Nonlinear trajectory tracking control of underactuated unmanned underwater vehicles under stochastic disturbances

This paper considers the nonlinear trajectory tracking control of underactuated unmanned underwater vehicles (UUVs) in the presence of stochastic environmental disturbances. Different from the traditional UUV dynamics, the nonlinear stochastic dynamical model of the vehicle in five-degrees-of-freedom (5-DOF) is derived with the aid of the theorem for stochastic system. Then, the adaptive trajectory tracking controllers are designed by virtue of backstepping and the finite-time control. The main difficulties are underactuation and Hessian terms in the infinite generator of Lyapunov functions for control design and stability analysis. It should be pointed out that the finite-time control not only inherits the advantage of faster convergence rate, but also can degrade to the conventional adaptive backstepping control by properly choosing the parameters. Rigorous stability analysis of overall closed-loop system is given by using Lyapunov synthesis, and the trajectory tracking errors consisting of position, attitude and velocity errors globally converge to a small neighborhood of zero.