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.

Maritime decarbonization and the emergence of autonomous vessel fleets are motivating cooperative sailing concepts in which formation geometry serves not only as a coordination variable but also as a potential means of reducing hydrodynamic resistance. Although favorable wake and wave-interference patterns can reduce resistance in specific configurations, translating these benefits into deployable formation-control laws remains challenging. The central difficulty is cross-layer: hydrodynamic models must capture spacing- and speed-dependent interaction effects while remaining sufficiently compact, differentiable, and transferable for constrained real-time control. This review examines hydrodynamics-aware formation control for energy-efficient multi-vessel systems using a structured Scopus corpus of 193 publications. It connects three research layers that are commonly treated separately: formation-control architecture, hydrodynamic-interaction modeling, and energy-accounting fidelity. The literature is classified using a five-level evidence axis ranging from single-vessel energy optimization to closed-loop interaction-aware formation control. Empirical, potential-flow, CFD/RANS-based, reduced-order, and surrogate models are compared in terms of real-time capability, differentiability, calibration burden, transferability, and compatibility with MPC and distributed MPC. The synthesis shows that the literature contains substantial CFD, experimental, and offline configuration-optimization evidence, but very limited closed-loop validation in which hydrodynamic interaction, propulsion-realistic energy metrics, actuator constraints, communication limitations, and safety requirements are addressed together. Control-ready hydrodynamic surrogates, propulsion-aware energy accounting, robustness in mixed traffic, and field validation are therefore identified as the highest-priority research directions. A validation ladder and reporting checklist are proposed to improve comparability and support future deployment in inland, coastal, and open-water scenarios.

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.