Knowledge as a Tool in Motion Planning under Uncertainty

Inspired by the success of the distributed computing community in applying logics of knowledge and time to reasoning about distributed protocols, we aim for a similarly powerful and high-level abstraction when reasoning about control problems involving uncertainty. Here we concentrate on robot motion planning, with uncertainty in both control and sensing. This problem has already been well studied within the robotics community. Our contributions include the following:•We define, a new, natural problem in this domain: obtaining a sound and complete termination condition, given initial and goal locations.•We define a high-level language, a logic of time and knowledge, to reason about motion plans in the presence of uncertainty, and use it to provide general conditions for the existence of sound and complete termination conditions for a broad class of motion plans.•We characterize the optimal sound termination conditions for the general problem, relate them to a class of fundamental knowledge based protocols and provide a natural example of knowledge based protocols lacking a canonical implementation.11The first part of this paper generalizes results of a previous paper by Brafman, Latombe and Shoham ([BLS93]). Sections 4.3 and 5 contain new material.