Control of manipulators with hyper degrees of freedom: Shape tracking using only joint angle information

Abstract

In this paper, we consider shape tracking control using only joint angle information for a manipulator with hyper degrees of freedom. A hyper degrees of freedom manipulator is a robotic arm with extraordinarily many degrees of freedom, like an elephant trunk. For the manipulator, not only its tip, but also its whole shape has to be controlled in order to make full use of its capability. For this reason, we have proposed a shape control for the dynamic model of the manipulator. In a shape tracking control, we desire the manipulator to follow a desired shape prescribed by a time-varying spatial curve. We have already derived a L yapunov-based shape tracking control law. However, the control law needs joint angle velocity signals which are usually difficult to obtain. To solve this problem, we propose a new shape tracking controller with a shape velocity observer. The controller is obtained by simple modifications of the L yapunov-based shape tracking controller derived previously. The shape velocity observer is designed to possess the closed-loop dynamics dual to that of the controller. This duality between the controller and the observer enables us to ensure asymptotic stability of the whole system by L yapunov stability theory.