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.

翻译：本文研究高斯信念空间中面向最小感知导航的运动规划问题。尽管采样算法在确定性场景中已被广泛应用并得到严格分析，但在高斯信念空间中，关于采样算法返回解质量的正式分析仍十分匮乏。本文旨在填补这一研究空白，通过分析基于高斯信念空间的采样算法随样本数量增加所获解代价的渐近行为。为此，我们提出一种名为信息几何PRM*（IG-PRM*）的采样运动规划算法，用于生成能够最小化欧几里得代价与信息论代价加权和的可行路径，并证明其返回解的代价在样本数量趋于无穷时必然收敛至全局最优。最后，我们考虑无障碍场景，利用文献中的"移动与感知"策略计算最优解，验证所提算法返回的代价随样本数增加而收敛至此最优解。