Existing studies on multi-vessel formations rarely combine physically based models of ship–ship hydrodynamic interaction with online formation control, so that energy benefits are typically assessed offline or only approximated through artificial potentials. This paper addresses this gap by embedding a reduced-order, hydrodynamics-aware resistance model into a hierarchical formation control framework for multi vessel systems. A three degree of freedom interaction model is incorporated into the cost function, enabling the supervisory controller to adaptively optimize inter ship spacing and formation geometry in a speed dependent and hydrodynamics aware manner. The lower level MPC ensures accurate trajectory tracking and stability under the guidance of the top level optimization. Four simulation studies are conducted to evaluate the proposed method. The platooning formation is first analyzed as a reference, followed by the triangular formation, which achieves balanced tracking performance and stability. The echelon formation is then examined, demonstrating significant energy savings in medium to high speed regimes while maintaining yaw stability. Finally, an unconstrained optimization scenario is explored, where the system autonomously adapts its geometry without prescribed patterns, revealing emergent energy efficient and stable arrangements across different speed ranges. Results show that the proposed approach not only reduces resistance and improves energy efficiency but also enhances formation adaptability and robustness under varying operating conditions. These findings provide new insights into hydrodynamics aware cooperative control and the development of energy conscious fleet management strategies for future maritime transportation.

The formation control of autonomous surface vessels presents significant challenges when operating in close proximity, where ship-to-ship interaction becomes non-negligible. While conventional formation control methods often neglect these interactions or simplify them excessively, this paper develops a centralized model predictive control (MPC) framework that explicitly incorporates a three-degrees-of-freedom interaction model. This interaction model is constructed empirically based on existing computational fluid dynamics results, offering an efficient and practical way to approximate proximity-induced forces in real-time. The proposed control strategy enables accurate trajectory tracking and effective disturbance adaptation in typical formation geometries, including platooning, parallel, and triangular formations. Simulation results demonstrate that the MPC controller can outperform traditional PID controllers in both tracking precision and interaction robustness across the configurations. Formation-specific performance differences are also analyzed in detail.