Traditional methods for robotic biped locomotion employing stiff actuation display low energy efficiency and high sensitivity to disturbances. In order to overcome these problems, a semi-passive approach based on the use of passive elements together with actuation has emerged, inspired by biological locomotion. However, the control strategy for such a compliant system must be robust and adaptable, while ensuring the success of the walking gait. In this paper, a Model Predictive Control (MPC) approach is applied to a simulated actuated Simplest Walker (SW), in order to achieve a stable gait while minimizing energy consumption. Robustness to slope change and to external disturbances are also studied.