Robust Trajectory Tracking for Surface Vehicles via $\mathcal{L}_{1}$-Augmented Model Predictive Control

This study presents a cascaded control strategy that integrates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{1}$</tex> adaptive control with model predictive control (MPC) to achieve robust trajectory tracking for surface vehicles in the presence of modeling errors and environmental disturbances. In this framework, MPC provides baseline performance for nominal trajectory tracking, while <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{1}$</tex> adaptive control compensates for uncertainties in surge and yaw dynamics. To validate the proposed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{1}$</tex>-MPC approach, a system identification process was conducted, followed by field experiments using an unmanned surface vehicle. The performance of the strategy was evaluated, considering thruster model asymmetries and wind disturbances. The overall experimental results demonstrate that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{L}_{1}$</tex>-MPC significantly outperforms standard MPC, reducing both root-mean-square-error (RMSE) and maximum position error.