Navigation Planning in Probabilistic Roadmaps with Uncertainty

Probabilistic Roadmaps (PRM) are a commonly used class of algorithms for robot navigation tasks where obstacles are present in the environment. We examine the situation where the obstacle positions are not precisely known. A subset of the edges in the PRM graph may possibly intersect the obstacles, and as the robot traverses the graph it can make noisy observations of these uncertain edges to determine if it can traverse them or not. The problem is to traverse the graph from an initial vertex to a goal without taking a blocked edge, and to do this optimally the robot needs to consider the observations it can make as well as the structure of the graph. In this paper we show how this problem can be represented as a POMDP. We show that while too large to be solved with exact methods, approximate point based methods can provide a good quality solution. While feasible for smaller examples, this approach isn't scalable. By exploiting the structure in the belief space, we can construct an approximate belief-space MDP that can be solved efficiently using recent techniques in MDP planning. We then demonstrate that this gives near optimal results in most cases while achieving an order of magnitude speed-up in policy generation time