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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. Background. Most of a PRM planner’s time is spent checking collisions We can get better results by: Improving collision checking

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on delaying collision checking in prm planning

On Delaying Collision Checking in PRM Planning

Gilardo Sánchez and Jean-Claude Latombe

January 2002

Presented by Randall Schuh

2003 April 23

background
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
sbl planner
SBL Planner
  • Single-query
  • Bi-directional
  • Lazy collision-checking
experimental foundations
Experimental Foundations

Observations from Hsu’s planner led to SBL:

  • Most local paths are not on the final path
  • Collision-free tests are most expensive
  • Short connections between two milestones have high prior probabilities of being free
  • If a connection is colliding, it’s midpoint has high probability of being in collision
fat obstacles
“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.

description of the sbl planner
Description of the SBL Planner

SBL Algorithm

  • Install qinit and qgoal as the roots of Tinit and Tgoal respectively
  • Repeat s times
    • EXPAND
    • τ ← CONNECT
    • If τ ≠ nil then return τ
  • Return failure
expand
EXPAND

EXPAND Algorithm

  • Pick T to be either Tinit or Tgoal, each with P=½
  • Pick a milestone m at random, with P π(m) ~ 1/η(m)
  • For i = 1,2,… until a new q been generated
    • Pick a configuration q uniformly at random from B(m, ρ/i)
    • If q is collision-free, then install it as a child of m in T
connect
CONNECT

CONNECT Algorithm

  • m ← most recently created milestone
  • m’ ← closest milestone to m in the other tree
  • If d(m,m’) < ρ then
    • Connect m and m’ by a bridge w
    • τ ← path connecting qinit and qgoal
    • Return TEST-PATH
  • Return nil
sbl example
SBL Example

qgoal

qinit

some examples
Some Examples

Nrobot = 3,000; Nobst = 50,000

Tav = 0.17 s

Nrobot = 5,000; Nobst = 83,000

Tav = 4.42 s

impact of lazy collision checking
Impact of Lazy Collision Checking

Average performance with lazy collision checking

Average performance without lazy collision checking

 Speed-ups ranging from 4 to 40