The Gaussian Sampling Strategy for Probalistic Roadmap Planners

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The Gaussian Sampling Strategy for Probalistic
Roadmap Planners

• Valdrie Boor, Mark H. Overmars, A. Frank van der
  Stappen, 1999
• Wai Kok Hoong

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Sampling a Point Uniformly at Random A Recap

• repeat
• sample a configuration q with a suitable
• sampling strategy
• if q is collision-free then
• add q to the roadmap R
• connect q to existing milestones
• return R

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Sampling a Point Uniformly at Random A Recap

• repeat
• sample a configuration q with a suitable
• sampling strategy
• if q is collision-free then
• add q to the roadmap R
• connect q to existing milestones
• return R

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The Gaussian Sampling Strategy for PRMs

• Obstacle-sensitive strategy
• Idea Sample near the boundaries of the C-space
  obstacles with higher probability.
• Rationale The connectivity of free space is more
  difficult to capture near narrow passages than in
  wide-open area

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The Gaussian Sampling Strategy for PRMs

• Random Sampler (about 13000 samples)

• Gaussian Sampler (about 150 samples)

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The Gaussian Sampling Strategy for PRMs

• Adopts the idea of Gaussian Blurring in image
  processing.

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs

• Algorithm

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The Gaussian Sampling Strategy for PRMs
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The Gaussian Sampling Strategy for PRMs

• Pros
• May lead to discovery of narrow passages or
  openings to narrow passages.
• Cons
• The algorithm dose not distinguish between open
  space boundaries and narrow passage boundaries.

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The Gaussian Sampling Strategy for PRMs

• Extension
• Use 3 samples instead of 2

• Gaussian Sampler (using pairs)

• Gaussian Sampler (using triples)

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The Gaussian Sampling Strategy for PRMs
Experimental Results

• Random sampler required about 13000 nodes.
• Gaussian sampler required 150 nodes.
• Random sampler took about 60 times longer than
  the Gaussian sampler.

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The Gaussian Sampling Strategy for PRMs
Experimental Results

• A scene requiring a difficult twist of the robot.
• Random sampler required about 10000 nodes.
• Gaussian sampler required 750 nodes.
• Random sampler took about 13 times longer than
  the Gaussian sampler.

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The Gaussian Sampling Strategy for PRMs
Experimental Results

• A scene with 5000 obstacles.
• Random sampler required over 450 nodes.
• Gaussian sampler required about 85 nodes.
• Random sampler took about 4 times longer than the
  Gaussian sampler.

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The Gaussian Sampling Strategy for PRMs
Experimental Results

• Running time of algorithm increases when sigma is
  chosen to be very small because hard to find a
  pair of nodes that generates a successful sample,
  thus performance deterioration.
• When sigma is chosen to be very large, output of
  sampler started to approximate random sampling,
  thus performance also deteriorated.
• Choose sigma such that most configurations lie at
  a distance of at most the length of the robot
  from the obstacles.

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The Bridge Test for Sampling Narrow Passages with
PRMs

• Narrow-passage strategy
• Rationale Finding the connectivity of the free
  space through narrow passage is the only hard
  problem.

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The Bridge Test for Sampling Narrow Passages with
PRMs

• The bridge test most likely yields a high
  rejection rate of configurations
• It generally results in a smaller number of
  milestones, hence fewer connections to be tested
• Since testing connections is costly, there can be
  significant computational gain

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Comparison between Gaussian Sampling and Bridge
Test
Gaussian Sampling
Bridge Test
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Summary

• Sample near the boundaries of the C-space
  obstacles
• The connectivity of free space is more difficult
  to capture near its narrow passages than in
  wide-open area
• Random Sampler is faster in scenes where the
  obstacles are reasonably distributed with wide
  corridors.
• Gaussian Sampler is faster in scenes where there
  is varying obstacle density, resulting in large
  open areas and small passages.

The End