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Trajectory tracking-based control of the chaotic behavior in the passive bipedal compass-type robot

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Abstract

This paper deals mainly with the control of the complex and rhythmic behaviors of the passive dynamic walk of the bipedal compass-type robot. The walking gait of such biped robot is modeled by an impulsive hybrid nonlinear system. We first show, using bifurcation diagrams, that the passive gait of the bipedal compass robot can exhibit surprising behaviors such as chaos and bifurcations. This complex nature of the walk of this type of bipedal robot requires a search for a 1-periodic walk, to better imitate human walking more faithfully, using the Poincaré map. Thus, to suppress these complex nonlinear behaviors, we control the bipedal compass-type robot to obtain a one-periodic gait by adopting two methods. The first control method is based on the passive dynamic walking of the biped robot, and then the objective is to track during the swing phase the period-1 passive trajectory. In contrast, the second control method is based on following a trajectory designed using a 4th-order Bézier function. Several simulation results are presented showing that the first control method, compared to the second one, provides an energy efficiency.

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Data availability statement

The data used to support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

This research work was funded by the Ministry of Higher Education and Scientific Research (Ministère de l’Enseignement Supérieur et de la Recherche Scientifique (MESRS)), Tunisia, for the project no. 20PEJC 06-02. The authors, therefore, acknowledge with thanks MESRS for technical and financial support.

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Authors and Affiliations

  1. Laboratory of Robotics, Informatics and Complex Systems (RISC-Lab, LR16ES07), National Engineering School of Tunis, Université de Tunis El Manar, BP. 37, Le Belvédère, 1002, Tunis, Tunisia

    Essia Added, Hassène Gritli & Safya Belghith

  2. Higher Institute of Information and Communication Technologies, Université de Carthage, 1164, Borj-Cedria, Tunis, Tunisia

    Hassène Gritli

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  1. Essia Added
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  2. Hassène Gritli
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Added, E., Gritli, H. & Belghith, S. Trajectory tracking-based control of the chaotic behavior in the passive bipedal compass-type robot. Eur. Phys. J. Spec. Top. 231, 1071–1084 (2022). https://doi.org/10.1140/epjs/s11734-022-00471-3

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