Self-stability of a simple walking model driven by a rhythmic signal |
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Authors: | Shinya Aoi Kazuo Tsuchiya |
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Institution: | (1) Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan |
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Abstract: | In this paper, we analyzed the dynamic properties of a simple walking model of a biped robot driven by a rhythmic signal from
an oscillator. The oscillator receives no sensory feedback and the rhythmic signal is an open loop. The simple model consists
of a hip and two legs that are connected at the hip. The leg motion is generated by a rhythmic signal. In particular, we analytically
examined the stability of a periodic walking motion. We obtained approximate periodic solutions and the Jacobian matrix of
a Poincaré map by the power-series expansion using a small parameter. Although the analysis was inconclusive when we used
only the first order expansion, by employing the second order expansion it clarified the stability, revealing that the periodic
walking motion is asymptotically stable and the simple model possesses self-stability as an inherent dynamic characteristic
in walking. We also clarified the stability region with respect to model parameters such as mass ratio and walking speed. |
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Keywords: | Simple walking model Central pattern generator (CPG) Self-stability Poincaré map |
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