On Delaying Collision Checking in PRM Planning--Application to

Multi-Robot CoordinationGildardo Sanchez & Jean-Claude Latombe

Presented by Chris VarmaApril 17, 2002

Presentation Outline

1. Introduction to SBL

2. SBLa. Collision Checking

b. Milestone sampling strategies

c. Connection strategies

3. Key Observations

4. Lazy collision-checking strategy

5. Experimental Results

6. Q&A

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

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

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

– 1st 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

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

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

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

SBL: Connection Strategy (1)

• Delayed collision-checking strategy– Collision checking consumes 99% of runtime– Avoid collision tests before absolutely needed

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

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)

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

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

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

Results

Example SBL FCCPa 23.78% 2.33%b 3.67% 0.14%c 3.81% 0.56%d 30.54% 5.04%e 3.66% 0.05%average 13.09% 1.62%

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.

Q&A

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