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On Delaying Collision Checking in PRM Planning Gilardo Sánchez and Jean-Claude Latombe January 2002 Presented by Randall Schuh 2003 April 23
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Background Most of a PRM planner’s time is spent checking collisions We can get better results by: – Improving collision checking – Designing smarter sampling strategies – Avoiding testing all connections between milestones
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SBL Planner Single-query Bi-directional Lazy collision-checking
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Experimental Foundations Observations from Hsu’s planner led to SBL: 1. Most local paths are not on the final path 2. Collision-free tests are most expensive 3. Short connections between two milestones have high prior probabilities of being free 4. If a connection is colliding, it’s midpoint has high probability of being in collision
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Short connections between two milestones have high prior probabilities of being free
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If a connection is colliding, it’s midpoint has high probability of being in collision
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“Fat Obstacles” A short colliding segment with collision free endpoints is necessarily almost tangential to an obstacle region in C, an event that has small probability of happening.
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Description of the SBL Planner SBL Algorithm 1. Install q init and q goal as the roots of T init and T goal respectively 2. Repeat s times 1. EXPAND 2. τ ← CONNECT 3. If τ ≠ nil then return τ 3. Return failure
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EXPAND EXPAND Algorithm 1. Pick T to be either T init or T goal, each with P=½ 2. Pick a milestone m at random, with P π (m) ~ 1/ η (m) 3. For i = 1,2,… until a new q been generated 1. Pick a configuration q uniformly at random from B(m, ρ/i) 2. If q is collision-free, then install it as a child of m in T
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Diffusion with a Grid Without diffusionWith diffusion
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CONNECT CONNECT Algorithm 1. m ← most recently created milestone 2. m’ ← closest milestone to m in the other tree 3. If d(m,m’) < ρ then 1. Connect m and m’ by a bridge w 2. τ ← path connecting q init and q goal 3. Return TEST-PATH 4. Return nil
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SBL Example q init q goal
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N robot = 5,000; N obst = 83,000 T av = 4.42 s N robot = 3,000; N obst = 50,000 T av = 0.17 s Some Examples
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Impact of Lazy Collision Checking Average performance with lazy collision checking Average performance without lazy collision checking Speed-ups ranging from 4 to 40
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Some Examples 2
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Some Examples 3
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Obstacle Jumping Example q init q goal
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