Path planning with moving obstacles using stochastic optimal control

Navigating a collision-free, optimal path for a robot poses a perpetual challenge, particularly in the presence of moving objects such as humans. In this study, we formulate the problem of finding an optimal path as a stochastic optimal control problem. However, obtaining a solution to this problem is nontrivial. Therefore, we consider a simplified problem, which is more tractable. For this simplified formulation, we are able to solve the corresponding Bellman equation. However, the solution obtained from the simplified problem does not sufficiently address the original problem of interest. To address the full problem, we propose a numerical procedure where we solve an optimization problem at each sampling instant. The solution to the simplified problem is integrated into the online formulation as a final-state penalty. We illustrate the efficiency of the proposed method using a numerical example.