## 1 Introduction
However, in 4 WAS and 4 WIS, the wheel angle is obtained by comprehensive judgment based on the driver's steering input and the vehicle state input to the controller. The first incarnation of 4 WS technology dates back to 1980, when it was introduced in Japan. Compared with 4 WAS and 4 WIS, 4 WS is one of the most widely studied and applied technologies, and many control strategies and methods are based on 4 WS technology [15; 16; 17]. [PERSON] et al. [18] used a linearization method to simplify the 3-DOF nonlinear vehicle model of 4 WS moderately, retaining the coupling characteristics of the vehicle model in terms of driving/braking and the wheel angle, and designed a decoupler of the 4 WS vehicle system to realize the decoupling control of the vehicle. [PERSON] [19] designed a dynamic decoupling controller for 4 WS vehicles, which is also a simplification of the 3-DOF nonlinear vehicle model. Unlike this, the decoupling controller does not require the observation or estimation of the lateral velocity but implements the decoupling of the yaw velocity and the lateral velocity through the input of additional front wheel angle and rear wheel angle. In addition, many studies have been conducted by other scholars. [PERSON] et al. [20] designed a trajectory tracking controller based on horizontal and vertical decoupling. The nonlinear problem in the model is alleviated by PID control with feedback and adaptive control. [PERSON] et al. [21] and [PERSON] [22] et al. designed trajectory tracking controllers for four-wheel steering vehicles, which improved the tracking accuracy compared to front wheel steering vehicles but did not consider the vehicle speed or road conditions. Some other researchers have designed trajectory tracking based on predictive tracking theory and have designed more accurate trajectory tracking simulators by optimizing the preview or direction control [23; 24; 25]. For example, [PERSON] et al. [26] proposed a kind of driver direction control model based on trajectory prediction on the basis of the assumption that the driver has the ability to predict the vehicle trajectory. We have analyzed the literature cited above as shown in Table 1.  
In this paper, a trajectory tracking control algorithm based on distributed driving is designed for 4 WS vehicles. Based on the distributed drive stability control strategy, it gives full play to the advantages of the distributed drive chassis system, solves the problem of vehicle trajectory tracking under extreme working conditions, and realizes the design of a trajectory tracking control algorithm for multi-objective coordinated control. The specific contributions are as follows:  
(1) The particle swarm optimization (PSO) algorithm is used to optimize the MPC controller. Q and R are the primary weight coefficients in the MPC control process. The PSO algorithm is used to optimize and adjust the weighting coefficients, the fitness function is iteratively reduced until the iteration number requirements are met, and the optimization is stopped to realize the goal of adaptive optimization of the MPC control parameters. (2) In the sliding mode controller of the rear wheel angle, a sliding mode surface referring to the PID controller is designed, and factors such as driving anti-slip are considered in the torque distributor so that the torque distribution of each wheel is more reasonable. (3) An improved phase plane stability judgment method is designed to judge the instability degree of the vehicle in real-time, and different partition controllers are designed according to the instability degree to control the additional yawing moment. It is verified that the tracking accuracy can be improved while ensuring the vehicle's stability.