Hostname: page-component-74656f9884-2dmjx Total loading time: 0 Render date: 2026-11-09T09:56:53.000Z Has data issue: false hasContentIssue false
  • English
  • Français

Energy-Efficient Bipedal Walking: From Single-Mass Model to Three-Mass Model

Published online by Cambridge University Press:  22 February 2021

Jiatao Ding ,
Jiangchen Zhou ,
Zhao Guo  and
Xiaohui Xiao Open the ORCID record for Xiaohui Xiao [Opens in a new window]
Jiatao Ding
Affiliation:
School of Power and Mechanical Engineering, Wuhan University, Wuhan, Hubei Province 430072, P.R. China E-mails: jtding@whu.edu.cn, zhoujc@whu.edu.cn, guozhao@whu.edu.cn Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen, Guangdong Province 518000, P.R. China
Jiangchen Zhou
Affiliation:
School of Power and Mechanical Engineering, Wuhan University, Wuhan, Hubei Province 430072, P.R. China E-mails: jtding@whu.edu.cn, zhoujc@whu.edu.cn, guozhao@whu.edu.cn
Zhao Guo
Affiliation:
School of Power and Mechanical Engineering, Wuhan University, Wuhan, Hubei Province 430072, P.R. China E-mails: jtding@whu.edu.cn, zhoujc@whu.edu.cn, guozhao@whu.edu.cn
Xiaohui Xiao*
Affiliation:
School of Power and Mechanical Engineering, Wuhan University, Wuhan, Hubei Province 430072, P.R. China E-mails: jtding@whu.edu.cn, zhoujc@whu.edu.cn, guozhao@whu.edu.cn
*
*Corresponding author. E-mail: xhxiao@whu.edu.cn
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.

The work aims to realize energy-efficient bipedal walking by employing the three-mass inverted pendulum model (3MIPM) and compare its energy performance with linear inverted pendulum model (LIPM). To do this, a general optimal index on center of mass (CoM) acceleration is first derived for energetic cost evaluation. After defining the equivalent zero moment point (ZMP) motion, an unconstrained optimization approach for CoM generation is extended for 3MIPM, which can track different ZMP references and address the height variation as well. To make use of the allowable ZMP movement, a constrained optimization method is also employed, contributing to lower energetic cost. Simulation and hardware experiments on a humanoid robot demonstrate that the 3MIPM could achieve higher energy efficiency.

Keywords

Energy efficiencyBipedal walkingThree-mass inverted pendulum modelAllowable ZMP movementBody height variation

Information

Type
Article
Information
Robotica , Volume 39 , Issue 9 , September 2021 , pp. 1537 - 1559
Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

Rose, J. and Gamble, J., eds, Human Walking, 2nd ed. (Williams and Wilkins, Baltimore, MD, 1994).Google Scholar
Sakagami, Y., Watanabe, R., Aoyama, C., Matsunaga, S., Higaki, N. and Fujimura, K., “The Intelligent Asimo: System Overview and integration,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (2002) pp. 2478–2483.Google Scholar
Fallon, M., Kuindersma, S., Karumanchi, S., Antone, M., Schneider, T., Dai, H., D’Arpino, C. P., Deits, R., DiCicco, M., Fourie, D. and Koolen, T., “An architecture for online affordance-based perception and whole-body planning,” J. Field Robot 32(2), 229–254 (2015).CrossRefGoogle Scholar
Tsagarakis, N. G., Caldwell, D. G., Negrello, F., Choi, W., Baccelliere, L., Loc, V. G., Noorden, J., Muratore, L., Margan, A., Cardellino, A. and Natale, L., “Walk-man: A high-performance humanoid platform for realistic environments,” J. Field Robot 34(7), 1225–1259 (2017).CrossRefGoogle Scholar
Kamioka, T., Kaneko, H., Kuroda, M., Tanaka, C., Shirokura, S., Takeda, M. and Yoshiike, T., “Dynamic Gait Transition Between Walking, Running and Hopping for Push Recovery,” Proceedings of the IEEE-RAS International Conference on Humanoid Robotics (2017) pp. 1–8.Google Scholar
Ding, J., Wang, Y., Yang, M. and Xiao, X., “Walking stabilization control for humanoid robots on unknown slope based on walking sequences adjustment,” J. Intell. Robot Syst. 90(3–4), 323–338 (2018).Google Scholar
Ding, J., Zhou, C., Guo, Z., Xiao, X. and Tsagarakis, N., “Versatile Reactive Bipedal Locomotion Planning Through Hierarchical Optimization,” Proceedings of IEEE International Conference on Robotics and Automation (2019) pp. 256–262.Google Scholar
Shahrokhshahi, A., Yousefi-Koma, A., Khadiv, M., Mansouri, S. and Mohtasebi, S. S., “Optimal stair climbing pattern generation for humanoids using virtual slope and distributed mass model,” J. Intell. Robot Syst. 94(1), 1–17 (2019).CrossRefGoogle Scholar
Kuo, A. D., “Choosing your steps carefully,” Robot Autom. Mag. 14(2), 18–29 (2007).CrossRefGoogle Scholar
Collins, S., Ruina, A., Tedrake, R., Wisse, M. and Wisse, M., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307(5712), 1082–1085 (2005).CrossRefGoogle ScholarPubMed
Ma, W. L., Hereid, A., Hubicki, C. M. and Ames, A. D., “Efficient HZD Gait Generation for Three-Dimensional Underactuated Humanoid Running,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (2016) pp. 5819–5825.Google Scholar
Cao, Y., Suzuki, S. and Hoshino, Y., “Uphill and level walking of a three-dimensional biped quasi-passive walking robot by torso control,“ Robotica 34(3), 483–496 (2016).CrossRefGoogle Scholar
Roozing, W., Li, Z., Caldwell, D. G. and Tsagarakis, N. G., “Design optimisation and control of compliant actuation arrangements in articulated robots for improved energy efficiency,” IEEE Robot. Autom. Lett. 1(2), 1110–1117 (2016).CrossRefGoogle Scholar
Vu, H. Q., Yu, X., Iida, F. and Pfeifer, R.,“Improving energy efficiency of hopping locomotion by using a variable stiffness actuator,” IEEE ASME Trans. Mechatron. 21(1), 472–486 (2016).Google Scholar
Sohn, K. and Oh, P., “Applying Human Motion Capture to Design Energy-Efficient Trajectories for Miniature Humanoids,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (2012) pp. 3425–3431.Google Scholar
Tomoyuki, T., Azuma, Y. and Shibata, T., “Acquisition of Energy-Efficient Bipedal Walking Using CPG-Based Reinforcement Learning,” IEEE/RSJ International Conference on Intelligent Robots and Systems (2009) pp. 827–832.Google Scholar
Kormushev, P., Ugurlu, B., Caldwell, D. G. and Tsagarakis, N. G., “Learning to exploit passive compliance for energy-efficient gait generation on a compliant humanoid,” Auton. Robot. 43(1), 79–95 (2019).CrossRefGoogle Scholar
Dau, V. H., Chew, C. M. and Poo, A. N., “Achieving energy-efficient bipedal walking trajectory through GA-based optimization of key parameters,” Int. J. H. R. 6(4), 609–629 (2009)Google Scholar
Hasaneini, S. J., Bertram, J. E. and Macnab, C. J., “Energy-optimal relative timing of stance-leg push-off and swing-leg retraction in walking,” Robotica 35(3), 654–686 (2017).CrossRefGoogle Scholar
Zhang, R., Liu, H., Meng, F., Kang, R., Yu, Z., Ming, A. and Huang, Q., “Energy Efficiency and Speed Optimization by Squad-Unit Genetic Algorithm for Bipedal Walking,” IEEE International Conference on Robotics and Biomimetics (2018) pp. 661–667.Google Scholar
Liang, Y., Liu, Z. and Chen, Y., “Energy efficient walking control for biped robots using interval type-2 fuzzy logic systems and optimized iteration algorithm,“ ISA Trans. 87, 143–153 (2019).Google Scholar
An, K., Liu, Y., Li, Y., Zhang, Y. and Liu, C., “Energetic walking gaits studied by a simple actuated inverted pendulum model,” J. Mech. Sci. Technol. 32(5), 2273–2281 (2018).CrossRefGoogle Scholar
Wang, Z., Yan, G., Lin, Z., Tang, C. and Song, S., “A switching control strategy for energy efficient walking on uneven surfaces,” Int. J. H. R. 12(04), 1550015 (2015).Google Scholar
Choi, C. and Frazzoli, E., “Torque Efficient Motion Through Singularity,” Proceedings of IEEE International Conference on Robotics and Automation (2017) pp. 5012–5018.Google Scholar
Hasaneini, S., Macnab, C., Bertram, J. and Leung, H., “Optimal Relative Timing of Stance Push-Off and Swing Leg Retraction,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (2013) pp. 3616–3623.Google Scholar
Kajita, S., Matsumoto, O. and Saigo, M., “Real-Time 3D Walking Pattern Generation for a Biped Robot with Telescopic Legs,” Proceedings of IEEE International Conference on Robotics and Automation (2001) pp. 2299–2306.Google Scholar
Brandao, M., Hashimoto, K., Santos-Victor, J. and Takanishi, A., “Footstep planning for slippery and slanted terrain using human-inspired models,” IEEE Trans. Robot. 32(4), 868–879 (2016).CrossRefGoogle Scholar
Santacruz, C. and Nakamura, Y., “Walking Motion Generation of Humanoid Robots: Connection of Orbital Energy Trajectories via Minimal Energy Control,” Proceedings of IEEE-RAS International Conference on Humanoid Robots (2011) pp. 695–700.Google Scholar
Lanari, L., Hutchinson, S. and Marchionni, L., “Boundedness Issues in Planning of Locomotion Trajectories for Biped Robots,” Proceedings of IEEE-RAS International Conference on Humanoid Robots (2014) pp. 951–958.Google Scholar
Lanari, L. and Hutchinson, S., “Optimal Double Support Zero Moment Point Trajectories for Bipedal Locomotion,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (2016) pp. 5162–5168.Google Scholar
Vukobratović, M. and Stepanenko, J., “On the stability of anthropomorphic systems,” Math. Biosci. 15(1–2), 1–37 (1972).Google Scholar
Erbatur, K. and Kurt, O., “Natural ZMP trajectories for biped robot reference generation,” IEEE Trans. Ind. Electron. 56(3), 835–845 (2009).CrossRefGoogle Scholar
Li, T. H. S., Su, Y. T., Liu, S. H., Hu, J. J. and Chen, C. C., “Dynamic balance control for biped robot walking using sensor fusion, kalman filter, and fuzzy logic,” IEEE Trans. Ind. Electron. 59(11), 4394–4408 (2012).Google Scholar
Zhu, H., Luo, M., Mei, T., Zhao, J., Li, T. and Guo, F., “Energy-efficient bio-inspired gait planning and control for biped robot based on human locomotion analysis,” J. Bionic. Eng. 13(2), 271–282 (2016).Google Scholar
Shin, H. K. and Kim, B. K., “Energy-efficient gait planning and control for biped robots utilizing the allowable ZMP region,” IEEE Trans. Robot. 30(4), 986–993 (2014).CrossRefGoogle Scholar
Ogura, Y., Shimomura, K., Kondo, H., Morishima, A., Okubo, T., Momoki, S., Lim, H. O. and Takanishi, A., “Human-Like Walking with Knee Stretched, Heel-Contact and Toe-Off Motion by a Humanoid Robot,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (2006) pp. 3976–3981.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. H. R. 13(4), 1650019 (2016).Google Scholar
Griffin, R. J., Bertrand, S., Wiedebach, G., Leonessa, A. and Pratt, J., “Capture Point Trajectories for Reduced Knee Bend Using Step Time Optimization,” Proceedings of IEEE-RAS International Conference on Humanoid Robotics (2017) pp. 25–30.Google Scholar
Zhu, H., Luo, M. and Li, J., “Optimization-based gait planning and control for biped robots utilizing the optimal allowable ZMP variation region,“ Ind. Robot 45(4), 469–489 (2018).CrossRefGoogle Scholar
Kajita, S., Benallegue, M., Cisneros, R., Sakaguchi, T., Nakaoka, S. I., Morisawa, M., Kaneko, K. and Kanehiro, F., “Biped Walking Pattern Generation Based on Spatially Quantized Dynamics,” Proceedings of IEEE-RAS International Conference on Humanoid Robotics (2017) pp. 599–605.Google Scholar
Ding, J., Zhou, C. and Xiao, X., “Energy-Efficient Bipedal Gait Pattern Generation via Com Acceleration Optimization,” Proceedings of IEEE-RAS International Conference on Humanoid Robots (2018) pp. 238–244.Google Scholar
Ding, J. and Xiao, X., “Two-stage optimization for energy-efficient bipedal walking,” J. Mech. Sci. Technol. 34(9), 3833–3844 (2020).CrossRefGoogle Scholar
Sato, T., Sakaino, S. and Ohnishi, K., “Real-time walking trajectory generation method with three-mass models at constant body height for three-dimensional biped robots,” IEEE Trans. Ind. Electron. 58(2), 376–383 (2011).CrossRefGoogle Scholar
Albert, A. and Gerth, W., “Analytic path planning algorithms for bipedal robots without a trunk,” J. Intell. Robot Syst. 36(2), 109–127 (2003).CrossRefGoogle Scholar
Sato, T., Sakaino, S. and Ohnishi, K., “Real-Time Walking Trajectory Generation Method at Constant Body Height in Single Support Phase for Three-Dimensional Biped Robot,” Proceedings of IEEE International Conference on Industrial Technology (2009) pp. 1–6.Google Scholar
Shimmyo, S., Sato, T. and Ohnishi, K., “Biped walking pattern generation by using preview control based on three-mass model,” IEEE Trans. Ind. Electron. 60(11), 5137–5147 (2013).CrossRefGoogle Scholar
Luo, R. C. and Chen, C. C., “Biped walking trajectory generator based on three-mass with angular momentum model using model predictive control,” IEEE Trans. Ind. Electron. 63(1), 268–276 (2016).CrossRefGoogle Scholar
Kim, I. S., Han, Y. J. and Hong, Y. D., “Stability control for dynamic walking of bipedal robot with real-time capture point trajectory optimization,” J. Intell. Robot Syst. 96(3), 1–17 (2019).CrossRefGoogle Scholar
Shin, H. K. and Kim, B. K., “Energy-efficient gait planning and control for biped robots utilizing vertical body motion and allowable ZMP region,” IEEE Trans. Ind. Electron. 62(4), 2277–2286 (2015).CrossRefGoogle Scholar
Englsberger, J., Ott, C. and Albu-Schäffer, A., “Three-dimensional bipedal walking control based on divergent component of motion,” IEEE Trans. Robot. 31(2), 355–368 (2015).CrossRefGoogle 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,” Proceedings of IEEE International Conference on Robotics and Automation (2003) pp. 1620–1626.Google Scholar