1. Finding Narrow Passages with Probabilistic Roadmaps: The Small-Step Retraction Method Presented by: Deborah Meduna and Michael Vitus by: Saha, Latombe, Chang, and Prinz

2. Outline Motivations Small-Step Retraction Planner –Object Thinning –Optimist Strategy –Pessimist Strategy Experimental Results Conclusions

3. 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

4. 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

5. Motivations (1) Increasing free-space slightly greatly increases the effectiveness of a PRM planner

6. Motivations (2) SBL prefers wider paths False passages created by object thinning are usually narrower than true passages

7. False Passages Thinning may generate a path through a passage that is not feasible for the robot in F. X s X g R w1w1 w2w2

8. 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 –

9. 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 ThinningCorrect Thinning

10. 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

11. 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

12. 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

13. SSRP - Overall Planner Pessimist is slower than optimist but faster than SBL N is small (i.e. N = 5)

14. Experimental Results(1)

15. Experimental Results(2)

16. 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