Petri Net-Aided Iterative Trajectory Optimization for Multi-CAV Coordination at Unsignalized Intersections

Coordination at unsignalized intersections has attracted increasing attention in recent years, which aims at improving the efficiency of intersection operations, while eliminating conflicts and deadlocks for Connected and Automated Vehicles (CAVs). This paper addresses the challenging issue of systematically optimizing CAV trajectories, tackling the high computational cost for finding a good solution, especially as the number of lanes and CAVs increases. To do so, a novel systematic optimal trajectory planning model is designed to efficiently guide CAVs through intersections without conflicts and deadlocks. To tackle the computational hurdles and enable real-time applications, based on the model, we develop a Petri net-aided Iterative Trajectory Optimization (P-ITO) solution algorithm. Leveraging the unique characteristics of the problem, this algorithm first designs a Petri net-based controller for conflict and deadlock avoidance so that initial feasible solutions are generated. Then, refinement is made on the initial feasible solutions to obtain an optimal or near optimal solution by designing an iterative process. This algorithm effectively ensures solution feasibility and enhances computing efficiency by searching for an optimal solution in the feasible region. Numerical experiments for intersections with bidirectional six-lane configurations illustrate the efficacy of our model in facilitating the safe and efficient passage of all CAVs while mitigating the risk of deadlocks. The P-ITO algorithm significantly outperforms the commercial solvers in both solution quality and computational time. Furthermore, our method is versatile, applicable to diverse intersection scenarios, and capable of maintaining high computational efficiency.