Finding Narrow Passages with Probabilistic Roadmaps: The

Small-Step Retraction Method

Presented by: Deborah Meduna and Michael Vitus

by: Saha, Latombe, Chang, and Prinz

Outline

• Motivations

• Small-Step Retraction Planner– Object Thinning– Optimist Strategy– Pessimist Strategy

• Experimental Results

• Conclusions

Overview

• PRM efficiency decreases dramatically with narrow passages

• Developed an efficient planner for configuration spaces with narrow passages– Built off an existing planner, SBL– Also efficient for configuration spaces without

narrow passages

SBL - review

• Single-query Bi-directional Lazy-collision-checking– “Single-query”: PRM is built for specific start

and goal configurations– Connect sample trees originating from start

and goal configurations

Motivations (1)

• Increasing free-space slightly greatly increases the effectiveness of a PRM planner

Motivations (2)

• SBL prefers wider paths

• False passages created by object thinning are usually narrower than true passages

False Passages

• Thinning may generate a path through a passage that is not feasible for the robot in F.

X

sX

g

Rw1 w2

Small-Step Retraction Planner (SSRP)

• Retract only colliding configurations which are likely to be near free-space and/or near useful passages

• Generate PRM in “fattened free space” F*. – Use “thinned” obstacles and/or robot.– Narrow passages become wider (i.e. easier)

• Retract points in F* to points in true free space F–

Object Thinning

• Space occupied by original robot, R(c), is related to space occupied by thinned robot, R*(c), by:

• Thinning should maintain kinematic constraints

Incorrect Thinning Correct Thinning

Object Thinning

Medial Axis Balls

• Objects are thinned using the Medial Axis (MA) technique

• Objects are thinned by uniformly reducing the size of MA balls

• Thinning adds to pre-computation costs

Sample Thinned Component

Optimist Algorithm

• Repairs conflicts at the end of the path planning

• Fast • Might not be able to

resolve conflicts at the end. (“false” passages)

• K = 100

Pessimist Algorithm• Immediately repairs conflicts before path

generation• Slow• Doesn’t get trapped in “false” passages• Does not repair edge collisions • Modifies SBL sampling in the configuration

space

SSRP - Overall Planner

• Pessimist is slower than optimist but faster than SBL

• N is small (i.e. N = 5)

Experimental Results(1)

Experimental Results(2)

Conclusions

• Fast planner which handles configuration spaces with/without narrow passages

• SSRP is more reliable and faster than SBL

• SSRP may still fail when passages are very narrow and curved– Small percentage of real problems