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

We present the design and validation of a centralized controller, called a supervisor, for collision avoidance of multiple human-driven vehicles at a road intersection, considering measurement errors, unmodeled dynamics, and uncontrolled vehicles. We design the supervisor to be least restrictive, that is, to minimize its interferences with human drivers. This performance metric is given a precise mathematical form by splitting the design process into two subproblems: verification problem and supervisor-design problem. The verification problem determines whether an input signal exists that makes controlled vehicles avoid collisions at all future times. The supervisor is designed such that if the verification problem returns yes, it allows the drivers' desired inputs; otherwise, it overrides controlled vehicles to prevent collisions. As a result, we propose exact and efficient supervisors. The exact supervisor solves the verification problem exactly but with combinatorial complexity. In contrast, the efficient supervisor solves the verification problem within a quantified approximation bound in polynomially bounded time with the number of controlled vehicles. We validate the performances of both supervisors through simulation and experimental testing.