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The authors consider one of the most popular approaches to path planning: hierarchical approximate cell decomposition. This approach consists of constructing successive decompositions of the robot's configuration space into rectangloid cells and searching the connectivity graph built at each level of decomposition for a path. Despite its conceptual simplicity, an efficient implementation of this approach raises many delicate questions that have not yet been addressed. The major contributions this work are (1) a novel approach to cell decomposition based on constraint reformulation and (2) a new algorithm for hierarchical search with a mechanism for recording failure conditions. These algorithms have been implemented in a path planner, and experiments with this planner have been carried out on various examples. These experiments show that the proposed planner is significantly (approximately 10 times) faster than previous planners based on the same general approach.>
Zhu et al. (Tue,) studied this question.