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 Cspace 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)

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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)

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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 ~
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