Skip to main content

Stable Dynamic Walking over Rough Terrain

Theory and Experiment

  • Conference paper
Robotics Research

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 70))

Abstract

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated mechanical systems. An important example of such a system is an underactuated “dynamic walking” biped robot walking over rough terrain. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to higher degree-of-freedom robots over arbitrary terrain and other impulsive mechanical systems.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Vukobratovic, M., Borovac, B.: Zero-moment point – thirty five years of its life. International Journal of Humanoid Robotics 1(1), 157–173 (2004)

    Article  Google Scholar 

  2. McGeer, T.: Passive dynamic walking. International Journal of Robotics Research 9(2), 62–82 (1990)

    Article  Google Scholar 

  3. Collins, S., Ruina, A., Tedrake, R., Wisse, M.: Efficient bipedal robots based on passive-dynamic walkers. Science 307(5712), 1082–1085 (2005)

    Article  Google Scholar 

  4. Byl, K., Tedrake, R.: Approximate optimal control of the compass gait on rough terrain. In: Proc. of the IEEE International Conference on Robotics and Automation, Pasadena, CA (2008)

    Google Scholar 

  5. Iida, F., Tedrake, R.: Minimalistic control of a compass gait robot in rough terrain. In: Proc. of the IEEE International Conference on Robotics and Automation, Kobe, Japan (2009)

    Google Scholar 

  6. Byl, K., Shkolnik, A., Roy, N., Tedrake, R.: Reliable dynamic motions for a stiff quadruped. In: Proc. of the 11th International Symposium on Experimental Robotics (ISER), thens, Greece (2008)

    Google Scholar 

  7. Goswami, A., Espiau, B., Keramane, A.: Limit cycles in a passive compass gait biped and passivity-mimicking control laws. Autonomous Robots 4(3), 273–286 (1997)

    Article  Google Scholar 

  8. Asano, F., Yamakita, M., Kamamichi, N., Luo, Z.W.: A novel gait generation for biped walking robots based on mechanical energy constraint. IEEE Transactions on Robotics and Automation 20(3), 565–573 (2004)

    Article  Google Scholar 

  9. Spong, M., Holm, J., Lee, D.: Passivity-based control of bipedal locomotion. IEEE Robotics and Automation Magazine 14(2), 30–40 (2007)

    Article  Google Scholar 

  10. Hurmuzlu, Y., Moskowitz, G.: The role of impact in the stability of bipedal locomotion. Dynamics and Stability of Systems 1, 217–234 (1986)

    Google Scholar 

  11. Grizzle, J., Abba, G., Plestan, F.: Asymptotically stable walking for biped robots: Analysis via systems with impulse effects. IEEE Transactions on Automatic Control 46(1), 51–64 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. Westervelt, E., Grizzle, J., Koditschek, D.: Hybrid zero dynamics of planar biped walkers. IEEE Transactions on Automatic Control 48(1), 42–56 (2003)

    Article  MathSciNet  Google Scholar 

  13. Wisse, M., Schwab, A., van der Linde, R., van der Helm, F.: How to keep from falling forward: elementary swing leg action for passive dynamic walkers. IEEE Transactions on Robotics 21(3), 393–401 (2005)

    Article  Google Scholar 

  14. Westervelt, E., Grizzle, J., Chevallereau, C., Choi, J., Morris, B.: Feedback Control of Dynamic Bipedal Robot Locomotion. CRC Press, Boca Raton (2007)

    Book  Google Scholar 

  15. Hobbelen, D., Wisse, M.: A disturbance rejection measure for limit cycle walkers: The gait sensitivity norm. IEEE Transactions on Robotics 23(6), 1213–1224 (2007)

    Article  Google Scholar 

  16. Hauser, J., Chung, C.: Converse Lyapunov function for exponential stable periodic orbits. Systems and Control Letters 23, 27–34 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  17. Banaszuk, A., Hauser, J.: Feedback linearization of transverse dynamics for periodic orbits. Systems and Control Letters 26, 95–105 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  18. Shiriaev, A.S., Freidovich, L.B., Manchester, I.R.: Can we make a robot ballerina perform a pirouette? Orbital stabilization of periodic motions of underactuated mechanical systems. Annual Reviews in Control 32(2), 200–211 (2008)

    Article  Google Scholar 

  19. Freidovich, L.B., Shiriaev, A.S., Manchester, I.R.: Stability analysis and control design for an underactuated walking robot via computation of a transverse linearization. In: Proceedings of the 17th IFAC World Congress, Seoul, Korea, July 6-11 (2008)

    Google Scholar 

  20. Shiriaev, A.S., Freidovich, L.B., Manchester, I.R.: Periodic motion planning and analytical computation of transverse linearizations for hybrid mechanical systems. In: Proceedings of the 47th IEEE Conference on Decision and Control, Cancun, Mexico (2008)

    Google Scholar 

  21. Leonov, G.: Generalization of the Andronov-Vitt theorem. Regular and chaotic dynamics 11(2), 281–289 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  22. Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.M.: Constrained model predictive control: Stability and optimality. Automatica 36(6), 789–814 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  23. Spong, M., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. John Wiley and Sons, New Jersey (2006)

    Google Scholar 

  24. Hurmuzlu, Y., Marghitu, D.: Rigid body collisions of planar kinematic chains with multiple contact points. The International Journal of Robotics Research 13(1), 82–92 (1994)

    Article  Google Scholar 

  25. Shiriaev, A., Perram, J., Canudas-de-Wit, C.: Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach. IEEE Transactions on Automatic Control 50(8), 1164–1176 (2005)

    Article  MathSciNet  Google Scholar 

  26. Spong, M.: Partial feedback linearization of underactuated mechanical systems. In: Proc. of International Conference on Intelligent Robots and Systems, Munich, Germany (2004)

    Google Scholar 

  27. Kwon, W., Bruckstein, A., Kailath, T.: Stabilizing state-feedback design via the moving horizon method. International Journal of Control 37(3), 631–643 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  28. Grizzle, J., Choi, J., Hammouri, H., Morris, B.: On observer-based feedback stabilization of periodic orbits in bipedal locomotion. In: Proc. Methods and Models in Automation and Robotics (2007)

    Google Scholar 

  29. http://groups.csail.mit.edu/locomotion/movies/cgexperiment20081222_4.mov .

  30. Kalman, R.: Contributions to the theory of optimal control. Bol. Soc. Mat. Mexicana 5, 102–119 (1960)

    MathSciNet  Google Scholar 

  31. Bainov, D., Simeonov, P.: Systems with Impulse Effects: Stability, Theory and Applications. Ellis Horwood, Chichester (1989)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Manchester, I.R., Mettin, U., Iida, F., Tedrake, R. (2011). Stable Dynamic Walking over Rough Terrain. In: Pradalier, C., Siegwart, R., Hirzinger, G. (eds) Robotics Research. Springer Tracts in Advanced Robotics, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19457-3_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-19457-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19456-6

  • Online ISBN: 978-3-642-19457-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics