Towards Knowledge-Level Analysis of Motion Planning

Ronen I. Brafman, Jean-Claude Latombe, Yoav Shoham

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 consider a specific class of (simple) motion plans in Rn from the literature, and provide necessary and sufficient conditions for the existence of sound and complete termination conditions for plans in that class. We define a high-level language, a logic of time and knowledge, to reason about motion plans in the presence of uncertainty, and use them to provide general conditions for the existence of sound and complete termination conditions for a broader class of motion plans.


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