Next, the gravitational and buoyant forces acting on link i are described as fx, = PV - mi)g,

Considering the hydrodynamic forces described above and using the Newton-Euler formulation, the following equation of motion can be obtained (Antonelli, 2003):

and M is the inertia matrix including the added mass i Ma and inertia i Ia , N£ is the vector of the Coliolis and centrifugal forces, f is the vector consisting of the drag and gravitational and buoyant forces and moments, fg and Tg are the force and torque vectors of the vehicle, respectively, and Tm is the joint torque vector of manipulator. Moreover, the relationship between ®„ and = y/y (* = 0, e) is described as w =

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