Active sensing for motion planning in uncertain environments via mutual information policies

This paper addresses path planning with real-time reaction to environmental uncertainty. The environment is represented as a robotic roadmap, or graph, and is uncertain in that the edges of the graph are unknown to the robot a priori. Instead, the robot’s prior information consists of a distribution over candidate edge sets, modeling the likelihood of certain obstacles in the environment. The robot can locally sense the environment, and at a vertex, can determine the presence or absence of some subset of edges. Within this model, the reactive planning problem provides the robot with a start location and a goal location and asks it to compute a policy that minimizes the expected travel and observation cost. In contrast to computing paths that maximize the probability of success, we focus on complete policies (i.e., policies that are guaranteed to navigate the robot to the goal or determine no such path exists). We prove that the problem is NP-hard and provide a suboptimal, but computationally efficient solution. This solution, based on mutual information, returns a complete policy and a bound on the gap between the policy’s expected cost and the optimal. We test the performance of the policy and the lower bound against that of the optimal policy and explore the effects of errors in the robot’s prior information on performance. Simulations are run on a flexible factory scenario to demonstrate the scalability of the proposed approach. Finally, we present a method to extend this solution to robots with faulty sensors.