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Many control strategies have been proposed to compensate for uncertainties of robotic system, where the uncertain parameters are assumed to be constant. However, this assumption may not be satisfied in practice. In this paper, we consider the tracking problem for robot manipulator with unknown and time-varying physical parameters and disturbances. Our proposed state feedback adaptive robust controller consists of a nonlinear compensation based on nominal physical parameters, a linear and a nonlinear state feedback, and an adaptation algorithm for adjustment of the gravitational parameters. The effects of time-varying parameters and disturbances on the tracking performance can be attenuated within a prescribed level. Exact asymptotic tracking can be achieved for set point control with vanishing disturbances and constant parameters. By adding feedback input to penalty variable, high gain feedback can be strategically avoided. The effectiveness of the proposed method is verified by simulation and experiments.