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In this paper, we consider the motion planning problem in Gaussian beliefspace for minimum sensing navigation. Despite the extensive use ofsampling-based algorithms and their rigorous analysis in the deterministicsetting, there has been little formal analysis of the quality of theirsolutions returned by sampling algorithms in Gaussian belief space. This paperaims to address this lack of research by examining the asymptotic behavior ofthe cost of solutions obtained from Gaussian belief space based samplingalgorithms as the number of samples increases. To that end, we propose asampling based motion planning algorithm termed Information Geometric PRM*(IG-PRM*) for generating feasible paths that minimize a weighted sum of theEuclidean and an information-theoretic cost and show that the cost of thesolution that is returned is guaranteed to approach the global optimum in thelimit of large number of samples. Finally, we consider an obstacle-freescenario and compute the optimal solution using the "move and sense" strategyin literature. We then verify that the cost returned by our proposed algorithmconverges to this optimal solution as the number of samples increases.

Optimal Sampling-based Motion Planning in Gaussian Belief Space for Minimum Sensing Navigation