## 1 Introduction
presents two methods to enable a 4 WIS 4 WID vehicle to accurately follow a predefined path as well as its reference trajectories including velocity and acceleration profiles [22]. In Reference [23], the projected error \(e^{p}\) combine the lateral position error \(e\) and the heading angle error \(\Delta\phi\) is used to design the lateral controller. An adaptive hierarchical trajectory following the control system is presented in Reference [24] to enhance the tracking performance and improve the lateral stability of autonomous 4 WID electric vehicles. These schemes enable the effective following of a desired path for an autonomous 4 WIS/4 WID vehicle. However, through the integrated chassis control system, the vehicle can have better performance while realizing the path tracking function. Since the four-wheel longitudinal and lateral forces of 4 WIS/4 WID electric vehicle are independently controllable, the performance of the vehicle can be improved by distributing the tire forces of each wheel. Therefore, the 4 WIS/4 WID vehicle is a good carrier to realize the function of automatic driving. Furthermore, the application of 4 WIS/4 WID vehicle to solve the coupling characteristics of lateral and longitudinal motion of vehicle dynamics needs further study. The main contributions of this paper are threefold. (1) To improve the control precision, the 4 WIS/4 WID vehicle control structure considering the lateral and longitudinal coupling characteristics of vehicle dynamics is proposed. (2) An adaptive control method is presented for different driving conditions. Three different evaluation indices are used to distribute the tire force of each wheel in order to further improve the vehicle performance while achieving trajectory tracking. (3) The proposed control structure can regulate the lateral velocity, in a reasonable range, for vehicle stability. Furthermore, the simulation experiments are carried out to verify the control method proposed in this paper. In this paper, a nonlinear NNPID controller is designed. The desired path of the 4 WIS/4 WID vehicle is tracked under the vehicle speed change condition to obtain the desired yaw rate. The Terminal sliding mode controller is designed to track the speed and the desired yaw rate, to converge the tracking error to zero in the limited time, and to ensure the robustness and global stability of the closed loop system. The desired resultant forces and desired resultant yaw moments are obtained. Considering the motor energy-saving control and tire wear performance index control, the multi-optimizationobjectives tire force distribution control strategy is designed to distribute the longitudinal and lateral forces of each wheel. An adaptive variable weight coefficient strategy based on vehicle speed and path curvature is designed to achieve optimal distribution of tire force. Finally, the wheel angles and driving torques are calculated by the four-wheel three-degree-of-freedom vehicle model and the tire model. The rest of the paper is organized as follows. The nonlinear four-wheel vehicle dynamics model and vehicle trajectory mode for the optimization controller is introduced in Section 2. The hierarchical control structure and the controller design method are proposed in Section 3. In Section 4, the tire force distribution method and actuator control method are proposed. Simulation results and analysis are illustrated in Section 5, followed by the conclusion in Section 6.