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A novel tracking controller is proposed in this paper for real-time navigation of a nonholonomic mobile robot based on a neural dynamics model and a conventional backstepping model. By taking advantage of the features of the neural dynamics in a gated dipole model, the proposed controller is capable of generating smooth, continuous control signals to track a desired path. In addition, it can deal with arbitrarily large initial tracking errors. It resolves the velocity jump problem in conventional backstepping controllers resulted from sudden changes of tracking errors. The proposed approach is not very sensitive to model parameters and converges faster than a previous tracking control model. The effectiveness and efficiency of the proposed approach is demonstrated by a series of simulation and comparison studies.