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Ali-akbar Agha-mohammadi, Suman Chakravorty, Nancy Amato, "On the Probabilistic Completeness of the Sampling-based Feedback Motion Planners in Belief Space," Technical Report, TR11-006, Parasol Laboratory, Department of Computer Science, Texas A&M University, Nov 2011.
Technical Report(pdf, abstract)

This paper extends the concept of “probabilistic completeness” defined for the motion planners in the state space (or configuration space) to the concept of “probabilistic completeness under uncertainty” 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 sampling-based method constructed based on the abstract framework of FIRM (Feedback-based Information Roadmap Method) are probabilistically complete under uncertainty.