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 ~