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Usually, the bipedal robots use knee joints with only one degree of freedom. However, several biomechanical researches have proved the human knee joint is a very complex articulation with more than one degree of freedom. Indeed, in the sagittal plain the human knee articulation allows a rolling and a sliding of the thigh on the shin. Moreover, we can use for a bipedal robot a closed structure, which gives an additional degree of freedom in translation for the knee joint in the sagittal plane. Therefore, the aim of this paper is to study two different bipedal robots. One with single axis knee joints and an other with four-bar knee joints. These bipeds are defined in the sagittal plain and are composed of two shins, two thighs and a trunk but they have no feet or arms. In the two cases, we use a parametric optimization method to produce reference cyclic trajectories in order to compare the energy consumption of the bipedal robots. A PoincareÂ¿ return map is defined for the walking gaits of the bipedal robots in order to study the influence of the two different knees on their orbital stability.