Capturing the Connectivity of High-Dimensional Geometric Spaces by Parallelizable Random Sampling Techniques

Finding paths in high-dimensional gemetric spaces is a provably hard problem. Recently, a general randomized planning scheme has emerged as an effective approach to solve this problem. In this scheme, the planner samples the space at random and build a network of simple paths, called a probabilistic roadmap. This paper describes a basic probabilistic roadmap planner, which is easily parallelizable, and provides a formal analysis that explains its empirical success when the space satisfies two geometric properties called e-goodness and expansiveness.