# Path Tracking Control Strategy Based on Adaptive MPC for Intelligent Vehicles
## 1 Introduction  
Path tracking control, a pivotal technology in autonomous driving, involves steering and speed regulation of the vehicle by leveraging information from environmental perception and planning decision-making modules. This technology enables intelligent vehicles to navigate along the planned path while maintaining accuracy and stability in path tracking. Recent advancements in path tracking control have leveraged AI-driven MPC adaptations, such as neural-network-based parameter tuning [1], and multi-sensor fusion for real-time curvature estimation [2]. However, challenges persist in achieving adaptive control under variable curvature conditions, where traditional MPC methods exhibit limitations in parameter flexibility [3, 4, 5]. The existing research primarily employs the pre-tracking theory [6, 7], the proportional integral derivative (PID) theory [8, 9], the linear optimal regulator (LQR) theory [10], sliding control algorithms [11, 12], genetic algorithms [13, 14], fuzzy adaptive control algorithms [15, 16] and model predictive control (MPC) algorithms [17, 18, 19, 20]. Among these, the traditional MPC is a model feedback and optimization-based control algorithm consisting of a predictive model, rolling optimization and feedback correction. It generally applies a set of predetermined parameters and constraints to the control process and is widely used in path tracking control due to the incorporation of dynamic constraints related to the controlled object. Consequently, MPC has found extensive application in path tracking control [21, 22]. [PERSON], [PERSON] et al. [23] developed an MPC-based obstacle avoidance controller with rollover prevention. However, high-speed scenarios cause excessive LTR growth, significantlydegrading tracking performance. [PERSON] et al. [24] developed a 3-DOF MPC controller with GA-optimized time domains; yet, significant tracking errors remain in high-speed/high-curvature scenarios. [PERSON] et al. [25] developed a radial basis function (RBF) neural-network-based controller with high-order sliding mode (HOSMC) adaptation to handle random disturbances. While effective in standard conditions, its offline-tuned time domain parameters limit robustness in variable operating conditions, compromising tracking accuracy in complex scenarios. [PERSON] et al. [26] developed a Koopman-operator-based MPC using extended dynamic mode decomposition (EDMD) to linearize non-linear dynamics, enabling simultaneous speed/fuel optimization. While effective for global energy management, the method may compromise path tracking accuracy due to weakened lateral dynamics and slower response from high-dimensional optimization. [PERSON] et al. [27] proposed an improved intelligent vehicle target path tracking method by enhancing the objective function, incorporating dynamic constraints for tire sideslip angle and adopting the vehicle dynamics model as the predictive model for model predictive control. However, this method exhibits significant sideslip at high speeds, resulting in tracking deviations. [PERSON] et al. [28] developed a curvature-aware MPC controller using LTR for stability assessment, optimizing trajectories via a normalized cost function. While polynomial fitting reduces computation, real-time performance remains challenging in dynamic environments. The method was only validated for static/uniformly moving obstacles at medium-low speeds, and LTR alone may insufficiently capture vehicle stability. [PERSON] et al. [29] developed a spline-based path planner with discrete optimization and a PSO-tuned fractional-order PID controller, improving tracking robustness. Despite integrating dynamic safety metrics, the high-complexity algorithm faces real-time challenges and lacks dynamic obstacle validation. [PERSON] et al. [30] integrated artificial potential field (APF) into the MPC's objective function for dynamic obstacle avoidance, with fuzzy control optimizing MPC weights to improve tracking.