where xt, yt, and zt are initial positions. There are no constraints imposed on attitude and velocities of the UUV. Control constraints are imposed on the physical systems to be controlled due to the limitations of actuators. Force or torque inputs are bounded by some upper limit. In control of the UUV, it is assumed that there is no constraint on control, since the aim of this study is to show the possibility of control of such a challenging mechanical system. However, the simulations are also done for considering the constraints on the thrust:

where Tc is the thrust value.

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