Soft Subdivision Search in Motion Planning, II: Axiomatics

We propose to design motion planning algorithms with a strong form of resolution completeness, called resolution-exactness. Such planners can be implemented using soft predicates within the subdivision paradigm. The advantage of softness is that we avoid the Zero problem and other issues of exact computation. Soft Subdivision Search (SSS) is an algorithmic framework for such planners. There are many parallels between our framework and the well-known Probabilistic Road Map (PRM) framework. Both frameworks lead to algorithms that are practical, flexible, extensible, with adaptive and local complexity. Our several recent papers have demonstrated these favorable properties on various non-trivial motion planning problems. In this paper, we provide a general axiomatic theory underlying these results. We also address the issue of subdivision in non-Euclidean configuration spaces, and how exact algorithms can be recovered using soft methods.