Trajectory tracking control for autonomous underwater vehicle with disturbances and input saturation based on contraction theory

Autonomous underwater vehicle (AUV) is a complex nonlinear system and its control is accompanied by various challenges. This paper focuses on the three dimensional (3D) trajectory tracking control of a fully-actuated AUV in the presence of model uncertainties, unmeasured velocity, time-varying external disturbance and input saturation. First, taking the model uncertainties and external disturbances as the total disturbances, an extended state observer (ESO) is designed to estimate the unmeasured velocity and total disturbances. Then, the saturated controller based on contraction theory and its application in singular perturbation system (SPS) is obtained so that the AUV tracks the desired trajectory and avoids exceeding the limit of the actuator. The estimation error, tracking error and the error between the ideal controller and the actual controller are analyzed by contraction theory, and the explicit bounds of these errors are given. At last, comparative numerical simulations are provided to show the effectiveness of the ESO and the advantages of the saturated controller. •Taking the model uncertainties and external disturbances as the total disturbances, an extended state observer (ESO) is designed to estimate the unmeasured velocity and total disturbances.•A saturation controller is designed using singular perturbation theory and contraction theory. Compared with the traditional anti-saturation controller, the controller designed in this paper is simple in form and convenient in application.•Contraction theory is applied to analyze the convergence properties of ESO and controller, and the explicit bounds of estimation error, tracking error and the error between the ideal controller and actual controller are given.