Global motion planning under uncertain motion, sensing, and environment map

Uncertainty in motion planning is often caused by three main sources: motion error, sensing error, and imperfect environment map. Despite the significant effect of all three sources of uncertainty to motion planning problems, most planners take into account only one or at most two of them. We propose a new motion planner, called Guided Cluster Sampling (GCS), that takes into account all three sources of uncertainty for robots with active sensing capabilities. GCS uses the Partially Observable Markov Decision Process (POMDP) framework and the point-based POMDP approach. Although point-based POMDPs have shown impressive progress over the past few years, it performs poorly when the environment map is imperfect. This poor performance is due to the extremely high dimensional state space, which translates to the extremely large belief space B. We alleviate this problem by constructing a more suitable sampling distribution based on the observations that when the robot has active sensing capability, 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. Utilizing these observations, GCS samples B in two-stages, 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. Simulation results on marine robotics scenarios suggest that GCS can generate reasonable policies for motion planning problems with uncertain motion, sensing, and environment map, that are unsolvable by the best point-based POMDPs today. 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, given enough time, GCS converges to the optimal policy. To the best of our knowledge, this is the first convergence result for point-based POMDPs with continuous action space.