Free-surface-constrained modelling and depth-scheduled control for an underactuated autonomous underwater vehicle

This study develops a free-surface-constrained hydrodynamic modelling and control simulation framework for an underactuated Autonomous Underwater Vehicle manoeuvring near the water surface. A baseline five-degree-of-freedom dynamic model is first established under the assumption of infinite depth. Depth-dependent corrections to hydrodynamic damping, added mass, hydrostatic restoring effects, and actuator effectiveness under semi-submerged conditions are then introduced as functions of the dimensionless submergence depth, G R , using a cylinder-slice approximation previously validated by Computational Fluid Dynamics analysis. The framework is calibrated for the present low-speed operating condition around U = 1 m/s Re = 10 6 , Fr = 0.31 and is restricted to non-cavitating operation. Based on the resulting model, a depth-scheduled controller is designed by combining stern-plane trim feedforward compensation with an adaptive line-of-sight guidance law that incorporates attack-angle correction. Straight-line depth keeping and depth-constrained turning experiments are conducted to validate the coupled vehicle dynamics and the controller performance. The results indicate that free-surface effects induce pronounced vertical deviation during turning manoeuvres, particularly through lift-related terms and semi-immersion-induced actuator constraints. Additional horizontal spiral and zigzag manoeuvre simulations further demonstrate that the proposed framework can reproduce the dominant physical constraints imposed by free-surface proximity, thereby providing an effective tool for near-surface AUV control design and motion prediction.