Global Motion Planning under Uncertain Motion, Sensing, and Environment Map

Motion planning that takes into account uncertainty in motion, sensing, and environment map, is critical for autonomous robots to operate reliably in our living spaces. Partially Observable Markov Decision Processes (POMDPs) is a principled and general framework for planning under uncertainty. Although recent development of point-based POMDPs have drastically increased the speed of POMDP planning, even the best POMDP planner today, fails to generate reasonable motion strategies when the environment map is not known exactly. This paper presents Guided Cluster Sampling (GCS), a new point-based POMDP planner for motion planning with uncertain motion, sensing, and environment map, when the robot has active sensing capability. It uses our observations that in this problem, the belief space B can be partitioned into a collection of much smaller sub-spaces, and an optimal policy can often be generated by sufficient sampling of a small subset of the collection. GCS samples B using two-stage cluster sampling, a subspace is sampled from the collection and then a belief is sampled from the subspace. It uses information from the set of sampled sub-spaces and sampled beliefs to guide subsequent sampling. Preliminary results suggest that GCS generates reasonable policies for motion planning problems with uncertain motion, sensing, and environment map, that are unsolvable by the best point-based POMDP planner today, within reasonable time. Furthermore, GCS handles POMDPs with continuous state, action, and observation spaces. We show that for a class of POMDPs that often occur in robot motion planning, GCS converges to the optimal policy, given enough time. To the best of our knowledge, this is the first convergence result for point-based POMDPs with continuous action space.