Enhancing self-sustainability via robust speed optimization for an unmanned photovoltaics-battery vessel under solar irradiance and sea wave uncertainties

Unmanned photovoltaics (PV)-battery vessels offer a promising green solution for long-voyage oceanographic survey and measurement tasks. However, uncertainties of solar irradiance intermittency and sea wave fluctuation challenge the speed scheduling for maintaining power self-sustainability during long-voyage navigation. Existing robust optimization (RO) methods, which assume the worst scenario predicted before the voyage and yield speeds iteratively from the initial states, often fail to maintain self-sustainability due to the rapid energy depletion under the worst scenario. To address this issue, a novel intra-voyage robust method, termed forecast-based robust model predictive control (F-RMPC), is proposed. The F-RMPC method incorporates weather forecast to narrow the ranges of irradiance uncertainty set to reduce conservativeness, and adjusts speeds based on real-time state feedback, accounting for the worst scenario identified within each prediction horizon. A new objective function integrating voyage distance maximization with a zero-speed penalty to enhance self-sustainability is formulated. Hardware-in-the-loop experiment is performed to examine the performance of the proposed F-RMPC. Under an actual scenario with low irradiance and high waves, the F-RMPC effectively maintains self-sustainability and extends voyage by 41.13 % compared to pre-voyage RO. Moreover, the zero-speed penalty coefficient is determined as 1.7 through an exhaustive search method, and its effectiveness is further validated by the 11-h power interruption when it is not applied. Detailed comparison between F-RMPC and conventional RMPC shows that the advantage of incorporating weather forecast grows with improving sky conditions.