Safety Verification and Control for Collision Avoidance at Road Intersections

This paper presents a supervisory algorithm that prevents side collisions among vehicles at an intersection by taking control of vehicles when necessary. Based on the vehicles' current state and drivers' desired inputs, the supervisor verifies whether there exists an input signal with which vehicles can cross the intersection without collision. Instead of directly searching for the existence of such an input signal, we solve an equivalent jobshop scheduling problem, which leads to a more tractable solution. The jobshop scheduling problem determines the existence of a schedule, i.e., times at which vehicles can enter conflict areas within an intersection, such that vehicles do not meet in any conflict area. This problem is approximately solved via two mixed integer linear programming problems formulated for simplified vehicle dynamics. The solutions to these problems provide over- and underapproximations of the solution to the jobshop scheduling problem with quantified approximation bounds. We theoretically demonstrate that this supervisor keeps the intersection safe and is non-blocking. Computer simulations further validate that the algorithm can run in real time for problems of realistic size.