Safety Verification Methods for Human-Driven Vehicles at Traffic Intersections: Optimal Driver-Adaptive Supervisory Control

We design an optimal, driver-adaptive supervisor for collision avoidance at an intersection. The algorithm is able to identify optimal corrections to the human-decided inputs and to keep the system collision free. To determine the set of safe control actions, we exploit the notion of maximal controlled invariant set. We leverage results from scheduling theory to verify the safety of a given control input, and propose an efficient optimization algorithm providing optimal solutions with respect to the drivers' intent. We also present an approximate supervisor algorithm that can be solved in polynomial time and has guaranteed error bounds. Finally, we validate our approach with simulation results, as well as on naturalistic data.