1. On Delaying Collision Checking in PRM Planning--Application to Multi-Robot Coordination Gildardo Sanchez & Jean-Claude Latombe Presented by Chris Varma April 17, 2002

2. Presentation Outline 1.Introduction to SBL 2.SBL a.Collision Checking b.Milestone sampling strategies c.Connection strategies 3.Key Observations 4.Lazy collision-checking strategy 5.Experimental Results 6.Q&A

3. Introduction to SBL SBL –Single-query in milestone sampling strategy –Bi-directional: build two trees—init. & goal –Lazy collision-checking planner No time wasted on testing non-candidate paths Little time spent on checking connections not collision-free –Adaptive sampler: locally adjusts sampling resolution to local obstacle density—shrinks neighborhood w/ each failure –Assumption: obstacle regions are “thick” in most directions Note: We do not cover application of SBL to multi-agent setting

4. SBL: Collision Checker SBL uses PQP to perform collision checks –Fast –Easy to use—i.e. requires little parameter tuning –Robust Alternative: checker that works symbiotically with sampling strategy –Sampling strategy picks each new configuration –Would enable some reuse of sampled configurations

5. Milestone Sampling Strategies Multi-stage –Uniformly generate milestones and paths –Enhancement step: select more milestones around milestones lying in narrow areas Obstacle-sensitive –Goal: capture F’s boundaries –E.g. Gaussian sampling: retain config as milestone only if collision-free & a forbidden config is a neighbor Narrow-passage –1 st roadmap: “dilated” free space F’—penetrate obstacles to widen narrow passages….so easier to find connections –Resample F’ to find neighbors that are collision-free milestones  define as F Diffusion –Idea: want roadmap tree(s) to diffuse across components of F

6. SBL: Milestone Sampling Strategy Single-query strategy –Computes new roadmap for each query Pre-computation justified only if 100’s of queries –Utilizes knowledge of query configurations Only explores restricted subsets of components of F reachable from configurations –Grows two trees—T(init) & T(goal) iteratively until connect Milestone m’ in neighborhood of m, connected by local path More efficient than single-directional Diffusion –Randomly select a milestone m w/ p = 1/w(m) –Pick successor m’ of m by randomly sampling neighborhood of m uniformly w = some sampling density function

7. Key Observations 1.Most local paths in a roadmap are not on final path 2.Test of a connection most costly when collision-free 3.Shorter connection between 2 milestones = higher prior probability of being collision-free So testing early is useless and costly 4.If connection between 2 milestones in collision, most likely to be midpoint

8. Explaining Points 3 and 4 Assume: q and q’ collision-free configurations close to each other a)q and q’ form connection that intersects “thick” object b)Lighter region is area in which q’ must be selected to cause intersection

9. SBL: Connection Strategy (1) Delayed collision-checking strategy –Collision checking consumes 99% of runtime –Avoid collision tests before absolutely needed

10. SBL: Connection Strategy (2) Lazy collision-checking –Check sampled configurations for collision  if no collision, add as milestone –Don’t check connections until identify path from initial to goal configurations –Then, midpoint of longest untested segment always tested next recursively Next segment isn’t necessarily sub-segment because each subsegment is ½ of original, thus neither may now be longest If collision found, transfer milestones between trees to preserve work done

11. Transferring Milestones a)Segment u is found to be in collision b)Thus, segment u is deleted and all milestones in T(goal) transferred to T(init)

12. Environments of Experiments a)6 dof robot arm equipped w/ welding gun b)6 dof robot arm in narrow config space c)Robot transfers large sheet from table d) Robot loads/unloads parts e) Environment of narrow passages

13. Convergence Rates Figure: Convergence rates for problems c and d, respectively. s = max # of milestones Small s = high failure rate of SBL High s = essentially 100% success rate of SBL Notice: exponential decrease in failures as s increases  PRM planner’s quality

14. Comparing Collision Checking SBL results for average of 100 runs on each example where s = 10K Full Collision-Checker Planner (FCCP) results for average of 100 runs on each example where s = 10K Differences between Planners –Milestones added in FCCP only if connection between them is collision-free –In FCCP, no milestone transferred from one tree to other

15. Results Figure: Ratio of (collision checks on the path) to (total # of collision checks performed) for each planner for each example and for the averages of examples Note: This provides good measure of overall improvement offered by SBL in running time since collision checking is 99% of computing time.

16. Q&A

17. Results Figure: SBL results for average of 100 runs on each example where s = 10K Figure: Full Collision-Checker Planner (FCCP) results for average of 100 runs on each example where s = 10K Differences Milestones added in FCCP only if connection between them is collision-free In FCCP, no milestone transferred from one tree to other