Safe Navigation With the Collision Avoidance of a Brownian Motion Obstacle

This paper develops a control that combines deterministic and stochastic optimal control solutions to the problem of safe navigation around a spherical obstacle in order to reach a way-point location. The solution for navigation towards the way-point is based on the deterministic minimum time optimal control. Since the intent of the obstacle is unknown to the navigating vehicle, the vehicle anticipates this uncertainty and uses a stochastic optimal control for navigation around the obstacle. The two navigation solutions are combined based on their value functions. Results are illustrated by numerical simulations.