Nonlinear diving stability and control for an AUV via singular perturbation

This paper presents control design and nonlinear stability analysis for path-following of an underactuated autonomous underwater vehicle (AUV), with dynamics restricted to the longitudinal plane. For this AUV motion control system, the speed of translational dynamics is much slower than that of orientation dynamics. Such characteristic allows for a mathematical setup which can be naturally treated by standard singular perturbation theory. Based on this analysis, a simple control law is designed with time scale decomposition method, which is able to stabilize an AUV to desired diving path by selecting desired collective pitch rate and pitch angle. Its nonlinear stability analysis is performed by constructing Lyapunov functions, in term of singular perturbation method. The paper also proves that the control law is robust in the presence of bounded disturbances and model uncertainties, using the small-gain theorem. Furthermore, simulation results are presented to illustrate the control performance.