Adaptive simplified surge-heading tracking control for underwater vehicles with thruster’s dead-zone compensation

Remotely operated underwater vehicles are usually equipped with four horizontal thrusters that form an X-shaped actuation configuration. Yet, thruster’s inherent dead-zone may possibly result in strong chatter of moment inputs and motion tracking of underwater vehicles. This paper proposes a two-layer cascade tracking controller together with a dead-zone compensator, in order to achieve simplified and effective surge-heading control of underwater vehicles equipped with an X-shaped horizontal actuation configuration. For the sake of brevity, the surge and heading dynamics are firstly unified as a second-order dynamic system where the known and unknown parts are separated, respectively. Based on this model, a feedback linearization control law with a combined error measure is designed in the first-layer cascade system for the simplified dynamics tracking. Then, a reduced-order extended state observer without using any priori knowledge of uncertainties is utilized in the second-layer cascade system to estimate the complex uncertainty of the dynamics. It is noted that this two-layer tracking controller has only two gains to be adjusted, ensuring a simple calculation and microprogramming. Subsequently, a dedicated dead-zone compensator is proposed for the X-shaped actuation configuration and the input-to-state stability of the whole tracking system is analyzed. Finally, comparative numerical cases are provided to demonstrate the adaptivity and robustness of the designed surge-heading tracking controller, i.e., up to 56% reduction of the maximum surge tracking error owing to this dead-zone compensator and less than 0.03∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^\circ $$\end{document} of the heading steady state error against different initial states.