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3D walking biped: optimal swing of the arms

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Abstract

A ballistic walking gait is designed for a 3D biped with two identical two-link legs, a torso, and two identical one-link arms. In the single support phase, the biped moves due to the existence of a momentum, produced mechanically, without applying active torques in the interlink joints. This biped is controlled with impulsive torques at the instantaneous double support to obtain a cyclic gait. The impulsive torques are applied in the seven interlink joints. Then an infinity of solutions exists to find the impulsive torques. An effort cost functional of these impulsive torques is minimized to determine a unique solution. Numerical results show that for a given time period and a given length of the walking gait step, there is an optimal swinging amplitude of the arms. For this optimal motion of the arms, the cost functional is minimum.

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Notes

  1. Therefore, there is a permutation operation between \(\dot{\mathbf{X}}^{a}\) and the solution of the boundary value problem to take into account the exchange of the role of both legs.

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Acknowledgements

This work was supported by Ministry of Education and Science of Russian Federation, Project 07.524.11.4012 and CNRS via a Project of International Collaboration Scientific, PICS 3866. Cooperation agreement CNRS/Russian Academy of Sciences (EDC25146).

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Authors and Affiliations

  1. L’UNAM, Institut de Recherche en Communications et Cybernétique de Nantes, UMR 6597, CNRS, École Centrale de Nantes, Université de Nantes, Nantes, France

    Y. Aoustin

  2. Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia

    A. M. Formalskii

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  1. Y. Aoustin
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  2. A. M. Formalskii
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Correspondence to Y. Aoustin.

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Aoustin, Y., Formalskii, A.M. 3D walking biped: optimal swing of the arms. Multibody Syst Dyn 32, 55–66 (2014). https://doi.org/10.1007/s11044-013-9378-3

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