Dynamic Modeling and Control of Small Scale Wire Driven Robotic Joints with Wire Elasticity

Abstract

In this paper, dynamic modeling and control of small scale wire driven robotic joints (WDRJ) with elastic wires is studied in detail. In the dynamic modeling, it is assumed that the dominant dynamics of wires which are the longitudinal vibrations of the wires can be approximated by a linear axial spring model. Moreover, the dynamic model of the WDRJ is converted to the standard form of singular perturbation, which allows the controller design on the base of the singular perturbation theory. The proposed control scheme consists of two major parts, slow and fast sub-controllers. First, a slow sub-controller is designed by considering WDRJ with ideal rigid wires, which is used to control the gross motion of the WDRJ. Then, this controller is extended to the WDRJ with elastic wires by adding the fast sub-controller, to counteract the longitudinal vibrations caused by the inevitable elasticity of the wires. Furthermore, to ensure all the wires remain in tension, the proposed control strategy is refined by adding the concept of internal force. Finally, the efficiency of the proposed control algorithm is investigated through simulations. And it is demonstrated that WDRJ is an appealing candidate for the design of small scale robotic system.