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Energy efficiency has been the focus of quadruped robot research.Decreasing the energy loss caused by the DC motor can contribute to the walking efficiency of electrically actuated quadruped robots.Most works have focused on the quadruped mechanisms or actuations such as the Series Elastic Actuation (SEA).This work proposes a better efficient controller to perform the stable 5 m·s-1 movements of quadruped robots.The dynamic model of the electrically actuated leg is established by Lagrangian formulation.The energy efficiency of the DC motors in the electrically actuated quadruped robot is formulated as an optimization problem.The Stochastic Linear Complementarity Problem (SLCP) and sinusoidal pulse force are proposed to reduce the energy consumption at the contact.The Bemstein polynomials are used for planning a quasi-elliptic foot motion trajectory.The stability and energy efficiency of the proposed controller are verified with computer simulation and an actual single leg robot prototype.Compared with other works,the proposed controller performs the optimal Cost of Transport (COT).