Optimal Control of Automated Vehicles Crossing a Lane-Free Signal-Free Intersection

Developing signal-free intersections, where connected automated vehicles (CAVs) for all OD (origin-destination) movements are appropriately guided to cross simultaneously, may significantly improve throughput and reduce fuel consumption. Naturally, vehicles in the intersection area are not bound to lanes; therefore, it is reasonable to consider the crossing area as a lane-free infrastructure for further improved exploitation. This paper proposes a joint optimal control approach for CAVs crossing signal-free and lane-free intersections. Specifically, the control inputs of all vehicles, comprising acceleration and steering angle, are optimized over a time-horizon by solving a single optimal control problem (OCP) based on the bicycle model of vehicle dynamics. The cost function includes proper terms to ensure smooth and collision-free motion, while also considering fuel consumption and desired-speed tracking, when possible. Appropriate constraints are designed to respect the intersection boundaries and ensure smooth vehicle movements towards their respective destinations. The defined OCP is solved numerically via an efficient Feasible Direction Algorithm (FDA), which is acceptably fast. A challenging demonstration example confirms the effectiveness of the suggested method.