A Virtual Spring Strategy for Cooperative Control of Connected and Automated Vehicles at Signal-Free Intersections

Emerging technologies of connected and automated vehicles (CAVs) applied at intersections have great potential to improve traffic efficiency, driving safety, and fuel economy. This paper proposes a virtual spring strategy for coordinating CAVs to pass through signal-free intersections. A virtual spring coordination system (VSCS) is established to force the movements of conflicting CAVs in terms of spring characteristics. Inspired by the properties of springs with dampers, a distributed control protocol is designed to regulate CAVs to reach a desired state of motion when crossing intersections. For ensuring the convergence of the VSCS, i.e., the total elastic potential energy approaches to zero, sufficient conditions for the internal stability are derived subject to the input saturation. To further improve the anti-disturbance capability of the VSCS, we ensure the upper bound of the disturbance propagation, which is characterized by an $H_{\infty }$ performance index. The proposed strategy is developed in a receding horizon framework and tested under the two scenarios in simulations. The simulation results show the effectiveness and superiority of the proposed strategy.