Autonomous surface vehicles (ASVs) are influenced by environmental disturbances such as wind and waves, making accurate trajectory tracking a persistent challenge in dynamic marine conditions. In this paper, we propose an efficient controller for trajectory tracking of marine vehicles under unknown disturbances by combining a convex error-state MPC on the Lie group augmented by an online learning module to compensate for these disturbances in real time. This design enables adaptive and robust tracking control while maintaining computational efficiency. Extensive evaluations in the Virtual RobotX (VRX) simulator and real-world field experiments demonstrate that our method achieves superior tracking accuracy under various disturbance scenarios compared with existing approaches.

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