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Feasible speeds for two optimal periodic walking gaits of a planar biped robot

Published online by Cambridge University Press:  04 June 2021

Mathieu Hobon ,
Víctor De-León-Gómez ,
Gabriel Abba ,
Yannick Aoustin Open the ORCID record for Yannick Aoustin [Opens in a new window]  and
Christine Chevallereau
Mathieu Hobon
Affiliation:
Laboratoire de Conception Fabrication Commande, EA 4495, Arts et Métiers ParisTech, Université de Lorraine, 4 rue Augustin Fresnel, 57078 Metz Cedex 3, France
Víctor De-León-Gómez
Affiliation:
Laboratoire des Sciences du Numérique, de Nantes, UMR 6004, CNRS, École Centrale de Nantes, Université de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes, France
Gabriel Abba
Affiliation:
Laboratoire de Conception Fabrication Commande, EA 4495, Arts et Métiers ParisTech, Université de Lorraine, 4 rue Augustin Fresnel, 57078 Metz Cedex 3, France
Yannick Aoustin*
Affiliation:
Laboratoire des Sciences du Numérique, de Nantes, UMR 6004, CNRS, École Centrale de Nantes, Université de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes, France
Christine Chevallereau
Affiliation:
Laboratoire des Sciences du Numérique, de Nantes, UMR 6004, CNRS, École Centrale de Nantes, Université de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes, France
*
*Corresponding author. Email: [email protected]
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Abstract

The purpose is to define the range of feasible speeds for two walking motions for a particular planar biped robot, which differ in the definition of their finite-time double support phases. For each speed, these two walking motions are numerically obtained by using a parametric optimization algorithm, regarding a sthenic criterion. Results allow us to define the range of allowable speeds for each walking. One result is that the first gait is less consuming in energy for moderate to fast velocity with respect to the second one, while the second gait is more efficient for low walking velocity.

Keywords

Walking gaitFinite-time doubleImpact with foot flatToe impactHeel impact
Type
Article
Information
Robotica , Volume 40 , Issue 2 , February 2022 , pp. 377 - 402
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Alexander, R., “The gaits of bipedal and quadrupedal animals,” Int. J. Rob. Res. 3(4), 49–59 (1984).CrossRefGoogle Scholar
Singh, R., Chaudhary, H. and Singh, A. K., Sagittal Position Analysis of Gait Cycle for a Five Link Biped Robot (Springer, 2016) pp. 387–396.Google Scholar
Saunders, J., Verne, T. I and Howard, D. E., “The major determinants in normal and pathological gait,” J. Bone Joint Surg. 35(3), 543–558 (1953).CrossRefGoogle ScholarPubMed
Winter, D., Biomechanics and Motor Control of Human Movement (John Wiley & Sons, Inc., Hoboken, NJ, 2005).Google Scholar
Chevallereau, C., Bessonnet, G., Abba, G. and Aoustin, Y., Bipedal Robots (ISTE Wiley, London, 2009).CrossRefGoogle Scholar
Nadubettu Yadukumar, S., Pasupuleti, M. and Ames, A., “Human-Inspired Underactuated Bipedal Robotic Walking with Amber on Flat-Ground, Up-Slope and Uneven Terrain,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Vilamoura, Algarve, Portugal (2012).CrossRefGoogle Scholar
Chevallereau, C., Abba, G., Aoustin, Y., Plestan, F., Westervelt, E., Canuddas-de Wit, C and Grizzle, J., “Rabbit: A testbed for advanced control theory,” IEEE Control Syst. Mag. 23(5), 57–79 (2003).Google Scholar
Kajita, S., Kanehiro, F., Morisawa, M., Nakaoka, S. and Hirukawa, H., “Biped Walking Pattern Generator Allowing Auxiliary ZMP Control,” 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, P.R. China (2006) pp. 2993–2999.Google Scholar
Omran, S., Sakka, S. and Aoustin, Y., “Effects of com vertical oscillation on joint torques during 3D walking of humanoid robots,” Int. J. Hum. Rob. 13(4), 1650019 (2016). https://doi.org/10.1142/S02198436165001951650019.CrossRefGoogle Scholar
Miossec, S. and Aoustin, Y., “A simplified stability for a biped walk with under and over actuated phase,” Int. J. Rob. Res. 24(7), 537–551 (2005).CrossRefGoogle Scholar
Hamed, K. K., Sadati, N., Gruver, W. A. and Dumont, G. A., “Stabilization of periodic orbits for planar walking with noninstantaneous double-support phase,” IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 42(3), 685–706 (2012).CrossRefGoogle Scholar
Ju, M. S. and Mansour, J. M., “Simulation of the double limb support phase of human gait,” J. Biomech. Eng. 110(3), 223–229 (1988).CrossRefGoogle ScholarPubMed
Sharma, N. and Stein, R., “Gait Planning and Double Support Phase Model for Functional Electrical Stimulation-based Walking,” 33th Annual International Conference of the IEEE EMBS, San Diego, California USA (2012).CrossRefGoogle Scholar
Bessonnet, G., Chesse, S. and Sardain, P., “Optimal gait synthesis of a seven-link planar biped,” Int. J. Rob. Res. 23(10–11), 1059–1073 (2004).CrossRefGoogle Scholar
Tlalolini Romero, D., Chevallereau, C. and Aoustin, Y., “Comparison of different gaits with rotation of the feet for a planar biped,” Rob. Auto. Syst. 57(4), 371–383 (2009).CrossRefGoogle Scholar
Rostami, M. and Bessonnet, G., “Impacless Sagittal Gait of a Biped Robot During the Single Support Phase,” IEEE International Conference on Robotics and Automation ICRA’98, Leuven, Belgium (1998).Google Scholar
Aoustin, Y. and Hamon, A., “Human like trajectory generation for a biped robot with a four-bar linkage for the knees,” Rob. Auto. Syst. 61(12), 1717–1725 (2013).CrossRefGoogle Scholar
Tan, M., Jenning, L. and Wang, S., Analysing Human Walking Using Dynamic Optimisation (Springer, Berlin, Heidelberg, 2015) pp. 1–34.Google Scholar
Dadashzadeh, D. and Macnab, C. J. B., “Slip-based control of bipedal walking based on two-level control strategy,” Robotica 38(8), 1434–1449 (2020).CrossRefGoogle Scholar
Kinugasa, T., Chevallereau, C. and Aoustin, Y., “Effect of circular arc feet on a control law for a biped,” Robotica 27(4), 621–632 (2009).CrossRefGoogle Scholar
Bertrand, S., Bruneau, O., Ouezdou, F. B. and Alfayad, S., “Closed-form solutions of inverse kinematic models for the control of a biped robot with 8 active degrees of freedom per leg,” Mech. Mach. Theory, Elsevier 49 117–140 (2012).Google Scholar
Chevallereau, C. and Aoustin, Y., “Optimal reference trajectories for walking and running of a biped robot,” Robotica 19(5), 557–569 (2001).CrossRefGoogle Scholar
Alfayad, S., Robot humanoïde hydroïd: Actionnement structure cinématique et stratégie de contrôle Ph.D. Thesis (Université de Versailles Saint-Quentin, 2009).Google Scholar
Hanavan, E. P., “A personalized mathematical model of the human body,” J. Spacecraft Rockets 3(3), 446–448 (1966).CrossRefGoogle Scholar
Bryson, A. E. and Ho, Y. C., Applied Optimal Control (Wiley, New-York, 1995).Google Scholar
Vainikko, G., “On the stability and convergence of the collocation method,” Differ. Uravnen. 1(2), 244–254 (1965).Google Scholar
El Daou, M. K. and Ortiz, E. L., “A recursive formulation of collocation in terms of caical polynomials,” Comput. 52(2), 177–202 (1994).CrossRefGoogle Scholar
Mombaur, K., Bock, H. G., Schlöder, J. P. and Longman, R. W., “Open-loop stable solutions of periodic optimal control problems in robotics,” ZAMM 85(7), 499–515 (2005).CrossRefGoogle Scholar
Groote, F. D., Kinney, A. L., Rao, A. V and Fregly, B. J., “Evaluation of direct collocation optimal control problem formulations for solving the muscle redundancy problem,” Ann. Biomed. Eng. 44(10), 2922–2936 (2016).CrossRefGoogle ScholarPubMed
Roussel, L., de Wit, C. C. and Goswami, A., “Generation of Energy Optimal Complete Gait Cycles for Biped,” Proceedings of the IEEE Conference on Robotics and Automation (1998) pp. 2036–2041.Google Scholar
Beletskii, V. V and Chudinov, P. S., “Parametric optimization in the problem of bipedal locomotion,” Izv. An SSSR. Mekhanika Tverdogo Tela [Mech. Solids] 12(1), 25–35 (1977).Google Scholar
Channon, P. H., Hopkins, S. H. and Pham, D. T., “Derivation of optimal walking motions for a bipedal walking robot,” Robotica 10(3), 165–172 (1992).CrossRefGoogle Scholar
Cabodevilla, G., Chaillet, N. and Abba, G., “Energy-Minimized Gait for a Biped Robot,” Proceedings of the AMS’95, Tampa, Florida, USA (2002) pp. 90–99.Google Scholar
Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N. and Tanie, K., “Planning walking patterns for a biped robot,” IEEE Trans. Rob. Autom. 17(3), 280–289 (2001).CrossRefGoogle Scholar
Roberts, D., Quacinella, J. and Kim, J. H., “Energy expenditure of a biped walking robot: Instantaneous and degree-of-freedom-based instrumentation with human gait implications,” Robotica 35(5), 1054–1071 (2017).CrossRefGoogle Scholar
Boor, C. D., A Practical Guide to Splines . Applied Mathematical Sciences (Springer-Verlag, New York, 1978).Google Scholar
Gill, P., Murray, W. and Wright, M., Practical Optimization (Academic Press, London, 1981).Google Scholar
Powell, M., Variable Metric Methods for Constrained Optimization, Lecture Notes in Mathematics (Springer, Berlin, Heidelberg, 1977) pp. 62–72.Google Scholar
Miossec, S. and Aoustin, Y., Dynamical Synthesis of a Walking Cyclic Gait for a Biped with Point Feet, Lecture Notes in Control and Information Sciences, vol. 340 (Springer, Berlin, Heidelberg, 2006) pp. 233–252.CrossRefGoogle Scholar
Cottalorda, J., Durst, C., Aubail, R., Belli, A. and Gautheron, V., , Geyssant, “Consommation énergétique à la vitesse de confort au sol et sur tapis roulant,” Annales de Réadaptation et de Médecine Physique, Editions scientifiques et médicales, Elsevier 43(1), 30–35 (2000).CrossRefGoogle Scholar
Mochon, S. and McMahon, T., Ballistic walking: An improved model,” Math. Bio-Sci. 52(3–4), 241–260 (1980).CrossRefGoogle Scholar
Rose, J. and Gamble, G., Human Walking, 3rd edn. (Lippincott Williams & Wilkins, Philadelphia, PA, 2006). p. 273.Google Scholar
Aoustin, Y., Chevallereau, C. and Arakelian, V., “Study and Choice of Actuation for a Walking Assist Device,” In: New Trends in Medical and Service Robots. Mechanisms and Machine Science, Vol. 38 (H. Bleuler, M. Bouri, F. Mondada, D. Pisla, A. Rodic and P. Helmer, eds.) (Springer, Cham, 2016). https://doi.org/10.1007/978-3-319-23832-6_1.CrossRefGoogle Scholar