Abstarct: Many robot control approaches require velocity signals. In this thesis, an adaptive observer is proposed for robust control of robotic manipulators in the task-space using voltage control strategy to calculate the velocity signal. This observer is free from robot model in the task-space. In order to compensate the uncertainties in the observer and controller, Fourier series is utilized. Using Lyapunov stability method and Barbalat’s lemma, the convergence of the observer estimation error and tracking error to zero is guaranteed. Simulation results on articulated robot show the effectiveness of the proposed observer comparing to linear observer and extended state observer. To eliminate the need for the upper bound of the approximation error in the observer and controller design, another scheme is proposed that the uncertainty is estimated using Chebyshev polynomials. Compared to fuzzy estimators, Chebyshev polynomials have simpler structure and lower computational burden for uncertainty estimation. The Chebyshev coefficients are adjusted baxsed on the adaptive laws obtained from the stability analysis. Moreover, a continuous robust control term is designed to compensate the approximation error of Chebyshev polynomials. The stability of the closed-loop system is proved baxsed on Lyapunov method and strictly-positive-real (SPR) lemma. Simulation results on SCARA robot demonstrate the superiority of the designed observer in comparison with linear observer, extended state observer and fuzzy observer.