Control of a City Road Network: Distributed Exact Verification of Traffic Safety

A least-restrictive supervisor for vehicle collision avoidance is a control algorithm that can detect an unsafe maneuver by a set of human-driven or autonomous vehicles, intervening with a corrective action only when needed to avoid a collision. It can help prevent collisions, and facilitate coexistence of autonomous and human-driven vehicles. Such an algorithm is based on a formal verification problem which, unfortunately, is known to be NP-hard in many cases of interest, for instance at traffic intersections. Here, we propose a strategy to dynamically decompose the formal verification problem of a large road network, exploiting vehicle dynamics and the constraints induced by road topology to separate nonconflicting vehicles. We split the global problem into smaller and treatable subproblems, while still allowing to compute an exact solution. We illustrate our results on three different scenarios.