Energy-Optimal Planning and Shrinking Horizon MPC for Vessel Docking in River Current Fields

The problem of controlling autonomous surface vessels in an energy-optimal way is important for the electrification of maritime systems and is currently being investigated by many researchers. In this paper, we use numerical optimal control to plan an energy-optimal docking trajectory in river currents and show that it can save energy compared to other widespread planning approaches. An optimal control problem including a detailed vessel model is defined, transcribed into a nonlinear optimization problem via direct multiple shooting, and solved using a homotopy procedure. The optimal solution is compared to a geometrical path planning approach with path-velocity decomposition. The results of this comparison show that prescribing a path with fixed vessel orientation leads to very suboptimal results. Further, we demonstrate how shrinking horizon MPC can control the vessel in an energy-optimal way even under severe disturbances, by replanning the energy-optimal trajectories in real-time. We believe that energy-optimal MPC could become a key technology for the electrification of maritime systems.