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In this paper, a neural network based torque controller is proposed for real-time collision-free navigation of nonholonomic mobile robots. A torque resulted from the obstacles is incorporated in the control design based on the artificial potential technique, which locally pushes the robot away from the obstacles to avoid collisions. All the needed environment information can be obtained from on-board robot sensors that have limited visibility range only. A torque from a simply single-layer neural network is employed to learn the completely unknown robot dynamics. The system stability is guaranteed by a Lyapunov stability theory. The real-time fine control of mobile robots is achieved through the on-line learning of the neural network. The effectiveness of the proposed controller is demonstrated by simulation studies in both static and dynamic environments.