Trajectory Optimization for High-Speed Railway Virtual Coupling: A Time Headway Approach with Convex Programming

Faced with the challenges of high-density operations and limited infrastructure resources in metropolitan railway systems, Virtual Coupling (VC) technology overcomes the constraints of traditional block signaling and offers a new approach for train cooperative control, providing a breakthrough in enhancing system capacity. This paper presents a time headway VC operation strategy, which formulates a trajectory optimization model with the objective of minimizing the time delay at identical track positions. This allows the following train to accurately track the leading train while maintaining a safe headway. To meet real-time computation requirements, the original non-convex problem is transformed into an efficiently solvable convex optimization model through the introduction of relaxation variables. Based on actual train parameters, a simulation is conducted for a 40-kilometer section with speed restriction disturbances, validating that the proposed method significantly reduces the minimum tracking headway between trains while ensuring safety. Additionally, a comparison between the relaxation variables and the original variables further confirms the accuracy of the model construction.