A heuristic for optimal coordination of autonomous vehicles: static problems

We consider the coordination of autonomous vehicles at unsignalized intersections, where trajectory planning and crossing-order decisions are intrinsically coupled, thereby making their simultaneous optimization intractable in practice. To this end, we propose a heuristic based on a hierarchical structure consisting of a series of nonlinear programs (NLP) in the lower level, which optimizes trajectories of each vehicle for a given crossing order, and a high-level heuristic to design new crossing schedules that exploits sensitivity information from the lower-level NLPs. Extensive numerical simulations across a broad range of traffic scenarios demonstrate that our strategy achieves substantially improved scheduling with respect to first-in-first-out ordering while preserving computational tractability.