Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T09:23:06.013Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Weimin Ge*
Affiliation:
School of Mechanical Engineering, Tianjin University of Technology, Tianjin, China
*
*Corresponding authors. E-mail: [email protected], [email protected]
*Corresponding authors. E-mail: [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Alexandrov, A. V., Lippi, V., Mergner, T., Frolov, A. A., Hettich, G. and Husek, D., “Human-inspired eigenmovement concept provides coupling-free sensorimotor control in humanoid robot,” Front. Neurorobot. 11, 1–13 (2017), Article 22.CrossRefGoogle ScholarPubMed
Audren, H., Vaillant, J., Kheddar, A., Escande, A., Kaneko, K. and Yoshida, E., “Model Preview Control in Multi-contact Motion-application to a Humanoid Robot,” IEEE International Conference on Intelligent Robots and Systems (2014) pp. 4030–4035.Google Scholar
Asker, A., Assal, S., Ding, M., Takamatsu, J., Ogasawara, T. and Mohamed, M., “Experimental Validation of a Motion Generation Model for Natural Robotics-Based Sit to Stand Assistance and Rehabilitation,” ROBIO International Conference on Robotics and Biomimetics (2016) pp. 214–219.Google Scholar
Berenson, D., Srinivasa, S. and Kuffner, J., “Task Space Regions: A framework for pose-constrained manipulation planning,” Int. J. Robot. Res. 12(30), 1435–1460 (2011).CrossRefGoogle Scholar
Liu, C., Ning, J. and Chen, Q., “Dynamic walking control of humanoid robots combining linear inverted pendulum mode with parameter optimization,” Int. J. Adv. Robot. Syst. 15(1), 1–15 (2018)CrossRefGoogle Scholar
Coba, R. G., Analysing of Postural Stabilisation Using Simplified Models of Humanoids Thesis (Warsaw University of Technology, 2018).Google Scholar
Contini, R., “Body segment parameters. Part II”, Artificial Limbs. Rev. Curr. Dev. 16(1), 1–19 (1972).Google Scholar
Full, R. J. and Koditschek, D. E., “Templates and anchors: Neuromechanical hypotheses of legged locomotion on land,” J. Exp. Biol. 202(23), 3325–3332 (1999).CrossRefGoogle ScholarPubMed
Gordon, C. C., Churchill, T., Clauser, C. E., Bradtmiller, B. and McConville, J. T., Anthropometric Survey of US Army Personnel: Methods and Summary Statistics. Technical Report (Anthropology Research Project Inc, Yellow Springs, OH, 1989)Google Scholar
Harada, K., Yoshida, E. and Yokoi, K., Motion Planning for Humanoid Robots (Springer Science & Business Media, Springer-Verlag London, 2010).CrossRefGoogle Scholar
Hase, K. and Yamazaki, N., “Computer simulation study of human locomotion with a three-dimensional entire-body neuro-musculo-skeletal model”, JSME Int. J. Ser. C Mech. Syst. Mach. Elements Manuf. 45(4), 1040–1050 (2002).Google Scholar
Hayot, Ch, Sakka, S., Fohanno, V. and Lacouture, P., “Biomechanical modeling of the 3D center of mass trajectory during walking,” Movement and Sport Sciences - Science and Motricité. ACAPS, EDP Sciences, pp. 1–11 (2013).Google Scholar
Hirai, K., Hirose, M., Haikawa, Y. and Takenaka, T., “The Development of Honda Humanoid Robot,” IEEE International Conference on Robotics and Automation Proceedings, vol. 2 (1998) pp. 1321–1326.Google Scholar
Hwang, J., Suh, I. H., Park, G. and Kwon, T., “Human Character Balancing Motion Generation Based on a Double Inverted Pendulum Model,” Proceedings of 10-th International Conference on Motion in Games (ACM) (2017) pp. 1–11.Google Scholar
Hyon, S. H., Morimoto, J. and Kawato, M., “From Compliant Balancing to Dynamic Walking on Humanoid Robot: Integration of CNS and CPG,” IEEE International Conference on Robotics and Automation (ICRA) (2010) pp. 1084–1085.Google Scholar
Ijspeert, A. J., “Central pattern generators for locomotion control in animals and robots: A review,” Neural Networks 21(4), 642–653 (2008).CrossRefGoogle ScholarPubMed
Kajita, S., Kanehiro, F., Kaneko, K., Yokoi, K. and Hirukawa, H., “The 3d Linear Inverted Pendulum Model: A Simple Modeling for a Biped Walking Pattern Generation,” IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 1 (2001) pp. 239–246.Google Scholar
Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K. and Hirukawa, H., “Biped Walking Pattern Generation by Using Preview Control of Zero Moment Point,” IEEE International Conference on Robotics and Automation Proceedings (ICRA), vol. 2 (IEEE, 2003) pp. 1620–1626.Google Scholar
Kajita, S., Hirukawa, H., Harada, K. and Yokoi, K., Introduction to Humanoid Robotics, vol. 101 (Springer, Springer-Verlag London, 2014).Google Scholar
Kasaei, M., Lau, N. and Pereira, A., “Comparison Study of Well-Known Inverted Pendulum Models for Balance Recovery in Humanoid Robot,” MAPiS 2019 - First MAP-i Seminar Proceedings (2019) pp. 1–6.Google Scholar
Lanari, L., Hutchinson, S. and Marchionni, L., “Boundedness Issues in Planning of Locomotion Trajectories for Biped Robots,” 14th IEEE-RAS International Conference on Humanoid Robots (Humanoids) (2014) pp. 951–958.Google Scholar
Lippi, V. and Mergner, T., “Human-derived disturbance estimation and compensation (dec) method lends itself to a modular sensorimotor control in a humanoid robot,” Front. Neurorobot. 11, 1–49 (2017).CrossRefGoogle Scholar
Mordatch, I., De Lasa, M. and Hertzmann, A., “Robust physics-based locomotion using low-dimensional planning,” ACM Trans. Graphics (TOG) 29(4), 71 (2010).CrossRefGoogle Scholar
Neusser, Z. and Valasek, M., “Control of the double inverted pendulum on a cart using the natural motion,” Acta Polytechnica 53(6), 883–889 (2013).CrossRefGoogle Scholar
Niemann, H. and Poulsen, J. K., “Design and analysis of controllers for a double inverted pendulum,” ISA Trans. 44(1), 145–163 (2005).CrossRefGoogle ScholarPubMed
Omran, S., Sakka, S. and Aoustin, Y., “Using the generalized inverted pendulum to generate less energy-consuming trajectories for humanoid walking,” Arch. Mech. Eng. 63(2), 245–262 (2016).CrossRefGoogle Scholar
Ott, C., Roa, M. A. and Hirzinger, G., “Posture and Balance Control for Biped Robots Based on Contact Force Optimization,” Proceedings of IEEE-RAS International Conference on Humanoid Robots (2011) pp. 26–33.Google Scholar
Jaiwat, P. and Ohtsuka, T., “Real-Time Swing-up of Double Inverted Pendulum by Nonlinear Model Predictive Control,” ADCONP International Symposium on Advanced Control of Industrial Processes (2014) pp. 290–295.Google Scholar
Qiu, Z., Escande, A., Micaelli, A. and Robert, T., “A Hierarchical Framework for Realizing Dynamically-Stable Motions of Humanoid Robot in Obstacle-Cluttered Environments,” Proceedings of IEEE-RAS International Conference on Humanoid Robots (2012) pp.867–874.Google Scholar
Shi, Z., Huang, X., Hu, T., Tan, Q. and Hou, Y., “Weighted augmented Jacobian matrix with variable coefficient method for kinematics mapping of space teleoperation based on human-robot motion similarity,” Adv. Space Res. 56(7), 1401–1416 (2016).CrossRefGoogle Scholar
Scianca, N., Cognetti, M., De Simone, D., Lanari, L. L. and Oriolo, G., “Intrinsically Stable MPC for Humanoid Gait Generation,” IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids) (2016) pp. 601–606.Google Scholar
Sugihara, T., Nakamura, Y. and Inoue, H., “Realtime Humanoid Motion Generation through ZMP Manipulation Based on Inverted Pendulum Control,” IEEE International Conference on Robotics and Automation, vol. 2 (2002) pp. 1404–1409.Google Scholar
Szumowski, M., Zurawska, M. and Zielinska, T., “Preview control applied for humanoid robot motion generation,” Arch. Control Sci. 59(LXV)(1), 111–132 (2019).Google Scholar
Villalobos, J. and Zielinska, T., “Study of postural adjustments for humanoidal helpmates,” J. Autom. Mobile Robot. Intell. Syst. 11(04), 15–25 (2017).Google Scholar
Vukobratovic, M., Legged Locomotion. Robots and Anthropomorphic Mechanisms (Mihailo Pupin Institute, Belgrade, 1975). Also published in: Japanese (Nikkan Shimbun Ltd. Tokyo, 1975), Russian (MIR, Moscow, 1976), Chinese (Beijing, 1983).Google Scholar
Vukobratovic, M. and Borovac, B., “Zero-moment point thirty five years of its life,” Int. J. Humanoid Robot. 1(01), 157–173 (2004).CrossRefGoogle Scholar
Vukobratovi, M., Potkonjak, V., Babković, K. and Borovac, B., “Simulation model of general human and humanoid motion,” Multibody Syst. Dyn. 17(1), 71–96 (2007).CrossRefGoogle Scholar
Walters, R., “Robotics Answers: Japan Out to Lead the Next Industrial Revolution,” [Online]. Available: https://journal.accj.or.jp/robotics-answers-japan-out-to-lead-the-next-industrial-revolution/.Google Scholar
Wang, T. and Chevallereau, C., “A New Control Law for a 3d Biped Robot Based on Regulation of the Zero Moment Point and Joint Path,” 10th IEEE-RAS International Conference on Humanoid Robots (Humanoids) (IEEE, 2010), pp. 27–32.Google Scholar
Winter, D. A., Biomechanics and Motor Control of Human Movement (John Wiley & Sons, 2009).CrossRefGoogle Scholar
Xue, F., Chen, X., Liu, J. and Nardi, D., “Real Time Biped Walking Gait Pattern Generator for a Real Robot,” Robot Soccer World Cup (Springer, 2011) pp. 210–221.Google Scholar
Yamaguchi, J., Soga, E., Inoue, S. and Takanishi, A., “Development of a Bipedal Humanoid Robot Control Method of Whole Body Cooperative Dynamic Biped Walking,” IEEE International Conference on Robotics and Automation Proceedings, vol. 1 (IEEE, 1999) pp. 368–374.Google Scholar
Zielinska, T., “Coupled oscillators utilised as a gait rhythm generators of two legged walking machine,” J. Biol. Cybern. 4(03), 263–273 (1996).CrossRefGoogle Scholar
Zielinska, T. and Chmielniak, A., “Biologically inspired motion synthesis method of two-legged robot with compliant feet,” Robotica 29(07), 1049–1057 (2011).CrossRefGoogle Scholar
Zielinska, T., Gao, Z., Zurawska, M., Zheng, Q., Mergner, T. and Lippi, V., “Postural Balance Using a Disturbance Rejection Method,” 11th IEEE Workshop on Robot Motion and Control (RoMoCo) (2017) pp. 23–28.Google Scholar
Zurawska, M., Szumowski, M. and Zielinska, T., “Reconfigurable double inverted pendulum applied to the modelling of human robot motion’, J. Autom. Mobile Robot. Intell. Syst. 11(2), 12–20 (2017).Google Scholar