Stabilization of a Relative Equilibrium for an Underactuated AUV With Disturbances Rejection

Abstract

This paper addresses the robust stabilization of a relative equilibrium for an underactuated autonomous underwater vehicle (AUV) with disturbances rejection. The AUV’s dynamics is described by the Hamiltonian equation in the presence of unknown external disturbances and uncertain hydrodynamic damping. The disturbances arising from slowly varying currents are assumed to be constant, which consists of matched disturbances and unmatched disturbances, simultaneously. The unmatched disturbances and the uncertain damping that make the realization of the system stabilization become more challenging. To achieve the control objective, first, a new Hamiltonian equation, which is stable around the desired relative equilibrium, is designed to serve as the closed-loop dynamics in which an integral action is added to suppress the disturbances. By matching the closed-loop equation and the open-loop equation, an anti-disturbance stabilizing controller is presented, which requires the knowledge of the uncertain damping. Then, the adaptive control method is employed to propose an improved controller, which enhances the robustness of the uncertain damping. The stability is analyzed by the Lyapunov method. The numerical simulations are conducted to demonstrate the obtained result.