## 1 Introduction
[PERSON] [12] adopted a control method based on the ideal articulation angle, which controls the steering angle of each wheel to ensure that the articulation angle is at the optimal value to eliminate the tracking error. Refs. [7; 13; 14] calculate the target state of the vehicle based on the established kinematics model and then propose a specific control law for the wheel steering angle. [PERSON] [15] also achieved path tracking under reversing conditions by accurately linearizing the nonlinear model of the vehicle. In order to improve passenger capacity, driving capacity, and operational quality, multi-module marshalling, all-axle steering, and distributed drive are the inevitable directions for the development of the VTT. However, the above research focuses on the tractor-trailer configuration, which is somewhat different from the multi-articulated and multi-actuator system of the VTT. The research on multi-articulated systems can be traced early [16], and is similar to the active trailer steering (ATS) problem in a wheeled mobile robot (WMR) [17; 18]. [PERSON] [19; 20] considered the tracking problem of a vehicle composed of a single tractor and an N-1 trailer equipped with off-axle hinges. A vehicle input-output feedback linearization model was established and a zero dynamic analysis of the system was conducted. Finally, the path-tracking control was completed by assigning closed-loop poles to the linearized system. [PERSON] [21] adopted Lyapunov-based methods to achieve asymptotic stability control of articulated vehicles' forward and backward motion. Refs. [22; 23] adopt a method based on extended Ackermann steering, which determines the instantaneous center of rotation based on the steering angle of the vehicle's first axle. By controlling the steering angle of other wheels to make the instantaneous centers of each wheel the same, all wheels can track the midpoint of the first axle. [PERSON] and [PERSON] [24] researched dynamics-based tracking methods. The article first establishes the dynamic and tire models of multi-articulated vehicles using the principle of virtual displacement and virtual work and proposes a feedforward and feedback control strategy. The lateral force at the axle required for path tracking is calculated based on tracking error, and then the wheel steering angle is obtained through reverse-solving the tire model. [PERSON] and [PERSON] [25; 26] proposed a full-state tracking control algorithm based on the vehicle dynamics model by taking all degrees of freedom (DOFs) as the vehicle state and taking the rotation angles of each axle and the driving torque of each wheel as control inputs. [PERSON] [27] proposed a universal tracking control method for N-unit wheeled robots. Moreover, thanks to the proposed cascaded control modules, the controller can quickly expand based on the number of marshalling, and the effectiveness of the control method was verified through a theoretical model. [PERSON] [28] proposed a scalable cascade modular path following a control strategy for the gantry virtual track train (G-VTT) based on a preview and tracking controller focusing on the lateral control for low-speed turning maneuvers, and the lag time was considered. [PERSON] [29] introduced the path-tracking control of the ART. Firstly, the tracking error was calculated through the image processing method, and two different control methods for the first module were proposed based on preview PID and Model Predictive Control (MPC). Then, the steering angle of each subsequent wheel was calculated based on the extended Ackermann method. Furthermore, a first-order delay was added to meet the different instantaneous rotation centers when the vehicle passes through the transition curve. Due to the characteristics of multi-module marshalling, all-axle steering, and distributed drive, the number of control inputs of the VTT is much greater than its DOFs, which makes the path-tracking problem difficult. Moreover, unreasonable control strategies can worsen hinge and tire force [30; 31].