Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T19:28:32.741Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust Control of Semi-passive Biped Dynamic Locomotion based on a Discrete Control Lyapunov Function

Published online by Cambridge University Press:  26 November 2019

Chengju Liu Open the ORCID record for Chengju Liu [Opens in a new window] ,
Jing Yang ,
Kang An ,
Ming Liu  and
Qijun Chen
Chengju Liu
Affiliation:
School of Electronics and Information Engineering, Tongji University, Shanghai, China. E-mails: liuchengju@tongji.edu.cn, 1252583@tongji.edu.cn, qjchen@tongji.edu.cn
Jing Yang
Affiliation:
School of Electronics and Information Engineering, Tongji University, Shanghai, China. E-mails: liuchengju@tongji.edu.cn, 1252583@tongji.edu.cn, qjchen@tongji.edu.cn
Kang An*
Affiliation:
The College of Information, Mechanical and Electrical Engineering, Shanghai Normal University, Shanghai, China
Ming Liu
Affiliation:
Department of Computer Science & Engineering, the Hong Kong University of Science and Technology, Hong Kong, China. E-mail: eelium@ust.hk
Qijun Chen
Affiliation:
School of Electronics and Information Engineering, Tongji University, Shanghai, China. E-mails: liuchengju@tongji.edu.cn, 1252583@tongji.edu.cn, qjchen@tongji.edu.cn
*
*Corresponding author. E-mail: ankang526@foxmail.com
Get access Rights & Permissions [Opens in a new window]

Summary

This paper focuses on robust control of a simplest passive model, which is established on a DCLF (discrete control Lyapunov function) -based control system, and presents gait transition method based on the study of purely passive walker. Firstly, the DCLF is introduced to stabilize walking process between steps exponentially by modulating the length of next step. Next, the swing leg trajectory from mid-stance position to foot-strike can be planned. Then the control law is calculated to resist external disturbance. Besides, an impulse is added just before foot-strike to realize a periodic walking pattern on flat or uphill ground. With walking terrain varying, the robot can transit to an adaptive walking gait in a few steps. With different push or pull disturbances acting on hip joint and the robot gait transiting on a continuously slope-changing downhill, the effectiveness of the presented DCLF-based method is verified using simulation experiments. The ability to walk on a changing environment is also presented by simulation results. The insights of this paper can help to develop a robust control method and adaptive walking of dynamic passive locomotion robots.

Keywords

Biped robotSemi-passive dynamic walkingDiscrete control Lyapunov function (DCLF)Gait transitionDynamic model
Type
Articles
Information
Robotica , Volume 38 , Issue 8 , August 2020 , pp. 1345 - 1358
Copyright
© Cambridge University Press 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Yao, X. Y., Ding, H. F. and Ge, M. F., “Task-space tracking control of multi-robot systems with disturbances and uncertainties rejection capability,” Nonlinear Dyn. 4, 1–16 (2018).Google Scholar
Khadiv, M., Moosavian, S. A. A., Yousefikoma, A. and Sadedel, M., “Optimal gait planning for humanoids with 3D structure walking on slippery surfaces,” Robotica 35(3), 569–587 (2017).CrossRefGoogle Scholar
Grizzle, J. W., Abba, G. and Plestan, F., “Asymptotically stable walking for biped robots: Analysis via systems with impulse effects,” IEEE Trans. Autom. Contr. 46(1), 51–64 (2001).CrossRefGoogle Scholar
Hasaneini, S. J., Bertram, J. E. A. and Macnab, C. J. B.. “Energy-optimal relative timing of stance-leg push-off and swing-leg retraction in walking,” Robotica 35(3), 654–686 (2017).CrossRefGoogle Scholar
Kinugasa, T. and Sugimoto, Y., “Dynamically and biologically inspired legged locomotion: A review,” J. Robot Mechatron. 29(3), 456–470 (2017).CrossRefGoogle Scholar
Zhakatayev, A., Rubagotti, M. and Varol, H. A., “Closed-loop control of variable stiffness actuated robots via nonlinear model predictive control,” IEEE Access 3, 235–248 (2017).CrossRefGoogle 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. Robot. Autom. 17(3), 280–289 (2001).CrossRefGoogle Scholar
McGeer, T.. “Passive dynamic walking,” Int. J. Robot. Res. 9(9), 62–82 (1990).CrossRefGoogle Scholar
Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M., “The simplest walking model: Stability, complexity, and scaling,” J. Biomech. Eng. 120(2), 281 (1998).CrossRefGoogle Scholar
Wisse, M., Schwab, A. L. and Helm, F. C.. “Passive dynamic walking model with upper body,” Robotica 22(6), 681–688 (2004).CrossRefGoogle Scholar
Wisse, M., Feliksdal, G., van Frankkenhuyzen, J. and Moyer, B., “Passive-based walking robot,” IEEE Robot. Autom. Mag. 14(2), 52–62 (2007).CrossRefGoogle Scholar
Hirata, K. and Kokame, H., “Stability Analysis of Linear Systems with State Jump-Motivated by Periodic Motion Control of Passive Walker,” Proceedings of 2003 IEEE Conference on Control Applications, Taipei, Taiwan (2003).Google Scholar
Gritli, H., Belghith, S. and Khraief, N., “OGY-based control of chaos in semi-passive dynamic walking of a torso-driven biped robot,” Nonlinear Dyn. 79(2), 1363–1384 (2015).CrossRefGoogle Scholar
Gritli, H. and Belghith, S., “Bifurcations and chaos in the semi-passive bipedal dynamic walking model under a modified OGY-based control approach,” Nonlinear Dyn. 83(4), 1955–1973 (2016).CrossRefGoogle Scholar
Huang, Y. and Wang, Q., “Torque-stiffness-controlled dynamic walking: Analysis of the behaviors of bipeds with both adaptable joint torque and joint stiffness,” IEEE Robot. Autom. Mag. 23(1), 71–82 (2016).CrossRefGoogle Scholar
Huang, Y., Vanderborght, B., Van, H. R. and Wang, Q., “Torque-stiffness-controlled dynamic walking with central pattern generators,” Biol. Cybern. 108(6), 803 (2014).CrossRefGoogle ScholarPubMed
Huang, Y., Huang, Q. and Wang, Q., “Chaos and bifurcation control of torque-stiffness-controlled dynamic bipedal walking,” IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1229–1240 (2017).CrossRefGoogle Scholar
Osuka, K. and Sugimoto, Y., “Stabilization of quasi-passive-dynamic-walking based on delayed feedback control,” Int. Conf. Cont. Autom. Robot. Vis. 2, 803–808 (2003).Google Scholar
Huang, Y., Gao, Y., Chen, B. and Wang, Q., “Adding adaptable stiffness joints to CPG-based dynamic bipedal walking generates human-like gaits,” In: Robot Intelligence Technology and Applications 2, Advances in Intelligent Systems and Computing, vol. 274 (Kim, J.-H., Matson, E., Myung, H., Xu, P. and Karray, F., eds.) (Springer International Publishing, 2014) pp. 569–580.Google Scholar
Huang, Y., Chen, L., Vanderborght, B. and Wang, Q., “Transitions of Three Gaits in Dynamic Bipedal Robot with Adaptable Joint Stiffness,” IEEE International Conference on Advanced Intelligent Mechatronics (AIM), Busan, Korea (2015) pp. 1–6.Google Scholar
Borzova, E. and Hurmuzlu, Y., “Passively walking five-link robot,” Automatica 40(1), 621–629 (2014). Pergamon Press, Inc.CrossRefGoogle Scholar
Tavakoli, A. and Hurmuzlu, Y., “Robotic locomotion of three generations of a family tree of dynamical systems. Part I: Passive gait patterns,” Nonlinear Dyn. 73(3), 1969–1989 (2013).CrossRefGoogle Scholar
Tavakoli, A. and Hurmuzlu, Y., “Robotic locomotion of three generations of a family tree of dynamical systems. Part II: Impulsive control of gait patterns,” Nonlinear Dyn. 73(3), 1991–2012 (2013).CrossRefGoogle Scholar
Tan, F., Fu, C. and Chen, K., “Biped Blind Walking on Changing Slope with Reflex Control System,” IEEE International Conference on Robotics and Automation (ICRA), Anchorage, Alaska (2010) pp. 1709–1714.Google Scholar
Fu, C., “Perturbation Recovery of Biped Walking by Updating the Footstep,” International Conference on Intelligent Robots and Systems (IROS), Chicago (2014) pp. 2509–2514.Google Scholar
Fu, C., Tan, F. and Chen, K., “A simple walking strategy for biped walking based on an intermittent sinusoidal oscillator,” Robotica 28(6), 869–884 (2010).CrossRefGoogle Scholar
Bhounsule, P. A., “Control of a compass gait walker based on energy regulation using ankle push-off and foot placement,” Robotica 33(6), 1314–1324 (2015).CrossRefGoogle Scholar
Bhounsule, P. A., “Foot placement in the simplest slope walker reveals a wide range of walking solutions,” IEEE Trans. Robot. 30(5), 1255–1260 (2014).CrossRefGoogle Scholar
Harata, Y. and Asano, F., “Asymptotically Stable and Deadbeat gait Generation of Four-Linked Bipedal Walker by Adjustment Control of Heel Strike Posture,” IEEE-RAS International Conference on Humanoid Robots, Osaka, Japan (2012) pp. 495–501.Google Scholar
Bhounsule, P. A. and Zamani, A., “Stable bipedal walking with a swing-leg protraction strategy,” J. Biomech. 51, 123–127 (2017).CrossRefGoogle ScholarPubMed
Zamani, A. and Bhounsule, P. A., “Foot Placement and Ankle Push-Off Control for the Orbital Stabilization of Bipedal Robots,” IEEE International Conference on Intelligent Robots and Systems (IROS), Vancouver, Canada (2017).CrossRefGoogle Scholar
An, K. and Chen, Q., “A passive dynamic walking model based on knee-bend behaviour: Stability and adaptability for walking down steep slopes,” Int. J. Adv. Robot. Syst. 10(4), 1–11 (2013).CrossRefGoogle Scholar
An, K. and Chen, Q., “Dynamic optimization of a biped model: Energetic walking gaits with different mechanical and gait parameters,” Adv. Mech. Eng. 7(5), 1–13 (2015).CrossRefGoogle Scholar
An, K., Li, C., Fang, Z. and Liu, C., “Efficient walking gait with different speed and step length: Gait strategies discovered by dynamic optimization of a biped model,” J. Mech. Sci. Technol. 31(4), 1909–1919 (2017).CrossRefGoogle Scholar
Bhounsule, P. A. and Zamani, A.. “A discrete control lyapunov function for exponential orbital stabilization of the simplest walker,” J. Mech. Robot. 9(5), 051011 (2017).CrossRefGoogle Scholar
Ralston, H. J., “Energy-speed relation and optimal speed during level walking,” Int. Z. Angew. Physiol. 17(4), 277–283 (1958).Google ScholarPubMed
Alexander, R. M. and Maloiy, G. M. O., “Stride lengths and stride frequencies of primates,” Proc. Zool. Soc. London 202(4), 577–582 (1984).CrossRefGoogle Scholar