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imit cycle walking including passive-dynamic walkers is mathematically modeled as a nonlinear hybrid dynamical system with state jumps in general. The generated motion is natural and energy efficient, but it is still pointed out that there are many differences between limit cycle walking and human walking. Non-existence of the period of double-limb support in the former comes from the assumption of instantaneous inelastic collision and is one of the biggest differences from the latter. In human walking, the period of double-limb support accounts for more than 10% of one cycle, and this must have significant effects on the gait stability and efficiency. Also in robot walking, utilizing the effects of double-limb support is essential to achieve more flexible, adaptive and human-like behavior. This paper then develops a novel mathematical model of a passive rimless wheel that emerges double-limb support by using the leg viscoelasticity, and numerically investigates the fundamental properties.

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