sampling strategies for narrow passages presented by rahul biswas april 21, 2003 cs326a: motion...

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

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

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

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

Narrow Passage

uniformsampling

took60 timeslongerthan

algorithm 1

Narrow Passage

uniformsampling

tookless time

thanalgorithm 2

Difficult Twist

uniformsampling


algorithm 1

Twisty Track

uniformsampling


algorithm 1

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

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

Clover

Two Squares

Depression

Zigzags

Bridge vs. Uniform

RBB = Bridge

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

sampling strategies for narrow passages presented by rahul biswas april 21, 2003 cs326a: motion...

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