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Robust control of underactuated bipeds using sliding modes

Published online by Cambridge University Press:  01 May 2007

Mehdi Nikkhah ,
Hashem Ashrafiuon  and
Farbod Fahimi
Mehdi Nikkhah
Affiliation:
Department of Mechanical Engineering, Villanova University, Villanova, PA 19085, USA
Hashem Ashrafiuon*
Affiliation:
Department of Mechanical Engineering, Villanova University, Villanova, PA 19085, USA
Farbod Fahimi
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada
*
*Corresponding author. E-mail: [email protected]
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Summary

The purpose of this paper is to present a robust tracking control algorithm for underactuated biped robots capable of self-balancing in the presence of external disturbances. The biped is modeled as a five-link planar robot with four actuators located at hip and knee joints. A sliding mode control law has been developed for the biped to follow a human-like gait trajectory while keeping the torso nearly upright. The control forces are calculated by defining four first-order sliding surfaces as a linear combination of the torso and the four joint tracking errors. The control approach is shown to guarantee that all trajectories will reach and stay on these surfaces during each step, while the walking cycle stability is maintained through a Lyapunov function. The criteria for asymptotic stability of the surfaces are presented and a numerical search method is implemented for the selection of the corresponding surface parameters. The paper further investigates the robustness of the controller in response to disturbances. Numerical simulations demonstrate the tracking stability of the biped's multistep walk and its human-like response to an external disturbance.

Keywords

Biped robotsUnderactuated systemsSliding mode controlStability analysis
Type
Article
Information
Robotica , Volume 25 , Issue 3 , May 2006 , pp. 367 - 374
Copyright
Copyright © Cambridge University Press 2007

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References

1.Raibert, M. H., Legged Robots That Balance (MIT Press, Cambridge, MA, 1986).Google Scholar
2.Vukobratovic, M., Borovac, B., Surla, D. and Stokic, D.. Biped Locomotion (Springer-Verlag, Berlin, Germany, 1990).CrossRefGoogle Scholar
3.Chew, C. M., Choong, E., Poo, A. N. and Hong, G. S., “From Science Fiction to Reality–Humanoid Robots,” International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment, and Management, Manila, Philippines (Mar. 2003).Google Scholar
4.Lohmeier, S., Löffler, K., Gienger, M., Ulbrich, H. and Pfeiffer, F., “Computer System and Control of Biped johnnie”, Proceedings of the IEEE International Conference on Robotics and Automation, New Orleans, LA (Apr. 2004) pp. 4222–4227.Google Scholar
5.Mitobe, K., Mori, N., Aida, K. and Nasu, Y., “Nonlinear Feedback Control of a Biped Walking Robot”, Proceedings of the IEEE International Conference on Robotics and Automation, Nagoya, Japan (May 1995) pp. 2865–2870.Google Scholar
6.Tzafestas, S., Raibert, M. H. and Tzafestas, C., “Robust sliding-mode control applied to a 5-link biped robot,” J. Intell. Robot. Syst. Theory Appl. 15, 67–133 (1996).Google Scholar
7.Tzafestas, S. G., Krikochoritis, T. E. and Tzafestas, C. S., “Robust sliding-mode control of nine-link biped robot walking,” J. Intell. Robot. Syst. Theory Appl. 20, 375–402 (1997).Google Scholar
8.Chang, T. H. and Hurmuzlu, Y., “Sliding control without reaching phase and its application to bipedal locomotion,” J. Dyn. Syst. Meas. Control, Trans. ASME 115, 447–455 (1993).CrossRefGoogle Scholar
9.Mu, X. and Wu, Q., “Development of a complete dynamic model of a planar five-link biped and sliding mode control of its locomotion during the double support phase,” Int. J. Control 77 (8), 789–799 (2004).Google Scholar
10.Vanderborght, B., Verrelst, B., Ham, R. Van and Lefeber, D., “Controlling a bipedal walking robot actuated by pleated pneumatic artificial muscles,” Robotica 24, 401–410 (2006).Google Scholar
11.Goswami, A., Espiau, B. and Keramane, A., “Limit Cycles and their Stability in a Passive Bipedal Gait”, Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, MN (Apr. 1996) pp. 246–251.Google Scholar
12.Grizzle, J. W., Abba, G. and Plestan, F., “Asymptotically stable walking for biped robots: Analysis via systems with impulse effects”, IEEE Trans. Autom. Control 46, 51–64 (2001).Google Scholar
13.Plestan, F., Grizzle, J. W., Westervelt, E. R. and Abba, G., “Stable walking of a 7-DOF biped robot,” IEEE Trans. Robot. Autom. 19, 653–668 (2003).CrossRefGoogle Scholar
14.Miossec, S. and Aoustin, Y., “A simplified stability study for a biped walk with underactuated and overactuated phases”, Int. J. Robot. Res. 24, 537–551 (2005).CrossRefGoogle Scholar
15.Plestan, F. and Laghrouche, S., “Sliding Mode Controller for the Walking of a Biped Robot: Arbitrary Order Sliding Mode Approach”, Proceedings of the Sixth International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, Catania, Italy (Sep. 2003) pp. 181–188.Google Scholar
16.Chevallereau, C., “Time-scaling control for an underactuated biped robot,” IEEE Trans. Robot. Autom. 19, 362–368 (2003).CrossRefGoogle Scholar
17.Chevallereau, C., Formal'sky, A. and Djoudi, D., “Tracking a joint path for the walk of an underactuated biped,” Robotica 22, 15–28 (2004).CrossRefGoogle Scholar
18.Chemori, A. and Loria, A., “Control of a planar underactuated biped on a complete walking cycle,” IEEE Trans. Autom. Control 49, 838–843 (2004).CrossRefGoogle Scholar
19.Aoustin, Y. and Formal'sky, A., “On the stabilization of a biped vertical posture in single support using internal torques,” Robotica 23, 65–74 (2005).Google Scholar
20.Nikkhah, M., Ashrafiuon, H. and Fahimi, F., “Sliding Mode Control of Underactuated Biped Robots”, Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Orlando, FL (Nov. 2005) pp. 1283–1288.Google Scholar
21.Spong, M. W., “Underactuated Mechanical Systems,” In: Control Problems in Robotics and Automation (Siciliano, B. and Valavanis, K. P., eds.) (Springer-Verlag, London, 1998) pp. 135–150, LNCIS, vol. 230.CrossRefGoogle Scholar
22.Utkin, V. I., “Variable structure systems with sliding modes,” IEEE Trans. Autom. Control 22, 212–222 (1977).CrossRefGoogle Scholar
23.Reyhanoglu, M., Schaft, A. van der, McClamroch, N. H. and Kolmanovsky, I., “Dynamics and control of a class of underactuated mechanical systems,” IEEE Trans. Autom. Control 44, 1663–1671 (1999).Google Scholar
24.Ashrafiuon, H. and Erwin, R. S., “Sliding Control Approach to Underactuated Multibody Systems”, Proceedings of the American Control Conference, Boston, MA (Jun./Jul. 2004) pp. 1283–1288.Google Scholar
25.Bernstein, D. S., Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory (Princeton University Press, Princeton, NJ, 2005).Google Scholar
26.Slotine, J.-J. E. and Li, W., Applied Nonlinear Control (Prentice-Hall, Englewood Cliffs, NJ, 1991).Google Scholar
27.Nikkhah, M., Ashrafiuon, H. and Muske, K., “Optimal Sliding Mode Control for Underactuated Systems”, Proceedings of the American Control Conference, Minneapolis, MN (Jun. 2006) pp. 4688–4693.Google Scholar