Coordinated Energy-Trajectory Economic Model Predictive Control for Autonomous Surface Vehicles under Disturbances

TL;DR

This work tackles energy-aware path following for autonomous surface vehicles (ASVs) under environmental disturbances by formulating a Coordinated Energy-Trajectory EMPC (CC-EMPC). It represents cross-track error as an energy penalty and decomposes the terminal energy into dynamic and static components with a yaw-rate profile to anticipate long-horizon energy usage, using CasADi for online optimization with horizon $H=10$ and $\Delta t=0.1$ s. The method jointly optimizes thruster commands and horizon-end conditions, achieving near-optimal energy performance while reducing tracking error; simulations against NMPC and EO-MPC with real disturbance data show cross-track error reductions of up to $18.61\%$ with small energy penalties, and lake-field experiments validate real-world feasibility on an Intel $\mathrm{N100}$ at a $10$ Hz control rate, yielding $0.22\,\text{m}$ average cross-track error. The results demonstrate a computationally tractable, robust approach for energy-constrained ASV operation in dynamic environments, with potential extensions to stability guarantees and obstacle-aware coordination.

Abstract

The paper proposes a novel Economic Model Predictive Control (EMPC) scheme for Autonomous Surface Vehicles (ASVs) to simultaneously address path following accuracy and energy constraints under environmental disturbances. By formulating lateral deviations as energy-equivalent penalties in the cost function, our method enables explicit trade-offs between tracking precision and energy consumption. Furthermore, a motion-dependent decomposition technique is proposed to estimate terminal energy costs based on vehicle dynamics. Compared with the existing EMPC method, simulations with real-world ocean disturbance data demonstrate the controller's energy consumption with a 0.06 energy increase while reducing cross-track errors by up to 18.61. Field experiments conducted on an ASV equipped with an Intel N100 CPU in natural lake environments validate practical feasibility, achieving 0.22 m average cross-track error at nearly 1 m/s and 10 Hz control frequency. The proposed scheme provides a computationally tractable solution for ASVs operating under resource constraints.

Figures (11)

• Figure 1: Reference frames and notations.
• Figure 2: Illustration of the dynamic and static modes beyond the prediction horizon.
• Figure 3: Approximation of the yaw rate profile during the dynamic stage.
• Figure 4: Schematic of cross-track error.
• Figure 5: Block diagram for the proposed CC-EMPC