A kinematically-constrained Hankel dynamic mode decomposition for short-term prediction of ship manoeuvring in ambient currents

Abstract

The accurate prediction of vessel manoeuvring dynamics is essential for ensuring navigational safety in the transition toward maritime autonomy. In this study, a kinematically-constrained Hankel dynamic mode decomposition (Hankel-DMD) approach is developed to model and predict vessel manoeuvring dynamics. The vessel motion is represented using a state formulation consisting of position and resultant speed, and the Hankel-DMD method, together with a component-wise normalisation of the position states, is used to extract the modes governing the system dynamics. To improve the physical consistency of the prediction, a kinematic constraint linking vessel position and speed is incorporated as a post-processing reconstruction step. The developed approach is examined using the data generated from a physics-based Maneuvering Modelling Group (MMG) manoeuvring model for an azimuth thruster-equipped tug. Three cases are considered, including manoeuvring in calm water, in the presence of ambient current along the X -direction (following), and current along the Y -direction (cross). Quantitative error metrics show that the kinematically-constrained reconstruction reduces the trajectory RMSE by 71% in calm water (from 1.09 m to 0.31 m) and by 60% for the following current (from 7.31 m to 2.90 m). For the cross current, however, the XY-normalised pure Hankel-DMD prediction achieves the slightly lower RMSE (1.34 m versus 2.80 m for the constrained reconstruction), indicating that the benefit of the kinematic constraint is scenario-dependent. These findings demonstrate that incorporating a kinematic constraint can improve the robustness of data-driven vessel trajectory prediction, although its benefit is case-dependent under environmental disturbances.

The authors' abstract, as published at the source. Ocean Engineering, 2026 · DOI ↗