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A novel hybrid control strategy is developed for real-time motion tracking control of a nonholonomic mobile robot. The biological neurons, called as shunting models, are embedded into the backstepping-based velocity planner to eliminate the sharp speed jumps of velocity commonly existing in mobile robots due to tracking errors changing suddenly. The outputs of the velocity planner are used as the command inputs of the torque controller based on sliding mode. The proposed control scheme includes a velocity planner with the neurons and a sliding mode torque controller. This control strategy achieved success in the position and smooth velocity tracking of motion of mobile robots. The effectiveness and efficiency of the proposed control strategy are demonstrated through simulations and comparison studies.