Adaptive control of n-link hydraulic manipulators with gravity and friction identification

Many industrial applications of hydraulic manipulators, such as settling in positioning, tracking control, and programming by demonstration, require precise compensation of the gravity and friction effects. In comparison with complete dynamic model identification, gravity and friction identification are more accessible in practical applications since they requires less measurement information and computation resources. However, for the multi-link serial hydraulic manipulator, there is still a lack of a theoretical and systematic approach for gravity and friction identification, which makes it challenging to achieve precise motion control in practice. To address this problem, this article first establishes a continuously differentiable nonlinear friction model that can capture complex friction behaviors and is more suitable for recursive backstepping design implementation. Then, based on the modified Denavit–Hartenberg model, a general gravity model of an n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{n}$$\end{document}-link hydraulic manipulator is established, which is not only applicable for the robotic manipulator with revolute or prismatic joints but also suitable for any installation forms, such as robotic manipulators installed on a vertical wall, a horizontal ground, a slope, etc. Moreover, a theoretical and systematic method is provided for gravity and friction identification. Eventually, an adaptive backstepping controller is integrated with gravity and friction identification to reduce the negative effect of identification errors and unmodeled dynamics on tracking performance. The effectiveness of the developed approach is substantiated on a six-degree-of-freedom hydraulic manipulator experimental platform.