Uncertain Probabilistic Roadmaps with Observations

Probabilistic roadmaps (PRMs) are a commonly used approach to path planning in continuous spaces with obstacles. We examine the case where the obstacle locations are not known with certainty but can be observed during execution of the plan. We abstract the problem to one of traversing a graph where some edges (referred to as uncertain edges) may or may not be present, and where noisy observations of these edges can be made from some of the vertices of the graph. We show that this problem can be represented as a POMDP, and then use the structure in the problem to derive a number of MDP approximations to the POMDP. We show that using these approximations we can solve larger PRMs efficiently while producing policies that are close to optimal for many problems, and that we can produce optimal solutions for PRMs with smaller numbers of uncertain edges.