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Real-time fine motion control of a nonholonomic mobile robot is investigated, where both the robot dynamics and geometric parameters are completely unknown. A neural network controller combining both kinematic control and dynamic control is developed. The neural network assumes a single layer structure, by taking advantage of the robot regressor dynamics that express the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot parameters. The learning algorithm is computationally efficient. The system stability and the convergence of tracking errors to zero are rigorously proved using a Lyapunov stability theory. The real-time fine control of a mobile robot is achieved through the online learning of the neural network. In addition, the developed controller is capable of learning the kinematic parameters online. The effectiveness and efficiency of the proposed controller is demonstrated by simulation studies.