The blindfolded traveler's problem: A search framework for motion planning with contact estimates.

We address the problem of robot motion planning under uncertainty where the only observations are through contact with the environment. Such problems are typically solved by planning optimistically assuming unknown space is free, moving along the planned path and re-planning if the robot collides. However this approach can be very inefficient, leading to many unnecessary collisions and unproductive motion. We propose a new formulation, the Blindfolded Traveler's Problem (BTP), for planning on a graph containing edges with unknown validity, with true validity observed only through attempted traversal by the robot. The solution to a BTP is a policy indicating the next edge to attempt given previous observations and an initial belief. We prove that BTP is NP-complete and show that exact modeling of the belief is intractable, therefore we present several approximation-based policies and beliefs. For the policy we propose graph search with edge weights augmented by the probability of collision. For the belief representation we propose a weighted Mixture of Experts of Collision Hypothesis Sets and a Manifold Particle Filter. Empirical evaluation in simulation and on a real robot arm shows that our proposed approach vastly outperforms several baselines as well as a previous approach that does not employ the BTP framework.