Primal decomposition of the optimal coordination of vehicles at traffic intersections

In this paper we address the problem of coordinating automated vehicles at intersections, which we state as a constrained finite horizon optimal control problem. We present and study the properties of a primal decomposition of the optimal control problem. More specifically, the decomposition consists of an upper problem that allocates occupancy time-slots in the intersection, and lower-level problems delivering control policies for each vehicle. We investigate the continuity class of the upper problem, and show that it can be efficiently tackled using a standard sequential quadratic programming and that most computations can be distributed and performed by the participating vehicles. The paper is concluded with an illustrative numerical example.