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Sampling Strategies for Narrow Passages
Presented by Rahul Biswas
April 21, 2003CS326A: Motion Planning
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
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
Overview Gaussian Strategy
What is Desired Two Proposed Algorithms Mixing and Parameterization Experimental Results
Bridge Test Proposed Algorithm Comparison with Previous Paper Experimental Results
Overview Gaussian Strategy
What is Desired Two Proposed Algorithms Mixing and Parameterization Experimental Results
Bridge Test Proposed Algorithm Comparison with Previous Paper Experimental Results
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
Overview Gaussian Strategy
What is Desired Two Proposed Algorithms Mixing and Parameterization Experimental Results
Bridge Test Proposed Algorithm Comparison with Previous Paper Experimental Results
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
saves time but not essential
hence the name
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 c3saves time but not essential
Overview Gaussian Strategy
What is Desired Two Proposed Algorithms Mixing and Parameterization Experimental Results
Bridge Test Proposed Algorithm Comparison with Previous Paper Experimental Results
Mixing and Parameterization
Introduce some uniformly sampled points
Sans mixing, inappropriate for simple regions
Parameters Variance of normal (smaller = closer to
obstacles) Mixing rate
S
G
Overview Gaussian Strategy
What is Desired Two Proposed Algorithms Mixing and Parameterization Experimental Results
Bridge Test Proposed Algorithm Comparison with Previous Paper Experimental Results
Overview Gaussian Strategy
What is Desired Two Proposed Algorithms Mixing and Parameterization Experimental Results
Bridge Test Proposed Algorithm Comparison with Previous Paper Experimental Results
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
c1
p c2
Overview Gaussian Strategy
What is Desired Two Proposed Algorithms Mixing and Parameterization Experimental Results
Bridge Test Proposed Algorithm Comparison with Previous Paper Experimental Results
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,
< 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
Bridge vs. Gaussian
Strategy Calls to Free
Expected#
Samples
Reuse Points
Point Quality
Gaussian 1
2 2p(1-p) yes, tainted
OK
Gaussian 2
3 - p2 3p(1-p)2
yes, tainted
Better
Bridge 1 + (1-p) + (1-p)2
p(1-p)2 yes Best
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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