Aiming at the tracking error and energy loss of an omni-directional mobile robot while tracking the predesigned target, this paper firstly constructs a novel robot energy consumption model which can effectively predict all kinds of energy consumption in the tracking task. Then, by taking the new energy consumption model into the performance index, a feedback energy-saving controller with disturbance robust compensation is proposed which oritents to the minimum of trajectory tracking error and energy consumption. Additionally, a robust compensation term is introduced into the conrller by employing an uncertainty and disturbance observer to cancel or minimum the effect of the the external disturbance under the premise of optimal energy consumption. Finally, the proposed energy-saving disturbance robust compensation control system is proved to be asymptotically stable based on the Lyapunov stability theory. The simulation results show that the proposed control method has higher control precision, lower energy loss and stronger robustness compared to the proportional perivative controller, the $H_\infty$ controller and the normal energy saving compensation controller.