# Tube-Based Robust Model Predictive Control for Autonomous Vehicle with Complex Road Scenarios
###### Abstract  
This study proposes a Tube-based Robust Model Predictive Control (Tube-RMPC) strategy for autonomous vehicle control to address model parameter uncertainties and variations in road-tire adhesion coefficients in complex road scenarios. More specifically, the proposed approach improves the representation of vehicle dynamic behavior by introducing a unified vehicle-tire modeling framework. To facilitate computational tractability and algorithmic implementation, the model is systematically linearized and discretized. Furthermore, the Tube-based Robust Model Predictive Control strategy is developed to improve adaptability to uncertainty in the road surface adhesion coefficient. The Tube-based Robust Model Predictive controller ensures robustness by establishing a robust invariant tube around the nominal trajectory, effectively mitigating road surface variations and enhancing stability. Finally, a co-simulation platform integrating CarSim and Simulink is employed to validate the proposed method's effectiveness. The experimental results demonstrate that Tube-RMPC improves the path-tracking performance, reducing the maximum tracking error by up to 9.17% on an 5-curve and 2.25% in a double lane change, while significantly lowering RMSE and enhancing yaw stability compared to MPC and PID. autonomous vehicle control; uncertainty in road surface adhesion coefficient; unified vehicle-tire modeling; Tube-based Robust Model Predictive Control (Tube-RMPC)  
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trajectory tracking. Effective control systems must be capable of handling not only modeling uncertainties but also real-world disturbances such as variations in road tire adhesion. These variations, which are difficult to measure directly in real-time, significantly affect lateral dynamics and must be addressed within the control framework to enhance safety and performance. In recent years, research on trajectory-tracking controller design has prioritized minimizing the deviation between a vehicle's real-time trajectory and its desired path. To address this critical challenge, a variety of advanced control methodologies have been developed, including fuzzy control [5], linear quadratic regulators [6], sliding-mode control [7], and model predictive control (MPC) [8; 9; 10; 11]. Among these, MPC has gained significant prominence due to its predictive capability for complex dynamic systems, effective constraint handling, and optimization-driven performance enhancement. Despite its inherent strengths, numerous studies have proposed refinements to the conventional MPC framework to tackle specific challenges encountered in practical applications. For instance, a study introduced an enhanced approach [12] to improve stability in complex operational scenarios. Failure to address these challenges can escalate into adverse phenomena, such as oversteering, drifting, or complete loss of vehicle stability, underscoring the need for further research and innovation in this domain. To address these phenomena, an MPC-based trajectory-tracking controller [13] was applied. A sophisticated model parameter adjustment strategy was utilized to improve control precision and enhance the trajectory-tracking performance of autonomous vehicles. Nevertheless, this approach remains highly sensitive to variations in road surface adhesion, potentially limiting its robustness and adaptability in complex driving conditions. To mitigate these limitations, an MPC algorithm incorporating dynamic parameter adaptation [14] was proposed to counteract parameter sensitivity issues. Through the introduction of a nonlinear predictive model and dynamic adjustment mechanisms, system behavior is effectively optimized, and trajectory constraints are managed in complex dynamic environments.