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On Delaying Collision Checking in PRM Planning – Application to Multi-Robot Coordination. By: Gildardo Sanchez and Jean-Claude Latombe Presented by: Michael Graeb and Samir Menon. Delayed Collision Checking. Motivations Experimental Foundations: Collision checks removed from planner - PowerPoint PPT Presentation
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On Delaying Collision On Delaying Collision Checking in PRM Planning – Checking in PRM Planning – Application to Multi-Robot Application to Multi-Robot CoordinationCoordinationBy: Gildardo Sanchez and Jean-Claude Latombe
Presented by:Michael Graeb and Samir Menon
Delayed Collision CheckingDelayed Collision CheckingMotivations
• Experimental Foundations: Collision checks removed from planner
Improved efficiency by 2-3 orders of magnitude Most paths remained collision free
• Most time is spent checking connections• Short connections likely to be collision-free anyway • Most collision-free connections not part of final path
Hence: Postpone testing a connection until it is absolutely needed
Single QuerySingle QueryMotivations
◦ 90% - 99.9% of milestones in multi-query roadmap unused by final path.
◦ Most roadmaps with “good coverage” only used for a single task
Hence: Single Query◦ Build a roadmap with your specific tasks in
mind◦ Bi-Directional trees are an efficient query
technique
S
G
SBL Algorithm – OverallSBL Algorithm – Overall1. Start roadmap with two trees
Rooted at start and goal, one node each
2. Try s times…
SBL Algorithm – OverallSBL Algorithm – Overall2a) Grow a tree by one node
SBL Algorithm – OverallSBL Algorithm – Overall2b) Find a path from start to goal
◦ We’re not certain all edges are valid
Start
Goal
SBL Algorithm – OverallSBL Algorithm – Overall2c) Test unknown edges in path
◦ Stop once a collision is found◦ Remember edges’ validity, for future use
SBL Algorithm – OverallSBL Algorithm – Overall2c) Test unknown edges in path
◦ Stop once a collision is found◦ Remember edges’ validity, for future use
SBL Algorithm – OverallSBL Algorithm – Overall2d) If all edges valid, return path
SBL Algorithm - EXPANDSBL Algorithm - EXPAND1. Pick which tree, T, will receive new
milestone Uniformly random choice, 50/50 odds
SBL Algorithm - EXPANDSBL Algorithm - EXPAND
2. From T, pick an existing milestone, m Random choice, with milestones in less-dense
regions more likely to be picked
SBL Algorithm - EXPANDSBL Algorithm - EXPAND3. Repeat until new milestone created:
3a) Take sample in neighborhood of m Distance from m is initially p and shrinks
with each successive attempt
3b) If sample collision free, add it as child of m
SBL Algorithm - EXPANDSBL Algorithm - EXPAND3. Repeat until new milestone created:
3a) Take sample in neighborhood of m Distance from m is initially p and shrinks
with each successive attempt
3b) If sample collision free, add it as child of m
SBL Algorithm - EXPANDSBL Algorithm - EXPAND3. Repeat until new milestone created:
3a) Take sample in neighborhood of m Distance from m is initially p and shrinks
with each successive attempt
3b) If sample collision free, add it as child of m
SBL Algorithm - EXPANDSBL Algorithm - EXPAND3. Repeat until new milestone created:
3a) Take sample in neighborhood of m Distance from m is initially p and shrinks
with each successive attempt
3b) If sample collision free, add it as child of m
SBL Algorithm - EXPANDSBL Algorithm - EXPAND3. Repeat until new milestone created:
3a) Take sample in neighborhood of m Distance from m is initially p and shrinks
with each successive attempt
3b) If sample collision free, add it as child of m
SBL Algorithm - EXPANDSBL Algorithm - EXPAND3. Repeat until new milestone created:
3a) Take sample in neighborhood of m Distance from m is initially p and shrinks
with each successive attempt
3b) If sample collision free, add it as child of m
SBL Algorithm - EXPANDSBL Algorithm - EXPAND3. Repeat until new milestone created:
3a) Take sample in neighborhood of m Distance from m is initially p and shrinks
with each successive attempt
3b) If sample collision free, add it as child of m
SBL Algorithm - CONNECTSBL Algorithm - CONNECT1. m is new milestone2. m’ is other tree’s nearest milestone to m
SBL Algorithm - CONNECTSBL Algorithm - CONNECT3. If( distance(m, m’) < ρ )
3.1 Connect m and m’ by bridge
SBL Algorithm - CONNECTSBL Algorithm - CONNECT3. If( distance(m, m’) < ρ )
3.1 Connect m and m’ by bridge
…3.2 τ is path from start to goal3.3 Return results of TEST_PATH( τ )
SBL Algorithm - CONNECTSBL Algorithm - CONNECT
SBL Algorithm – SBL Algorithm – TEST_PATH(TEST_PATH(pathpath))Continually test “most unsafe” segment until
we we encounter a collision, or all segments are known to be safe. Save results for future use.
ResultsResults
Results for configuration shown in the figure
Performance Evaluation & Performance Evaluation & Convergence RateConvergence Rate
Comparative Performance Comparative Performance EvaluationEvaluationExperimental results for the full
collision-check planner
DiscussionDiscussionAssumes two spatially close configurations in
configuration space have low probability of collision
Saves time by checking collision between milestones only when part of candidate path from start to goal.
Valid assumption in practice & supported by experiments
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