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This paper extends the concept of â€œprobabilistic completenessâ€ defined for the motion planners in the state space (or configuration space) to the concept of â€œprobabilistic completeness under uncertaintyâ€ for the motion planners in the belief space. Accordingly, an approach is proposed to verify the probabilistic completeness of the sampling-based planners in the belief space. Finally, through the proposed approach, it is shown that under mild conditions the samplingbased method constructed based on the abstract framework of FIRM (Feedback-based Information-state Roadmap Method) are probabilistically complete under uncertainty.
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