Stabilization of a relative equilibrium of an underactuated AUV in three-dimensional space

This paper presents the stabilization of a relative equilibrium of an underactuated autonomous underwater vehicle(AUV) with three independent control inputs: moment of pitch, moment of yaw and thrust, in three-dimensional space. The dynamics of an AUV can be described by the Kirchhoff's equations which couples actuated variables and underactuated variables together and which is helpful to control underactuated variables via actuated variables. Physically, relative equilibria correspond to trim trajectories, which can save power. In this study, the relative equilibrium corresponds to a marine vehicle translation along the longitudinal axis and rotation around the same axis with a desired velocity. Based on the interconnection and damping assignment(IDA) method, a new desired Hamiltonian function, in which translational and rotational velocities are coupled together, is constructed and served as a Lyapunov function. Although there's no control inputs for the underactuated variables, the coupling between translational and rotational velocities in the new desired Hamiltonian function plays an essential role to stabilize the desired relative equilibrium. Simulation results complete the work.