This paper introduces a robust task-space control scheme for a robotic system with an adaptive observer. The proposed
approach does not require the availability of the system states and an adaptive observer is developed to estimate the
state variables. These estimated states are then used in the control scheme. First, the dynamic model of a robot is
derived. Next, an observer-based robust control scheme is designed to compensate the uncertainties occurring in the
control system. Moreover, upper bound of the lumped uncertainty is essential in the design of the robust controller.
However, the upper bound of the lumped uncertainty is difficult to obtain in practical applications. Therefore, an
adaptive law is derived to adapt the value of the lumped uncertainty, and an adaptive observer-based robust task-space
controller is obtained. In this paper, we prove that the proposed adaptive observer-based controller can guarantee that
the task-space tracking error and also the observation error converge to zero. To demonstrate the effectiveness of the
proposed method, simulation results are illustrated in this paper.