Efficient Touch Based Localization through Submodularity

We explore the problem of selecting a sequence of information gathering actions to localize an object quickly. We present two approaches to this problem, applied to touch based localization with a robotic end effector. In the first, we greedily select actions at each step of the sequence that minimize the Shannon entropy of our current belief. In the second, we consider many possible hypotheses of the object's pose, and greedily select actions expected to disprove the most hypotheses. We show that this formulation is adaptive submodular \cite{golovin_adaptive_2011}, and thus derive guarantees compared to the optimal sequence of actions. This enables us to derive guarantees compared to the \emph{optimal} sequence. We evaluate these approaches in simulation by comparing accuracy and computation time for localizing and grasping known objects.