Sample several configurations in the same region
  of configuration space
• If a pattern is detected, then retain one of
  the configurations as a roadmap node
• More sampling work, but better distribution of
  nodes
• Less time wasted connecting un-interesting
  nodes
• Gaussian sampling
• Bridge Test
• Hybrid

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Gaussian Sampling

• Sample a configuration q uniformly at random from
  configuration space
• Sample a real number x at random with Gaussian
  distribution N0,s(x)
• Sample a configuration q in the ball B(q,x)
  uniformly at random
• If only one of q and q is in free space, retain
  the one in free space as a node else retain none

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Gaussian Distribution
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Gaussian Sampling

• Sample a configuration q uniformly at random from
  configuration space
• Sample a real number x at random with Gaussian
  distribution N0,s(x)
• Sample a configuration q in the ball B(q,x)
  uniformly at random
• If only one of q and q is in free space, retain
  the one in free space as a node else retain none

What is the effect? What is the intuition?
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Example of Node Distribution
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Bridge Test

• Sample two conformations q and q using Gaussian
  sampling technique
• If none is in free space, then
• if qm (qq)/2 is in free space, then retain
  qm as a node
• Else retain none

What is the effect? What is the intuition?
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Bridge Test
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Distribution
8-joint robot with mobile base
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Distribution
7-joint robot with fixed base
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Hybrid

• Sample two configurations q and q using Gaussian
  sampling technique
• If both are in free space, then retain one (any
  of the two) as a node with low probability (e.g.,
  0.1)
• Else if only one is in free space, then retain it
  as a node with intermediate probability (e.g.,
  0.5)
• Else if qm (qq)/2 is in free space, then
  retain it as a node with probability 1

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Adaptive Strategies

• Principle Use intermediate sampling results to
  identify regions of the free space whose
  connectivity is more difficult to capture
• Example Two-stage sampling strategy
• Construct initial PRM with uniform sampling
• Identify milestones that have few connections
  to their close neighbors
• Sample more configurations around them
• ? Greater density of milestones in difficult
  regions of the feasible space

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Adaptive Strategies

• Principle Use intermediate sampling results to
  identify regions of the free space whose
  connectivity is more difficult to capture
• Example Two-stage sampling strategy
• Construct initial PRM with uniform sampling
• Identify milestones that have few connections
  to their close neighbors
• Sample more configurations around them
• ? Greater density of milestones in difficult
  regions of the feasible space

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Deformation Strategies
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Free Space Dilatation

• Pre-computationSlim the robot
• Planning
• Compute a path for slimmed robot
• Deform this path for original robot

dilated free space
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Role of Randomness

• Adversary argument
• Implementation convenience
• Efficiency? Not really