A new control algorithm for manipulators with joint flexibility

Abstract

The new industrial robot is equipped with gear-boxes such as harmonic drives, which introduce elastic deformations at the joints. These deformations are regarded a source of problems, especially when accurate trajectory tracking of high sensitivity to end-effector forces is mandatory. It is shown that the joint elasticity should be taken into account in modeling a robotic manipulator and designing a control algorithm. If we assume that the elasticity may be modeled as a linear spring, we obtain a dynamic model which is twice of the order of the model of the same robot with rigid joints. In this case the design of a control algorithm is a difficult task. If dynamic parameters are not known exactly, adaptive control laws must be designed to guarantee stabilization or tracking. Control of a system with uncertain elements has been discussed in the robotics literature [1], [4], [6], [8]. In this paper, we consider an adaptive tracking controller for a manipulator with only revolute joint. This algorithm is an extension of the controller proposed by Loria and Ortega [9]. We have assumed that the model in [9] has in addition dynamic friction components on both link and motor sides. We have incorporated a harmonic drive into our system. The construction of this controller is based on Lyapunov theory [1], [2], [5], [12]. We assume that link and motor positions are available for measurements. Under these assumptions we propose a semiglobal adaptive tracking control algorithm. The paper is organized as follows. The mathematical description of the robot model and the control algorithm are described in Section 11.2. The concluding remarks are given in Section 11.3. © Springer-Verlag London Limited 2007.