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This paper presents a Lyapunov based approach to design an asymptotic trajectory tracking controller for robot manipulator using RBF neural network and an adaptive bound on disturbance terms. The controller is composed of computed torque type part, RBF network and an adaptive controller. The controller is able to learn the existing structured and unstructured uncertainties in the system in online manner. The RBF network learns the unknown part of the robot dynamics with no requirement of the offline training. The adaptive controller is used to estimate the unknown bounds on unstructured uncertainties and neural network reconstruction error. The overall system is proved to be asymptotically stable. Finally, the simulation results are performed on a Microbot type of manipulator to show the effectiveness of the controller.