Train Trajectory Optimization based on Quadratic Programming for Virtual Coupling Concepts.

The concept of virtual coupling train convoys shows promise for improving railway capacity. This approach typically involves a “leader-follower” control strategy for multiple objects, such as vehicles and drones. In order to allow followers to enter the convoy, the operation status and trajectory of the leader vehicle must be optimized. This paper examines field data collected on Guangzhou Metro Line 22, and the velocity-distance curve shows consistency among the test runs, enabling coupling possibilities. Considering constraints such as safety constraints, train dynamic model constraints, and velocity limitation constraints, when the train operating trajectory expressed by polynomial curves is incorporated into the objective function, the resulting optimization strategy can be solved using quadratic programming methods. With the optimized trajectory by the proposed method, the average acceleration decreased by 0.009 m/s ² to 0.024 m/s ² , and the standard deviation decreased by 0.024 m/s ² to 0.181 m/s ² , Using the field collected data, the paper simulates train operations under virtual coupling, leader train using the optimized train trajectory, follower train employing the pure pursuit. The correlation coefficient of the velocity time series between the leader train and the follower train is 0.9996. The headway can also be shortened to 193.15 m average and a standard deviation of 6.44 m.