Sampling Strategies for Narrow Passages

1
Sampling Strategies for Narrow Passages

• Presented by Rahul Biswas
• April 21, 2003
• CS326A Motion Planning

2
Motivation

• Building probabilistic roadmaps is slow
• Two major costs
• FREE - Check if points are in free space
• JOIN Check if path between points in free space
• JOIN is 10 to 100 times slower than FREE
• Better points
• Fewer required edges
• Substantial speedups

3
Two Similar Approaches

• The Gaussian Sampling Strategy for PRMs
• Valerie Boor, Mark H. Overmars, A. Frank van der
  Stappen
• ICRA 1999
• The Bridge Test for Sampling Narrow Passages with
  PRMs
• David Hsu, Tingting Jiang, John Reit, Zheng Sun
• ICRA 2003

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Overview

• Gaussian Strategy
• What is Desired
• Two Proposed Algorithms
• Mixing and Parameterization
• Experimental Results
• Bridge Test
• Proposed Algorithm
• Comparison with Previous Paper
• Experimental Results

5
Overview

• Gaussian Strategy
• What is Desired
• Two Proposed Algorithms
• Mixing and Parameterization
• Experimental Results
• Bridge Test
• Proposed Algorithm
• Comparison with Previous Paper
• Experimental Results

6
What is Desired

• Goal more samples in hard regions
• more samples near obstacles
• Sampling Density of each point
• Convolution(Gaussian, Obstacles)

High Density
Low Density
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Overview

• Gaussian Strategy
• What is Desired
• Two Proposed Algorithms
• Mixing and Parameterization
• Experimental Results
• Bridge Test
• Proposed Algorithm
• Comparison with Previous Paper
• Experimental Results

8
Proposed Algorithm I

• loop
• c1 random config.
• d distance sampled from Gaussian
• c2 random config. distance d from c1
• if Free(c1) and !Free(c2), add c1 to graph
• if Free(c2) and !Free(c1), add c2 to graph
• intuition pick free points near blocked points

hence the name
saves time but not essential
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Proposed Algorithm II

• loop
• c1 random config.
• d1,d2 distances sampled from Gaussian
• c2,c3 random configs distance d1,d2 from c1
• if Free(c1) and !Free(c2) and !Free(c3), add c1
• if !Free(c1) and Free(c2) and !Free(c3), add c2
• if !Free(c1) and !Free(c2) and Free(c3), add c3

saves time but not essential
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Overview

• Gaussian Strategy
• What is Desired
• Two Proposed Algorithms
• Mixing and Parameterization
• Experimental Results
• Bridge Test
• Proposed Algorithm
• Comparison with Previous Paper
• Experimental Results

11
Mixing and Parameterization

• Introduce some uniformly sampled points
• Sans mixing, inappropriate for simple regions
• Parameters
• Variance of normal (smaller closer to
  obstacles)
• Mixing rate

G
S
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Overview

• Gaussian Strategy
• What is Desired
• Two Proposed Algorithms
• Mixing and Parameterization
• Experimental Results
• Bridge Test
• Proposed Algorithm
• Comparison with Previous Paper
• Experimental Results

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Narrow Passage
uniform sampling took 60 times longer than algorit
hm 1
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Narrow Passage
uniform sampling took less time than algorithm 2
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Difficult Twist
uniform sampling took 13 times longerthan algorit
hm 1
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Twisty Track
uniform sampling took 4 times longer than algorith
m 1
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Overview

• Gaussian Strategy
• What is Desired
• Two Proposed Algorithms
• Mixing and Parameterization
• Experimental Results
• Bridge Test
• Proposed Algorithm
• Comparison with Previous Paper
• Experimental Results

18
Bridge Test

• loop
• c1 random config.
• if Free(c1), continue (restart the loop)
• d distance sampled from Gaussian
• c2 random config. distance d from c1
• if Free(c2), continue (restart the loop)
• p midpoint(c1,c2)
• if Free(p), add p

p
c2
c1
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Overview

• Gaussian Strategy
• What is Desired
• Two Proposed Algorithms
• Mixing and Parameterization
• Experimental Results
• Bridge Test
• Proposed Algorithm
• Comparison with Previous Paper
• Experimental Results

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Bridge vs. Gaussian

• Paper mentions Gaussian but no comparison
• Want to compare
• Expected of calls to free (lower is better)
• Expected points generated (higher better, lt 1)
• If points can be reused in a hybrid strategy
• Quality of sampled points
• Let p be prior probability of Free
• Assume I(pi,pj) for i ? j

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Bridge vs. Gaussian
Strategy Calls to Free Expected Samples Reuse Points Point Quality
Gaussian 1 2 2?p?(1-p) yes, tainted OK
Gaussian 2 3 - p2 3?p?(1-p)2 yes, tainted Better
Bridge 1 (1-p) (1-p)2 p?(1-p)2 yes Best
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Overview

• Gaussian Strategy
• What is Desired
• Two Proposed Algorithms
• Mixing and Parameterization
• Experimental Results
• Bridge Test
• Proposed Algorithm
• Comparison with Previous Paper
• Experimental Results

23
Clover
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Two Squares
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Depression
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Zigzags
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Bridge vs. Uniform
RBB Bridge
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Conclusion

• Better configurations fewer configurations
  less edge computations faster running time
• Gaussian
• Points near obstacles
• Points near two obstacles
• Bridge
• Points between parts of obstacles