In this paper, an adaptive observer for robust control of robotic manipulators is proposed. The lumped uncertainty is estimated using Chebyshev polynomials. Usually, the uncertainty upper bound is required in designing observer-controller structures. However, obtaining this bound is a challenging task. To solve this problem, many uncertainty estimation techniques have been proposed in the literature based on neuro-fuzzy systems. As an alternative, in this paper, Chebyshev polynomials have been applied to uncertainty estimation due to their simpler structure and less computational load. Based on strictly-positive-real (SPR) Lyapunov theory, the stability of the closed-loop system can be verified. The Chebyshev coefficients are tuned based on the adaptation rules obtained in the stability analysis. Also, to compensate the truncation error of the Chebyshev polynomials, a continuous robust control term is designed while in previous related works, usually a discontinuous term is used. An SCARA manipulator actuated by permanent magnet DC motors is used for computer simulations. Simulation results reveal the superiority of the designed method.

在本文中，提出了一种用于机器人机械手鲁棒控制的自适应观测器。集总不确定性使用Chebyshev多项式估算。通常，在设计观察者-控制器结构时需要不确定性上限。但是，获得此界限是一项艰巨的任务。为了解决这个问题，文献中已经提出了许多基于神经模糊系统的不确定性估计技术。作为替代方案，由于结构更简单且计算量较小，本文将Chebyshev多项式应用于不确定性估计。基于严格正实（SPR）李雅普诺夫理论，可以验证闭环系统的稳定性。根据在稳定性分析中获得的自适应规则调整切比雪夫系数。也，为了补偿切比雪夫多项式的截断误差，设计了一个连续的鲁棒控制项，而在先前的相关工作中，通常使用不连续的项。由永磁直流电动机驱动的SCARA机械手用于计算机仿真。仿真结果表明了所设计方法的优越性。