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The biped Lucy, powered by pleated pneumatic artificial muscles, has been built and controlled and is able to walk up to a speed of 0.15 m/s. The pressures inside the muscles are controlled by a joint trajectory tracking controller to track the desired joint trajectories calculated by a trajectory generator. However, the actuators are set to a fixed stiffness value. In this paper a compliance controller is proposed which can be added in the control architecture to reduce the energy consumption by exploiting the natural dynamics. The goal of this research is to preserve the versatility of actively controlled humanoids, while reducing their energy consumption. A mathematical formulation has been developed to find an optimal stiffness setting depending on the desired trajectory and physical properties of the system and the proposed strategy has been validated on a pendulum structure powered by artificial muscles. This strategy has not been implemented on the real robot because the walking speed of the robot is currently too slow to benefit already from compliance control.