## 1 Introduction
This approach achieved stable and effective control outcomes, particularly in complex control scenarios. MPC stands out as a popular choice for autonomous vehicle lateral control, primarily due to its adeptness in handling constraints [19]. [PERSON] et al. [20] introduced a model-predictive integrated controller employing Bezier curve fitting for lane changing, maintaining tracking accuracy without frequent parameter updates. [PERSON] et al. [21] integrated an event-triggering mechanism, enhancing real-time performance. [PERSON] et al. [22] optimized LTV-MPC for adaptability and robustness, even on challenging paths. To address network attacks, [PERSON] et al. [23] employed a fuzzy system and asynchronous elastic event-triggering mechanism for closed-loop control. [PERSON] et al. [24] optimized momentum using robust MPC for hybrid electric vehicles. For handling uncertainties, [PERSON] et al. [25] utilized MPC and H infinity design, ensuring robustness and accuracy through linear matrix inequalities. While the aforementioned MPC control methods enhance robustness against interference during AV trajectory tracking, they may not fully meet real-time requirements. [PERSON] et al. [26] have made a significant contribution to enhancing the robustness of MPC by developing an adaptive fuzzy MPC that takes into account load variations and time-varying parameters. In addition, to address the computational efficiency challenge of the controller, they have introduced an optimization method called time-cost compromise CPoP, which notably improves the computational efficiency of the controller [27]. All of the aforementioned lateral control methods have prioritized aspects of robustness and computational efficiency in vehicle tracking. However, it is crucial to note that the MPC controller, due to its requirement of solving a constrained optimization problem at each sampling time, can incur a substantial online computational burden, necessitating further optimization efforts. In response to these challenges, this study introduces an MPC framework founded on the linear complementarity problem (LCP) solution method. This novel approach replaces the traditional quadratic programming (QP) method and aims to address both robustness and computational efficiency issues within the existing MPC framework. The primary objective is to enhance the real-time performance and stability of self-driving car controllers. The key contributions of this study can be summarized as follows:  
1. A comprehensive model of the vehicle's steering system has been developed. This model, combined with a dynamic tire model, enables precise control of the motor torque used to adjust the steering angle. This well-crafted model enhances vehicle control accuracy. 2. By integrating LCP solving techniques, this study enhances the efficiency of solving QP problems within the MPC framework. 3. The vehicle has been experimentally analyzed under two challenging road conditions--high friction and low friction--and compared with PID and conventional QP solution methods. This empirical validation validates the reliability of the proposed algorithm. This article's structure is organized into several sections as follows:  
Section 2 dives into the modeling of the vehicle system, including discussions on the electric power assist system (Section 2.1), vehicle dynamics, and tire characteristics (Section 2.2), as well as the integration of steering structure and dynamics (Section 2.3). In Section 3, the focus shifts to the design of the controller. This chapter outlines the composition of the controller (Section 3.1), discusses the design of the QP solver (Section 3.2), and introduces the LCP solver (Section 3.3). Additionally, Section 3.4 offers an analysis of the system's stability, followed by a detailed explanation of the controller's computation process in Section 3.5. Lastly, in Section 4, this article provides validation of the controller's effectiveness through a series of simulation experiments.