A heuristic for optimal coordination of autonomous vehicles: real-time algorithms

When coordinating connected and automated vehicles at an unsignalized intersection, the crossing order and the vehicle trajectories must be decided jointly. For a fixed crossing order, the problem can be formulated conveniently in a bi-level form where each vehicle solves its own optimal control problem, whose optimal value is a function of its entry and exit times, and a coordinator optimizes these times subject to precedence constraints. We compute the first and second order sensitivities of lower-level problems, which are required to solve the upper-level problem, by means of algorithmic differentiation using the real-time software package \texttt{acados}. This implementation exploits tailored algorithms to obtain a computationally efficient implementation of the optimal coordination algorithm. We validate our implementation in numerical simulations that demonstrate both real-time feasibility and effectiveness of our algorithm.