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Multistability of gaits, the basin of attraction and its external topology in the simplest passive walking model on stairs

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  • Rao, XiaoBo
  • Gao, JianShe
  • Ding, ShunLiang
  • Liang, Jie
  • Zhang, Jiangang

Abstract

For the passive walking robot, the basin of attraction is very small and thin, and thus makes it a great challenge to produce stable passive dynamic walking. This paper reports systematically the effect of initial conditions on gait dynamics of the simplest passive walking model on stairs. We find two new gaits with period-3 and period-4, and they both lead to higher periodic gaits and chaos by period-doubling bifurcations. The critical period-3 unstable orbit generated via the cyclic-fold bifurcation takes part in the annihilation of chaotic attractors twice, and this double boundary crisis becomes the main cause to the falling down on stairs of the passive walker. In particular, we compute the Lyapunov exponents to verify the effectiveness of the bifurcation process of these new gaits. More importantly, through analyzing the topology of phase space, the external domain of basin of attraction is classified in detail and marked precisely with different falling patterns. We believe such findings to add significantly to the knowledge of the selection of initial values and to be potentially helpful in the design and optimization of passive walking robots.

Suggested Citation

  • Rao, XiaoBo & Gao, JianShe & Ding, ShunLiang & Liang, Jie & Zhang, Jiangang, 2023. "Multistability of gaits, the basin of attraction and its external topology in the simplest passive walking model on stairs," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004939
    DOI: 10.1016/j.chaos.2023.113592
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    References listed on IDEAS

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    1. Fathizadeh, Maysam & Mohammadi, Hossein & Taghvaei, Sajjad, 2019. "A modified passive walking biped model with two feasible switching patterns of motion to resemble multi-pattern human walking," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 83-95.
    2. Fangyan Yang & Yongming Cao & Lijuan Chen & Qingdu Li, 2020. "Sequence of Routes to Chaos in a Lorenz-Type System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-10, January.
    3. Znegui, Wafa & Gritli, Hassène & Belghith, Safya, 2020. "Design of an explicit expression of the Poincaré map for the passive dynamic walking of the compass-gait biped model," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
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