# Trajectory-Tracking Control of Unmanned Vehicles Based on Adaptive Variable Parameter MPC
## 1 Introduction  
The advancement and development of automated driving technology, along with the modernization of economic levels, have led to the development of new automobile technology that is becoming more intelligent and electrified. Additionally, unmanned electric vehicles that can operate in challenging environments are being used extensively. With its fully wire-control integrated chassis and independent-driving and -braking capabilities, the unmanned electric vehicle can significantly increase operational accuracy and efficiency, in addition to taking the place of manual labor in challenging conditions [1]. Thus, the key to the development of China's modern industry is the research and development of unmanned vehicles with autonomous precision operation functions that are suitable for complex working conditions. Trajectory-tracking control is the foundation that enables unmanned vehicles to realize autonomous, precise operation. Many academics are currently conducting extensive research on trajectory-tracking control techniques. PID control [2], optimal control [3], sliding mode control [4], fuzzy control [5], and other techniques are frequently utilized in trajectory-tracking control. These methods can reduce computational time and simplify the control model. Because of the non-linearity of the vehicle system, the weight parameters must be modified to account for the system's ability to adapt to changing operating conditions. Consequently, there is a great deal of reliance on the weight parameters. The most versatile among them is model predictive control (MPC), which possesses the qualities of a predictive model, rolling optimization, and feedback correction. It can handle multi-objective and multi-variable optimization problems with constraints [6], has drawn the interest of numerous academics, and has the widest range of applications. For instance, [PERSON] [7] created a fuzzy MPC controller thatenhanced trajectory-tracking accuracy by adaptively modifying the weight coefficients in response to field roads' curvature. By introducing a gradient-projection technique, [PERSON] [8] et al. decreased the number of iterative steps in the MPC algorithm and increased the trajectory-tracking controllers' response time. [PERSON] [9] optimized the controller's overall efficiency by adaptively adjusting the adaptive MPC controller's predictive time domain based on the curvature of roadways. [PERSON] et al. 's adjustments to the weight matrix of the goal function in the MPC increase the controller's accuracy and stability [10; 11; 12]. For the vehicle lane-changing problem with constraints on multiple state quantities, [PERSON] [13] proposed a multi-constrained model predictive trajectory-tracking control method by creating a reference predetermined trajectory based on the trapezoidal acceleration method. However, on low-adhesion roads, the yaw rate does not accurately reflect the lateral stability of the vehicle. Despite the trajectory-tracking control problem of unmanned vehicles under changes in the road lateral inclination and the coefficient of road adhesion, the above studies have not considered the influence of such road surface factors on the MPC trajectory-tracking controller, and in this regard, in recent years, variable-parameter MPCs have been developed to improve the model accuracy and adaptability to working conditions. [PERSON] et al. [14] used model switching to meet the computational efficiency requirements under complex working conditions and improve tracking performance under simple working conditions, but their method also faced the problem of a loss of precision and accuracy. Some scholars have improved the adaptivity by changing the time domain [15; 16] and sampling frequency [17], but this method causes rough changes in control quantity, and the accuracy and reliability of the control inputs are thus difficult to guarantee.