ALT Illustration of PRM and BRM algorithms. (a) PRM and the planned path (red line). PRM does not consider motion and observation uncertainties. The planned path has a high probability of collision. (b) BRM and the planned path. BRM nodes are distributions of the state sampled in the belief space. BRM makes informed plans by considering both safety and path efficiency. One challenge of the BRM algorithm is to derive the edge controller that achieves node reachability, i.e., steers the system from one distribution to another. Here, only Gaussian distributions are assumed, characterized by their mean and 3σ covariance ellipses.