1. CS 326 A: Motion Planning http://robotics.stanford.edu/~latombe/cs326/2003 Probabilistic Roadmaps Basic Techniques

2. Motivation Geometric complexity Space dimensionality

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

4. Initial idea: Potential Field + Random Walk

5. But Pathological Cases …

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

7. Single-Query PRM Planning mbmbmbmb mgmgmgmg

8. Two Tenets of PRM Planning Checking sampled configurations and connections between samples for collision can be done efficiently.  Hierarchical collision checking 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. Second Tenet of PRM Planning A relatively small number of milestones and local paths are sufficient to capture the connectivity of the free space. Visibility properties of free space  Notion of expansive free space (2 nd paper)

10. Issues  Why random sampling? Convenient incremental scheme  Smart sampling strategies Topic for next two classes  Final path smoothing