Online Partial Conditional Plan Synthesis for POMDPs with Safe-Reachability Objectives

Abstract

The framework of Partially Observable Markov Decision Processes (POMDPs) offers a standard approach to model uncertainty in many robot tasks. Traditionally, POMDPs are formulated with optimality objectives. However, for robotic domains that require a correctness guarantee of accomplishing tasks, boolean objectives are natural formulations. We study POMDPs with a common boolean objective: safe-reachability, which requires that, with a probability above a threshold, the robot eventually reaches a goal state while keeping the probability of visiting unsafe states below a different threshold. The solutions to POMDPs are policies or conditional plans that specify the action to take contingent on every possible event. A full policy or conditional plan that covers all possible events is generally expensive to compute. To improve efficiency, we introduce the notion of partial conditional plans that only cover a sampled subset of all possible events. Our approach constructs a partial conditional plan parameterized by a replanning probability. We prove that the probability of the constructed partial conditional plan failing is bounded by the replanning probability. Our approach allows users to specify an appropriate bound on the replanning probability to balance efficiency and correctness. We validate our approach in several robotic domains. The results show that our approach outperforms a previous approach for POMDPs with safe-reachability objectives in these domains.