Dynamic stability allows running animals to maintain preferred speed during locomotion over rough terrain. It appears that rapid disturbance rejection is an emergent property of the mechanical system. In running robots, simple motor control seems to be effective in the negotiation of rough terrain when used in concert with a mechanical system that stabilizes passively. In this paper, we show that a quadruped robot could be able to perform self-stable running behavior in significantly broader ranges of forward speed and pitch rate with suitable mechanical design. The results presented here are derived by studying the stability of passive dynamics of a quadruped robot running in the sagittal plane in a dimensionless context and can be summarized as: (a) the self-stabilized behavior of a quadruped robot for a particular gait is related to the magnitude of its dimensionless inertia, (b) the values of hip separation, normalized to rest leg length, and the leg relative stiffness of a quadruped robot affect the stability and should be in inverse proportion to its dimensionless inertia, and (c) the self-stable regime of quadruped running robots is enlarged at relatively high forward speeds.
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