This study investigates the constraint-force driven control problem of virtual coupling. To solve the constraint force, the explicit equation of vehicle motion with equality constraints is established using the Udwadia–Kalaba approach. First of all, this study introduces a brief overview of virtual coupling concepts in the European Railway Traffic Management System and some scenes of virtual coupling. The control method is proposed to enable the mechanical system to follow the designed constraint. Moreover, the dynamic model for virtual coupling problem is established. Second, combined with the dynamic model, the equation constraint is designed to make the rail vehicle movenment reach the control objective. By solving the equation based on the Udwadia–Kalaba approach, the control inputs that can render the vehicle to move along the desired trajectory. Third, numerical simulation results demonstrate the effectiveness of the proposed method in virtual coupling problem.

这项研究调查了虚拟耦合的约束力驱动控制问题。为了解决约束力，使用Udwadia–Kalaba方法建立了具有相等约束的车辆运动的显式方程。首先，本研究简要介绍了欧洲铁路交通管理系统中的虚拟耦合概念以及虚拟耦合的一些场景。提出了控制方法，以使机械系统能够遵循设计的约束条件。此外，建立了虚拟耦合问题的动力学模型。其次，结合动力学模型，设计方程约束条件，使轨道车辆的运动达到控制目标。通过基于Udwadia–Kalaba方法求解方程，可以使车辆沿着所需轨迹运动的控制输入。第三，数值仿真结果证明了该方法在虚拟耦合问题中的有效性。