Belief roadmap search: Advances in optimal and efficient planning under uncertainty

We characterize and propose advances in the technique of Belief Roadmap Search (BRMS), the process of searching a roadmap in belief space for robot motion planning under localization uncertainty. We discuss the conditions required for optimal substructure in the single-source search of a roadmap in belief space, demonstrating that there are several desirable cost functions for which this property cannot be achieved. Practical performance issues of BRMS are discussed, including the implications of a commonly-used anti-cycling rule, and the computational complexity realized in practical applications of the technique. We propose a best-first implementation of BRMS, in contrast to the standard breadth-first implementation, which we show to improve the computational cost of search by up to 49% by eliminating unnecessary node expansions — the mechanics of both approaches are compared in detail. A variety of motion planning examples are explored.

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