On the Probabilistic Foundations of

Why are probabilistic roadmap (PRM) planners “probabilistic”? This paper tries to establish the probabilistic foundations of PRM planning and reexamines previous work in this context. It shows that the success of PRM planning depends mainly and critically on the assumption that the configuration space C of a robot often verifies favorable “visibility” properties that are not directly dependent on the dimensionality of C. A promising way of speeding up PRM planners is to extract partial knowledge on such properties during roadmap construction and use this knowledge to adjust the sampling measure continuously. This paper also shows that the choice of the sampling source—pseudo-random or deterministic—has small impact on a PRM planner's performance, compared to that of the sampling measure. These conclusions are supported by both theoretical arguments and empirical results.