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In this paper it is shown that, for a one-legged robot, there exists a particular passive gait, of all those possible, for which the dissipated energy per meter of travel is minimized. An analytical method is used to identify the optimal gait. A SLIP model of the robot is used to simplify the dynamics. Both mechanical and electrical losses are taken into account. A numerical analysis of a complete robot model follows, to evaluate the accuracy of the analytical prediction. Finally, the limitations imposed by a torque limited motor, with regard to the optimal gait, are studied.