The document discusses probabilistic roadmaps (PRM), a motion planning technique. PRM was developed as an alternative to potential field and heuristic planners that are either too slow or unreliable. PRM works by sampling configurations in free space and connecting nearby configurations with local paths if collision-free. This captures the connectivity of free space using relatively few milestones and paths. PRM has probabilistic completeness, meaning the probability of finding a solution increases exponentially as planning time increases, if a solution exists.

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 [Kavraki, Svetska, Latombe,Overmars, 95] m b m g milestone 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)