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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
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