A Lyapunov-Based Economic Model Predictive Controller for Autonomous Surface Vehicle Path Following

Abstract

In this paper, we propose a Lyapunov-based economic model predictive control (LEMPC) framework to balance energy consumption and tracking accuracy for autonomous surface vehicle (ASV) path following. The controller achieves motion control under wave disturbances through rolling optimization while accounting for actual physical constraints. We employ a vehicle dynamics decomposition technique to estimate terminal energy costs, while quantifying cross-track error as equivalent energy penalty coefficients. This yields a unified cost function that jointly optimizes energy and tracking precision. To address stability challenges under model underactuation, a dual-mode strategy is introduced: inside a safe region, pure economic optimization is performed; once the state escapes, a Lyapunov contraction constraint is activated to drive the system back. The proposed approach embeds closed-loop stability guarantees within predictive optimization, maintaining lower solving time. Simulation results on curved paths demonstrate that our LEMPC method consistently improves tracking accuracy and computational efficiency while approaching optimal energy consumption. Field experiments are conducted using an ASV equipped with an Intel N100 CPU, confirming the controllers feasibility and effectiveness under natural disturbances. Note to Practitioners—This work addresses a practical challenge: enabling Autonomous Surface Vehicles (ASVs) to accurately follow planned paths over long-term missions, such as environmental monitoring or surveys. In these missions, energy efficiency is as important as tracking precision. Existing control methods do not explicitly minimize energy use under real-world limits and disturbances, which can reduce operational range or increase wear. Thus, we introduce a Lyapunov-based Economic Model Predictive Control (LEMPC) framework. Our method allows the controller to automatically balance tracking accuracy and propulsion energy consumption in a single step. Stability is guaranteed by constraints derived from a Lyapunov-based controller, ensuring safe operation even with a limited prediction horizon. The results show that this approach significantly improves tracking accuracy and robustness while maintaining near optimal energy consumption. Although developed for ASVs, the LEMPC framework is general and can be adapted to other uncrewed systems.