  In this work we propose a family of trajectory tracking controllers for
marine craft in the port-Hamiltonian (pH) framework using virtual differential
passivity based control (v-dPBC). Two pH models of marine craft are considered,
one in a body frame and another in an inertial frame. The structure and
workless forces of pH models are exploited to design two virtual control
systems which are related to the original marine craft's pH models. These
virtual systems are rendered differentially passive with an imposed
steady-state trajectory, both by means of a control scheme. Finally, the
original marine craft pH models in closed-loop with above controllers solve the
trajectory tracking problem. The performance of the closedloop system is
evaluated on numerical simulations.
