Online Learning-Enhanced Lie Algebraic MPC for Robust Trajectory Tracking of Autonomous Surface Vehicles

TL;DR

This work tackles robust trajectory tracking for autonomous surface vehicles under unknown disturbances by integrating a convex error-state MPC on the Lie group $SE(3)$ with an online Fourier-based disturbance estimator. The method predicts residual disturbances $\tilde{h}$ via a bi-level learned Fourier feature map $\Phi_{f^\star}$ and injects these forecasts into the MPC horizon, enabling real-time compensation on a single CPU core. Key contributions include the offline bi-level feature extraction to identify dominant disturbance frequencies, an online residual learning scheme without pre-training, and comprehensive validation in both physics-based VRX simulations and real-field experiments, where the approach consistently outperforms nominal Lie-MPC, L1 adaptive-MPC, and PID baselines. The results demonstrate improved tracking accuracy and robustness in dynamic marine conditions, highlighting a practical, low-cost solution for ASVs operating in uncertain environments.

Abstract

Autonomous surface vehicles (ASVs) are easily 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 with an online learning module to compensate for these disturbances in real time. This design enables adaptive and robust control while maintaining computational efficiency. Extensive evaluations in numerical simulations, 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.

Figures (7)

• Figure 1: Our method employs Fourier features to estimate the residual in an online manner and can be implemented efficiently on a single-core CPU. In contrast, prior online approaches rely on neural networks that require pre-training on large datasets.
• Figure 2: This figure illustrates the overall pipeline. At each control cycle, a residual term is first computed by comparing the measured state derivative with the nominal dynamics model. A sliding buffer containing the most recent residual samples serves as the input to the Fourier-based online estimator. Then, the estimator updates the weight matrix to approximate this residual-history buffer and predicts a full horizon of future residual terms. These predicted residuals are then injected into the Lie-MPC, allowing the controller to account for upcoming disturbances over the entire planning horizon. In this manner, the proposed framework achieves real-time disturbance compensation without any weight pre-training and operates efficiently on resource-limited ASV platforms.
• Figure 3: The VRX environment.
• Figure 4: Tracking performance of baselines and our method under different wind conditions in the VRX simulator.
• Figure 5: Tracking performance of baselines and our method under different wind conditions in the VRX simulator.