Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T10:00:43.644Z Has data issue: false hasContentIssue false
  • English
  • Français

Robust tracking of bio-inspired references for a biped robot using geometric algebra and sliding mode control

Published online by Cambridge University Press:  27 February 2014

J. Oviedo-Barriga ,
L. González-Jiménez ,
B. Castillo-Toledo  and
E. Bayro-Corrochano
J. Oviedo-Barriga
Affiliation:
CINVESTAV, Campus Guadalajara, Av. Del Bosque 1145, Col. El Bajío, C.P. 45019, Zapopan, Jalisco, México
L. González-Jiménez
Affiliation:
CINVESTAV, Campus Guadalajara, Av. Del Bosque 1145, Col. El Bajío, C.P. 45019, Zapopan, Jalisco, México
B. Castillo-Toledo
Affiliation:
CINVESTAV, Campus Guadalajara, Av. Del Bosque 1145, Col. El Bajío, C.P. 45019, Zapopan, Jalisco, México
E. Bayro-Corrochano*
Affiliation:
CINVESTAV, Campus Guadalajara, Av. Del Bosque 1145, Col. El Bajío, C.P. 45019, Zapopan, Jalisco, México
*
*Corresponding author. E-mail: edb@gdl.cinvestav.mx
Get access Rights & Permissions [Opens in a new window]

Summary

Controlling a walking biped robot is a challenging problem due to the robot's complex and uncertain dynamics. In order to tackle this problem, we propose a sliding mode controller based on a dynamic model that we obtained using the conformal geometric algebra (CGA) approach. An important contribution of this paper is the development of algorithms using the CGA framework. The CGA framework permits us to use lines, points, and other geometric entities to obtain the Lagrange equations of the system. The references for the joints of the robot were obtained in a bio-inspired way following the kinematics of a walking human body. The first and second derivatives of the reference signal were obtained via an exact robust differentiator based on a high-order sliding mode. We analyzed the performance of the proposed control schemes by using bio-inspired walking patterns and simulations.

Keywords

Bio-inspired signalTrackingConformal geometric algebra
Type
Articles
Information
Robotica , Volume 33 , Issue 1 , January 2015 , pp. 209 - 224
Copyright
Copyright © Cambridge University Press 2014 

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

1.Vukobratovic, M. and Borovac, B., “Zero-moment point thirty five years of its life,” Int. J. Humanoid Robot. 1 (1), 157–173 (2004).CrossRefGoogle Scholar
2.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 the IEEE International Conference on Robotics and Automation (ICRA 2003), vol. 2 (2003) pp. 1620–1626.Google Scholar
3.Kajita, S., Kanehiro, F., Kaneko, K., Yokoi, K. and Hirukawa, H., “The 3D Linear Inverted Pendulum Mode: A Simple Modeling for a Biped Walking Pattern Generation,” Proceedings of the 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2001), vol. 1 (2001) pp. 239–246.Google Scholar
4.Choi, Y., You, B.-J. and Oh, S.-R., “On the Stability of Indirect ZMP Controller for Biped Robot Systems,” Proceedings of the 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2004), vol. 2 (2004) pp. 1966–1971.Google Scholar
5.Park, J. and Youm, Y., “General ZMP Preview Control for Bipedal Walking,” Proceedings of the 2007 IEEE International Conference on Robotics and Automation (ICRA 2007) (2007) pp. 2682–2687.Google Scholar
6.Noh, K.-K., Kim, J.-G. and Huh, U.-Y., “Stability Experiment of a Biped Walking Robot with Inverted Pendulum,” Proceedings of the 30th Annual Conference of IEEE Industrial Electronics Society (IECON 2004), vol. 3 (2004) pp. 2475–2479.Google Scholar
7.Park, I.-W., Kim, J.-Y. and Oh, J.-H., “Online Biped Walking Pattern Generation for Humanoid Robot KHR-3 (KAIST Humanoid Robot-3: HUBO),” Proceedings of the 6th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2006) (2006) pp. 398–403.Google Scholar
8.Katayama, T., Ohki, T., Inoue, T. and Kato, T., “Design of an optimal controller for a discrete-time system subject to previewable demand,” Int. J. Control 41 (3), 677–699 (1985).Google Scholar
9.Bayro-Corrochano, E., Geometric Computing: For Wavelet Transforms, Robot Vision, Learning, Control and Action (Springer, London, 2010).Google Scholar
10.Utkin, V. I., Guldner, J. and Shi, J., Sliding Mode Control in Electromechanical Systems (Taylor and Francis, Boca Raton, FL, 1999).Google Scholar
11.Li, H., Hestenes, D. and Rockwood, A., “Generalized Homogeneous Coordinates for Computational Geometry,” In: Geometric Computing with Clifford Algebras (Somer, G., ed.) (Springer-Verlag, Heidelberg, Germany, 2001) pp. 27–52.Google Scholar
12.Zamora, J. and Bayro-Corrochano, E., “Kinematics and Differential Kinematics of Binocular Heads,” Proceedings of the International Conference of Robotics and Automation (ICRA 2006), Orlando, FL (2006) pp. 4130–4135.Google Scholar
13.Zamora, J. and Bayro-Corrochano, E., “Parallel Forward Dynamics: A Geometric Approach,” Proceedings of the International Conference on Intelligent Robots and Systems (IROS 2010), Taiwan (2010) pp. 18–22.Google Scholar
14.Gonzáles-Jiménez, L., Loukianov, A. and Bayro-Corrochano, E., “Integral Nested Sliding Mode Control for Robotic Manipulators,” Proceedings of the 17th World Congress of the International Federation of Automatic Control, Seoul, Korea (2008) pp. 9899–9904.Google Scholar
15.Levant, A., “Higher order modes, differentiation and output feedback control,” Int. J. Control 76, 924–941 (2003).CrossRefGoogle Scholar
16.Levant, A., “Sliding order and sliding accuracy in sliding mode control,” Int. J. Control 58, 1247–1263 (1993).Google Scholar
17.Moreno, J. A. and Osorio, M. “A Lyapunov Approach to Second-Order Sliding Mode Controllers and Observers,” Proceedings of the 47th Conference on Decision and Control, Cancún, México (Dec. 9–11, 2008) pp. 2856–2861.Google Scholar
18.Oviedo-Barriga, J., Carbajal-Espinosa, O., González-Jiménez, L., Castillo-Toledo, B. and Bayro-Corrochano, E., “Robust Tracking of Bio-Inspired References for a Biped Robot Using Geometric Algebra and Sliding Mode,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA 2013), Karlsruhe, Germany (May 6–10, 2013) pp. 5297–5302.Google Scholar