A fast terminal sliding mode control for autonomous vehicle path tracking: lyapunov analysis and numerical simulation

This paper presents a Fast Terminal Sliding Mode Control (FTSMC) strategy for robust lateral path tracking of autonomous vehicles under external disturbances and severe parametric uncertainties. The proposed controller is derived from the linearized dynamic bicycle model and incorporates a nonlinear fast terminal sliding surface with a saturation-based switching function to guarantee finite-time convergence while significantly mitigating chattering effects. Unlike conventional sliding mode and adaptive approaches, the controller is designed using nominal vehicle parameters only, and modeling uncertainties and external disturbances are treated as matched lumped disturbances, whose effects are compensated through Lyapunov-based stability guarantees without online parameter adaptation. Extensive numerical simulations in MATLAB demonstrate the effectiveness of the proposed method in three critical scenarios: normal operation, impulsive disturbance, and ± 90% parametric uncertainty. In nominal conditions, the proposed FTSMC reduces the average integral of absolute lateral displacement error from 0.1863 to 0.0882, achieving more than 50% improvement over the benchmark PD Sliding Mode Controller (PDSMC), while reducing the settling time to approximately 1.25 s. Under impulse disturbance, the lateral position error increases by less than 1% and remains bounded below 0.025 m, confirming strong disturbance rejection capability. Moreover, in the presence of severe parametric uncertainties, the position error remains below 0.1036, less than half of that obtained using PDSMC (0.2463). The main innovation of this work lies in the integration of a fast terminal nonlinear sliding manifold with a gain-optimized saturation switching law, achieving robust finite-time stability, reduced actuator effort, and real-time feasibility without relying on predictive optimization, disturbance observers, or data-driven training. These results confirm that the proposed FTSMC provides a computationally efficient, robust, and high-performance lateral control solution suitable for embedded autonomous driving and mobile robotic applications.