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Passive dynamic walking refers to a class of bipedal machines that are able to walk down a gentle slope with no external control or energy input. The legs swing naturally as pendula, and conservation of angular momentum governs the contact of the swing foot with the ground. Previous machines have been limited to planar motions. We extend the planar motions to allow for tilting side to side (roll motion). Passive walking cycles exist, but the roll motion is unstable, resembling that of an inverted pendulum. The instability is due to mismatching of roll velocity with the ground contact conditions. Several strategies are presented for stabilizing this motion, of which the quasi-static control of step width is determined to be both simple and efficient.
Arthur D. Kuo (Wed,) studied this question.