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Variable Inverted Pendulum Applied to Humanoid Motion Design

Published online by Cambridge University Press:  04 February 2021

Teresa Zielinska Open the ORCID record for Teresa Zielinska [Opens in a new window] ,
Gabriel R. Rivera Coba  and
Weimin Ge
Teresa Zielinska*
Affiliation:
Faculty of Power and Aeronautical Engineering, Warsaw University of Technology, Warsaw, Poland
Gabriel R. Rivera Coba
Affiliation:
Ecuador, Quito, sector: La Concepción de Alpahuma, Alangasí, Calle A, Betania, ref. Urbanización Mirador del Colegio. E-mail: grivera@soindec.com
Weimin Ge*
Affiliation:
School of Mechanical Engineering, Tianjin University of Technology, Tianjin, China
*
*Corresponding authors. E-mail: teresaz@meil.pw.edu.pl, geweimin@email.tjut.edu.cn
*Corresponding authors. E-mail: teresaz@meil.pw.edu.pl, geweimin@email.tjut.edu.cn
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Double inverted pendulum model, stationary or on a cart, is computationally the simplest out of the range of reasonable models used for anthropomorphic robots motion synthesis. However, it is still not sufficient for describing more complex situations. The novel concept of variable double inverted pendulum (VDIP) for static postures and VDIP on cart (VDIPC) for dynamic cases is proposed. It provides a simplified but a sufficiently accurate tool for planning the human-like static and dynamic robot postures. Its variable parameters enable the description of both human static postures and motion dynamics. The variable length of the lower link is essential for the representation of postures attained by bending legs. The studies of a set of static and dynamic postures were used for deducing and verifying the locations of lower and upper joint of a double pendulum and the point masses. To justify the concept, human body and pendulum behaviors are compared taking into account a typical model of the human body. Static analysis was conducted by considering static human postures. Dynamic conditions were analyzed using the data acquired from human motion and thus the VDIPC definition was established. The zero moment point trajectories of the human and of VDIPC were compared, validating the correctness of VDIPC in dynamic situations. The formal description of VDIPC is provided together with the torques equilibrium condition needed for evaluating the dynamic postural stability, with the VDPIC representing the robot configuration. The VDPIC state equations are formulated in a form required by the predictive control method. The paper contributes to the motion synthesis methods of anthropomorphic robots taking into account postural control.

Keywords

Double inverted pendulumsHumanoidsMotion synthesisHuman postures and movements
Type
Article
Information
Robotica , Volume 39 , Issue 8 , August 2021 , pp. 1368 - 1389
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0), which permits non-commercial re-use, distribution, and reproduction in any medium, provided that no alterations are made and the original article is properly cited. The written permission of Cambridge University Press must be obtained prior to any commercial use and/or adaptation of the article.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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