Abstract
In this paper, the tracking of the zero moment point (ZMP) trajectory for humanoid locomotion is addressed. For that, a combination of a repetitive controller (RC) and a linear quadratic regulator (LQR) is proposed. The RC controller achieves a zero steady state tracking error for any periodic desired output with a fixed period. Here, the robot model is simplified as a cart table model. In the first stage, a walking pattern with constant gait is considered to allow the use of a repetitive controller. The results are then compared to a classical PD control. In the second part, the proposed controller is applied to track a desired ZMP profile generated using a central pattern generator (CPG). Here, the speed of the oscillator is adjusted via a proper selection of the parameters of the CPG and the RC design is simultaneously updated to assure the perfect tracking of the ZMP.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Gupta and A. Kumar, A brief review of dynamics and control of underactuated biped robots, Advanced Robotics, 31 (12) (2017) 607–623.
J. Li, S. Li, Y. Ke and S. Li, Safety design and performance analysis of humanoid rehabilitation robot with compliant joint, Journal of Mechanical Science and Technology, 33 (1) (2019) 357–366.
M. Srinivasan and A. Ruina, Idealized walking and running gaits minimize work, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 463 (2086) (2007) 2429.
J. Nassour et al., Multi-layered multi-pattern CPG for adaptive locomotion of humanoid robots, Biol Cybern, 108 (3) (2014) 291–303.
T. McGeer, Passive dynamic walking, The International Journal of Robotics Research, 9 (2) (1990) 62–82.
S. Collins et al., Efficient bipedal robots based on passive-dynamic walkers, Science, 307 (5712) (2005) 1082–1085.
M. Arbulú et al., The Rh-1 full-size humanoid robot: Design, walking pattern generation and control, Applied Bionics and Biomechanics, 6 (3-4) (2009) 301–344.
M. Martins et al., A review of the functionalities of smart walkers, Medical Engineering & Physics, 37 (10) (2015) 917–928.
Y. Nakamura et al., Reinforcement learning for a biped robot based on a CPG-actor-critic method, Neural Networks, 20 (6) (2007) 723–735.
C. Liu et al., Adaptive walking control of biped robots using online trajectory generation method based on neural oscillators, Journal of Bionic Engineering, 13 (4) (2016) 572–584.
M. Vukobratovic and B. Borovac, Zero-moment point -Thirty five years of its life, International J. of Humanoid Robotics, 1 (2004) 157–173.
A. S. A. Yahmedi and M. A. Sayari, Efficient walking of a simple biped with a torso, 2nd Middle East Conference on Biomedical Engineering (2014) 382–384.
M. Tomizuka and C. Kempf, Design of discrete time repetitive controllers with applications to mechanical systems, IFAC Proceedings Volumes, 23 (8, Part 3) (1990) 243–248.
M. Yamada, Z. Riadh and N. Mizuno, Adaptive zero phase error tracking controller with precision tracking performance, IFAC Proceedings Volumes, 30 (11) (1997) 837–842.
S. Kajita et al., Biped walking pattern generation by using preview control of zero-moment point, IEEE International Conference on Robotics and Automation, 2 (2003) 1620–1626.
C. Liu, C. G. Atkeson and J. Su, Biped walking control using a trajectory library, Robotica, 31 (2) (2012) 311–322.
G. A. Ramos, R. Costa-Castelló and J. M. Olm, Repetitive control, Digital Repetitive Control under Varying Frequency Conditions, Lecture Notes in Control and Information Sciences, Springer, Berlin, Heidelberg, 446 (2013).
W. Huang, C.-M. Chew, Y. Zheng and G.-S. Hong, Bio-inspired locomotion control with coordination between neural oscillators, I. J. Humanoid Robotics, 6 (2009) 585–608.
K. Matsuoka, Sustained oscillations generated by mutually inhibiting neurons with adaptation, Cybern, 52 (1985) 367.
Acknowledgments
The authors acknowledge The Research Council of Oman for their financial support.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Hak Yi
Mohamed A. Sayari was born in Tunis, Tunisia in 1989. He received the M. Eng. degree in electromechanical engineering from the National Engineering School of Sfax, Tunisia in 2013 where he is currently pursuing a Ph.D. in Mechanical Engineering. He received as well the MITx credential in Supply Chain Management in 2018. He joined in 2013 Esi-Group, France as a project engineer and worked as a Research Assistant and Consultant for the Sultan Qaboos University, Oman where he has been conducting a leading research on the biologically inspired locomotion control for humanoid robots. He is currently an Automation Specialist for a Consulting Firm in Canada and is a member of the LASEM, Laboratory. His research interests are in the broad area of artificial intelligence, automation and control systems with a focus on humanoid locomotion.
Riadh Zaier (SM’99) was born in Nabeul, Tunisia in 1966. He received the B.E. degree in electromechanical engineering from the National Engineering School of Tunis, Tunisia in 1991, and the M. Eng. and Dr. Eng. Degrees, both in Discrete-Time Tracking Control Systems from the Department of Systems Engineering, Nagoya Institute of Technology, Japan in 1996 and 1999, respectively. He joined Fujitsu Automation Ltd. in 1999. Then he joined Fujitsu Laboratories Ltd., as a researcher in 2004. He has been conducting a leading research on the biologically inspired locomotion control for humanoid robots, which were demonstrated by sound IEEE conference papers, best paper awards in Clawar 2012, Paris, and six issued US Patents. He is currently a faculty member of Sultan Qaboos University and Coordinator of the Mechatronics Engineering Program. His research interests are in the broad area of intelligent sensing and information fusion and control systems. He is a member of IEEE Society.
Neila Khabou Masmoudi was born in Nabeul, Tunisia in 1962. She received the BE. degree in mechanical conception from ENSET of Tunisia, Tunisia, in 1985, the M.Tech. in mechanical from National Engineering School of Tunisia I in 1987 and Ph.D. degrees in mechanical of materials of the National College of Art and Design in Paris (ENSAM Paris) in 1990. In 1990, she joined the Department of Mechanical Engineering of National Engineering School of Sfax, University of Sfax, Tunisia as an Assistant Professor, became an Associate Professor in 1994, and a Professor in 2014. Her current research interests include mechanical of materials, mechanical design.
Rights and permissions
About this article
Cite this article
Sayari, M.A., Zaier, R. & Masmoudi, N. Perfect tracking of ZMP trajectory for humanoid locomotion using repetitive control. J Mech Sci Technol 33, 6037–6043 (2019). https://doi.org/10.1007/s12206-019-1147-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-019-1147-7