This paper presents a method to optimize the en- ergy efficiency of walking bipedal robots by more than 50 % in a speed range from 0.3 to 2.3 m/s using elastic couplings – mechanical springs with movement speed independent pa- rameters. The considered robot consists of a trunk, two stiff legs and two actuators in the hip joints. It is modeled as un- deractuated system to make use of its natural dynamics and feedback controlled with input-output linearization. A nu- merical optimization of the joint angle trajectories as well as the elastic couplings is performed to minimize the average energy expenditure over the whole speed range. The elastic couplings increase the swing leg motion’s natural frequency thus making smaller steps more efficient which reduce the impact loss at the touchdown of the swing leg. The pro- cess of energy turnover is investigated for the robot with and without elastic couplings. Furthermore, the influence of the elastic couplings’ topology, its degree of nonlinearity, the mass distribution, the joint friction, the coefficient of static friction and the selected actuator is analyzed. It is shown that the optimization of the robot’s motion and elastic coupling towards energy efficiency leads to a slightly slower conver- gence rate of the controller, yet no loss of stability and a
lower sensitivity with respect to disturbances. The optimal elastic coupling discovered by the numerical optimization is a linear torsion spring between the legs.