Skip to main content

An Alternative to the Measurement of Five-Links Biped Robot Absolute Orientation: Estimation Based on High Order Sliding Mode

  • Chapter

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 375))

Abstract

The knowledge of the posture of a biped robot is a hard task, by a technological point-of-view. However, this information is crucial (in particular for walking dynamical bipeds in single support) for numerous advanced control laws which require all state variables. Observers design is then necessary.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Micheau, P., Roux, M.A., Bourassa, P.: Self-tuned trajectory control of a biped walking robot. In: Proc. Int. Conf. on Climbing and Walking Robot CLAWAR 2003, Catania, Italy (2003)

    Google Scholar 

  2. Grizzle, J.W., Choi, J.H., Hammouri, H., Morris, B.: On Observer-Based Feedback Stabilization of Periodic Orbits in Bipedal Locomotion. In: Proc. Methods and Models in Automation and Robotics (MMAR 2007), Szczecin, Poland (2007)

    Google Scholar 

  3. Aoustin, Y., Garcia, G., Janot, A.: Estimation of the Absolute Orientation of a Two-link biped using discrete observers. In: Proc. Mechatronics and Robotics Conf. MECHROB, Aachen, Germany (2004)

    Google Scholar 

  4. Lebastard, V., Aoustin, Y., Plestan, F.: Observer-based control of a biped robot. In: Proc. Int. Workshop on Robot Motion and Control ROMOCO, Puszczykowo, Poland (2004)

    Google Scholar 

  5. Slotine, J.J.E., Li, W.: Applied nonlinear control. Prentice Hall, New-York (1991)

    MATH  Google Scholar 

  6. Hashimoto, H., et al.: VSS observer for linear time varying system. In: Proc. IECON 1990, Pacific Grove, California (1990)

    Google Scholar 

  7. Utkin, J., Guldner, J., Shi, J.: Sliding modes in electromechanical systems. Taylor and Francis, London (1999)

    Google Scholar 

  8. Boukhobza, T., Barbot, J.P.: High order sliding modes observer. In: Proc. 1998 IEEE Conf. on Decision and Control CDC 1998, Tampa, Florida, USA (1998)

    Google Scholar 

  9. Lebastard, V., Aoustin, Y., Plestan, F.: Observer-based control of a walking biped robot: stability analysis. In: Proc. Int. Conf. on Climbing and Walking Robot CLAWAR 2006, Catania, Italy (2006)

    Google Scholar 

  10. Lebastard, V., Aoustin, Y., Plestan, F.: Step-by-step sliding mode observer for control of a walking biped robot by using only actuated variables measurement. In: Proc. IEEE Int. Conf. on Intelligent Robots and Systems IROS 2005, Edmonton, Canada (2005)

    Google Scholar 

  11. Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotationnal double integrator. IEEE Transactions on Automatic Control 43, 678–682 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Fridman, L., Levant, A.: Higher order sliding modes. In: Perruquetti, W., Barbot, J.P. (eds.) Sliding Mode Control in Engineering. Control Engineering Series. Marcel Dekker, New-York (2002)

    Google Scholar 

  13. Davila, J., Fridman, L., Levant, A.: Second-order sliding-mode observer for mechanical systems. IEEE Transactions on Automatic Control 50, 1785–1789 (2005)

    Article  MathSciNet  Google Scholar 

  14. Davila, J., Fridman, L., Levant, A.: Observation of linear systems with unknown inputs via high order sliding modes. International Journal of Systems Science 38, 773–791 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  15. Fridman, L., Shtessel, Y., Edwards, C., Yan, X.G.: Higher-order sliding-mode observer for state estimation and input reconstruction in nonlinear systems. International Journal of Robust and Nonlinear Control 18, 399–412 (2007)

    Article  Google Scholar 

  16. Chevallereau, C., et al.: Rabbit: a testbed for advanced control theory. IEEE Control Systems Magazine 23, 57–79 (2003)

    Article  Google Scholar 

  17. Spong, M.W., Vidyasagar, M.: Robot dynamics and control. John Wiley, New-York (1991)

    Google Scholar 

  18. Aoustin, Y., Formal’sky, A.M.: Control design for a biped: reference trajectory based on driven angles as functions of the undriven angle. International Journal of Computer and Systems Sciences 42, 159–176 (2003)

    MathSciNet  Google Scholar 

  19. Formal’sky, A.M.: Locomotion of Anthropomorphic Mechanisms, Nauka, Moscow, Russia (in Russian) (1982)

    Google Scholar 

  20. Grizzle, J.W., Abba, G., Plestan, F.: Asymptotically stable walking for biped robots: analysis via systems with impulse effects. IEEE Transactions on Automatic Control 46, 51–64 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  21. Miossec, A., Aoustin, Y.: Mouvement de Marche Composé de Simple et Double Supports pour un Robot Bipède Planaire sans Pieds. In: Proc. Conf. Int. Francophone d’Automatique CIFA 2003, Nantes, France (in french) (2003)

    Google Scholar 

  22. Chevallereau, C., Aoustin, Y.: Optimal reference trajectories for walking and running of a biped. Robotica 19, 557–569 (2001)

    Article  Google Scholar 

  23. Djoudi, D., Chevallereau, C., Aoustin, Y.: Optimal reference motions for walking of a biped robot. In: Proc. IEEE Int. Conf. on Robotics and Automation ICRA 2005, Barcelona, Spain (2005)

    Google Scholar 

  24. Krener, A.J., Respondek, W.: Nonlinear observers with linearizable error dynamics. SIAM J. Contr. Opt. 2, 197–216 (1985)

    Article  MathSciNet  Google Scholar 

  25. Lebastard, V., Aoustin, Y., Plestan, F.: Observer-based control of a walking biped robot without orientation measurement. Robotica 24, 385–400 (2006)

    Article  Google Scholar 

  26. Lebastard, V., Aoustin, Y., Plestan, F.: Absolute orientation estimation for observer-based control of a five-link walking biped robot. In: Kozlowski, K. (ed.) Robot Motion and Control: Recent Developments. Lecture Notes in Control and Information Sciences, vol. 335. Springer, Berlin (2006)

    Chapter  Google Scholar 

  27. Filippov, A.: Differential Equations with Discontinuos Right-hand Sides. Kluwer Academic Publishers, Dordrecht (1988)

    Google Scholar 

  28. Lebastard, V., Aoustin, Y., Plestan, F.: Finite time observer for absolute orientation estimation of a five-link walking biped robot. In: Proc. IEEE American Control Conf. ACC 2006, Minneapolis, Minnesota (2006)

    Google Scholar 

  29. Menini, L., Tornambè, A.: Velocity observers for linear mechanical systems subject to single non-smooth impacts. Systems and Control Letters 43, 193–202 (2001)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Giorgio Bartolini Leonid Fridman Alessandro Pisano Elio Usai

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lebastard, V., Aoustin, Y., Plestan, F., Fridman, L. (2008). An Alternative to the Measurement of Five-Links Biped Robot Absolute Orientation: Estimation Based on High Order Sliding Mode. In: Bartolini, G., Fridman, L., Pisano, A., Usai, E. (eds) Modern Sliding Mode Control Theory. Lecture Notes in Control and Information Sciences, vol 375. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79016-7_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-79016-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79015-0

  • Online ISBN: 978-3-540-79016-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics