NUS CS5247

The Gaussian Sampling The Gaussian Sampling Strategy for Strategy for

Probalistic Roadmap Probalistic Roadmap PlannersPlanners

-Valdrie Boor, Mark H. Overmars, A. Frank van der Stappen, 1999 1999

Wai Kok HoongWai 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 ~