STABILITY AND ROBUSTNESS OF A HIGH-GAIN NONLINEAR ROBOT MANIPULATOR CONTROLLER

作     者：MILLS, JK 

作者机构：Robotics and Automation Laboratory Department of Mechanical Engineering University of Toronto Toronto Ontario M5S 1A4 Canada 

出 版 物：《MECHANISM AND MACHINE THEORY》 (机构学与机械原理)

年 卷 期：1990年第25卷第5期

页      面：529-545页

核心收录：

学科分类：08[工学] 0802[工学-机械工程] 

摘      要：A nonlinear controller is proposed for the trajectory control of an n degree of freedom rigid link robotic manipulator, using task space feedback of the end-effector position and orientation. With a Lyapunov approach, a proof of the local asymptotic stability of the proposed nonlinear control law is given. The closed-loop system is shown analytically to be robust to two separate classes of parameter uncertainty. This parameter uncertainty includes dynamic (i) parameter perturations caused by manpulation of unknown payloads and manipulator operation in the presence of unknown viscous joint friction and (ii) controller parameter error arising from uncertainty in the kinematic and dynamic parameters of the manipulator. Through the choice of a particular high gain nonlinear controller term, it is shown that sufficient conditions are satisfied for local asymptotic stability in the presence of large dynamic parameter perturbations caused principally by manipulation of unknown payloads. Hence, for sufficiently high gain the closed-loop system is robust to large parameter perturbations. In addittion to an analytic proof of the asymptotic trajectory capability for constant reference input signals, close trajectory tracking is also demonstrated analytically for a particular class of input trajectories, again a result of the high gain nonlinear controller term. Finally, a numerical simulation of a two degree of freedom robot demonstrates both the asymptotic trajectory tracking capability for constant reference inputs and the close trajectory tracking capability for time varying trajectories with high gain feedback in the presence of kinematic and dynamic controller modelling errors and large dynamic parameter uncertainty.