Modeling and gain-scheduled control of an aerial manipulator

Aerial manipulators (AMs) are flying robotic systems composed of a multicopter equipped with one or more robotic arms. The dynamic modeling of AMs is complex due to the highly coupled interactions between the multicopter and the robotic arms. In this paper, the dynamics and kinematics of a quadcopter are combined with the Newton–Euler recursive method to obtain the forces applied by the robotic arm on the multicopter. The complete dynamic model is then linearized and expressed in terms of the articulation angles of the robotic arm for controller synthesis purposes. A novel gain-scheduled controller based on structured H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {H}}_\infty $$\end{document} synthesis is proposed using the joint angles of the robotic arm as scheduling variables. The controller is tuned according to multiple performance objectives on a family of parameterized linearized models. Simulations on the non-linear model with the gain-scheduled controller demonstrate its ability to compensate for robotic arm movements, while keeping the desired dynamic characteristics regardless of arm position. The advantage of gain scheduling is demonstrated by a comparison with a non-scheduled version of the controller. Finally, the controller is shown to be able to compensate for a 10%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10\%$$\end{document} uncertainty on the nominal tuning values of the physical parameters.