1. CS 326A: Motion Planning ai.stanford.edu/~latombe/cs326/2007/index.htm Probabilistic Roadmaps: Basic Techniques

2. Motivation Geometric complexity Space dimensionality

3. Weaker Completeness  Complete planner  Too slow  Heuristic planner  Too unreliable  Probabilistic completeness: If a solution path exists, then the probability that the planner will find one is a fast growing function that goes to 1 as the running time increases

4. Initial idea: Potential Field + Random Walk  Attract some points toward their goal  Repulse other points by obstacles  Use collision check to test collision  Escape local minima by performing random walks

5. But many pathological cases …

6. Illustration of a Bad Potential “Landscape” U q Global minimum

7. Probabilistic Roadmap (PRM) free space mbmbmbmb mgmgmgmg milestone [Kavraki, Svetska, Latombe,Overmars, 95] local path

8. Two Tenets of PRM Planning  Checking sampled configurations and connections between samples for collision can be done efficiently.  Hierarchical collision checking [Hierarchical collision checking methods were developed independently from PRM, roughly at the same time]  A relatively small number of milestones and local paths are sufficient to capture the connectivity of the free space.  Exponential convergence in expansive free space (probabilistic completeness)

9. Two Tenets of PRM Planning  Checking sampled configurations and connections between samples for collision can be done efficiently.  Hierarchical collision checking [Hierarchical collision checking methods were developed independently from PRM, roughly at the same time]  A relatively small number of milestones and local paths are sufficient to capture the connectivity of the free space.  Exponential convergence in expansive free space (probabilistic completeness)