Vehicle Safety of the Velocity Obstacle Algorithm

This paper presents a mathematical analysis of the velocity obstacle algorithm applied to a nonholonomic vehicle for avoiding a moving obstacle in the plane. The velocity obstacle algorithm can be used for local navigation among dynamic obstacles by continually computing a set of unsafe velocities, and avoid the velocities inside of this set. The method is commonly used for reactive collision avoidance as it requires only limited knowledge of the obstacle behaviour and is computationally inexpensive. A drawback of previous analyses is the assumption that the vehicle and the obstacle are constrained to follow specific types of paths, or the velocities are assumed constant. We analyze the algorithm without such constraints and derive a set of conditions to prove that vehicle safety can be guaranteed in the general case. Moreover, we prove that the method can safely be applied to vehicles subject to nonholonomic constraints, with limited turning rates.