A Dynamic Model for Underwater Vehicle Maneuvering Near a Free Surface*

This paper introduces a physics-based and control-oriented underwater vehicle model for near-surface operations. To construct the model, we follow an energy-based Lagrangian approach, where the presence of the free surface is incorporated using a free surface Lagrangian. This effectively modifies the system energy commonly used to derive the Kirchhoff equations, which govern underwater vehicle motion in an unbounded ideal fluid. The system Lagrangian is then used to derive the 6-DOF equations of motion for an underwater vehicle maneuvering near the free surface in otherwise calm seas. To illustrate the additional capabilities of the proposed model, we present an analytical hydrodynamic solution for a circular cylinder traveling parallel to the free surface. Comparisons are also drawn between the proposed model and the Cummins model (Cummins, 1962). While Cummins' model exactly satisfies the free surface boundary condition and approximately satisfies the body boundary condition, we choose to exactly satisfy the body boundary condition and approximately satisfy the free surface condition. This exchange removes the restriction that limits the Cummins equations to slow-maneuvering in a seaway.