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To realize the accurate tracking of the vehicle speed in the process of vehicle speed tracking, a neural network adaptive robust output feedback control (NAROFC) method for the driving robot is proposed. Firstly, considering the dynamic modeling error of the mechanical leg and the time-varying disturbance force, the dynamic model of the driving robot is established. Besides, an Extended State Observer (ESO) is designed to estimate the uncertainty and constant disturbance of modeling parameters in the system. In addition, the recurrent neural network (RNN) is used to estimate the time-varying disturbances existing in the system. Finally, the system control rate is redesigned with an ESO-designed adaptive robust controller, and the switching controller is combined to realize output feedback control. The stability of the designed controller is proved by Lyapunov theorem.