A Smoothing Algorithm for Minimum Sensing Path Plans in Gaussian Belief Space

Abstract: This paper explores minimum sensing navigation of robots in environments cluttered with obstacles. The general objective is to find a path plan to a goal region that requires minimal sensing effort. In [1], the information-geometric RRT* (IG-RRT*) algorithm was proposed to efficiently find such a path. However, like any stochastic sampling-based planner, the computational complexity of IG-RRT* grows quickly, impeding its use with a large number of nodes. To remedy this limitation, we suggest running IG-RRT* with a moderate number of nodes, and then using a smoothing algorithm to adjust the path obtained. To develop a smoothing algorithm, we explicitly formulate the minimum sensing path planning problem as an optimization problem. For this formulation, we introduce a new safety constraint to impose a bound on the probability of collision with obstacles in continuous-time, in contrast to the common discrete-time approach. The problem is amenable to solution via the convex-concave procedure (CCP). We develop a CCP algorithm for the formulated optimization and use this algorithm for path smoothing. We demonstrate the efficacy of the proposed approach through numerical simulations.