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Herein,a control method based on the optimal energy efficiency of a hydraulic quadruped robot was proposed,which not only realizes the optimal energy efficiency of flying trot gait but also ensures the stability of high-speed movement.Concretely,the energy consumption per unit distance was adopted as the energy efficiency evaluation index based on the constant pressure oil supply characteristics of the hydraulic system,and the global optimization algorithm was adopted to solve the optimal parameters.Afterward,the gait parameters that affect the energy efficiency of quadruped were analyzed and the mapping relationship between each parameter and energy efficiency was captured,so as to select the optimum combination of energy efficiency parameters,which is significant to improve endurance capability.Furthermore,to ensure the stability of the high-speed flying trot gait motion of the hydraulic quadruped robot,the active compliance control strategy was employed.Lastly,the proposed method was successfully verified by simulations and experiments.The experimental results reveal that the flying trot gait of the hydraulic quadruped robot can be stably controlled at a speed of 2.2 m/s.