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Real-time collision-free path planning and tracking control of a nonholonomic mobile robot in a dynamic environment is investigated using a neural dynamics based approach. The real-time robot path is generated through a dynamic neural activity landscape of a topologically organized neural network that represents the changing environment. The dynamics of each neuron is characterized by an additive neural dynamics model. The real-time tracking velocities are generated by a novel tracking controller, which is also based on a shunting neural dynamics model. The effectiveness and efficiency of this approach are demonstrated through simulation studies.