Robust Supervisors for Intersection Collision Avoidance in the Presence of Legacy Vehicles

Vehicle coordination at road intersections to prevent collisions has recently drawn a lot of research attention, but still remains challenging due to a large volume of traffic composed of autonomous and human-driven vehicles. In this paper, we present the design and validation of a supervisory algorithm for collision avoidance at road intersections, in the simultaneous presence of measurement errors, unmodeled dynamics, and vehicles that are not equipped with autonomous driving features. We design a supervisor that takes control of vehicles that are capable of communication and autonomous actions, only when necessary to avoid a collision, or otherwise leaves control to their drivers. This supervisor is least restrictive, that is, it takes control away from drivers only when necessary to avoid future collisions. Since the complexity of the supervisor algorithm is combinatorial with the number of vehicles, we also design an approximate supervisor that can handle more realistic scenarios with a larger number of vehicles in polynomially bounded time at the expense of an additional, yet quantified, restrictiveness. The least restrictive supervisor is validated through experimental testings using three small-scale vehicles, and the approximate supervisor is validated through computer simulations.