Lane-Free Crossing of CAVs through Signal-Free Intersections as a Minimum-Time Optimal Control Problem

Unlike traditional cars, connected and autonomous vehicles (CAVs) can cross intersections in a lane-free and signal-free order to increase the temporal-spatial capacity of intersections. This paper presents an optimal strategy to centrally control the CAVs entering an intersection to minimise the worst crossing time of the vehicles, or equivalently maximise the throughput of the intersection. The strategy is the solution of a minimum-time optimal control problem (OCP) that is highly non-convex due to the existence of constraints to avoid collision of vehicles with each other and with road boundaries. An algorithm is proposed to solve the formulated OCP by smoothing and convexifying the obstacle avoidance constraints using their dual equivalent problems in the form of relaxed necessary conditions. Simulation results show an average of 52% improvement in the crossing time of intersections as compared to the state-of-the-art reservation-based methods. Furthermore, it is shown that the minimum crossing time of an intersection is fixed and does not change regardless of the number of CAVs.