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