Lyapunov-Based Nonlinear Disturbance Observer for n-Links Flexible Joint Robot Manipulators

Abstract

In this paper, the nonlinear disturbance observer (NDO) is presented for serial flexible joint robot manipulators (FJM). To this end, a planar robot manipulator with n flexible joints is considered. After deriving the general form of dynamic equations for serial n-links FJM, a nonlinear disturbance observer is proposed on the basis of the system dynamic equations. The main challenge here is to obtain the acceptable range of the observer gain which guarantees the stability condition. So by choosing the proper Lyapunov candidate, stability analysis of the proposed observer is performed by using the Lyapunov’s direct method. Since the proposed NDO makes the system robust against internal and external disturbances, no accurate dynamic model is required to achieve the high precision motion control. The effectiveness of the proposed observer in the regulation problem is investigated by numerical simulations for a two-links robot manipulator. To this end an optimal LQR controller is designed to stabilize the system besides the optimal state observer in order to estimate the angular velocity of the links and motors. Simulation results show the ability of the proposed method to properly estimate and compensate different disturbances.