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The angular positions of the lower limb joints play important roles on the energy consumption and stability for the bipedal walking up slopes. In this study, the ranges of angular position of lower limb joints are confined and the velocity of swing foot is zero when it touches the ground, which result in the construction of the impactless planar bipedal model. Motion/force control scheme combined with genetic algorithm (GA) is used to ensure stability and low energy cost of bipedal walking at different speeds. The optimized parameters of gaits are obtained by GA, which include walking speed, step length and the maximum height of swing ankle joint. The results demonstrate that more energy is consumed when the optimal walking speed increases for the biped walking on slopes with the same gradient. There are no great differences in optimal step length of the biped when the walking speed changes. The optimal step length declines as the slope increases at the same walking speed. The ankle torques of standing leg have higher values in single support phase at fast speed compared to those at slow and normal speeds. Modifications of boundary conditions can not only be used to realize the stable walking for the biped negotiating slopes, but also be applied to analyze bipedal gaits for walking on stairs and uneven surfaces.