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Adaptive Four Legged Locomotion Control Based on Nonlinear Dynamical Systems

  • Giorgio Brambilla
  • Jonas Buchli
  • Auke Jan Ijspeert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4095)

Abstract

Dynamical systems have been increasingly studied in the last decade for designing locomotion controllers. They offer several advantages over previous solutions like synchronization, smooth transitions under parameter variation, and robustness. In this paper, we present an adaptive locomotion controller for four-legged robots. The controller is composed of a set of coupled nonlinear dynamical systems. Using our controller the robot is capable of adapting its locomotion to the physical properties of the robot, in particular its resonant frequency. Our approach aims at developing an on-line learning system that attempts to minimize the energy necessary for the gait. We have implemented the model both in a simulated physical environment (Webots) and on a Sony Aibo robot. We present a series of experiments which demonstrate how the controller can tune its frequency to the resonant frequency of the robot, and modify it when the weight of the robot is changed.

Keywords

Knee Angle Walking Gait Central Pattern Generator Model Walking Frequency Hopf Oscillator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Movies and more technical details of the implementation are available online at: http://birg.epfl.ch/page57636.html
  2. 2.
    Blickhan, R.: The spring-mass model for running and hopping. J. Biomechanics 22(11-12), 1217–1227 (1989)CrossRefGoogle Scholar
  3. 3.
    Buchli, J., Iida, F., Ijspeert, A.J.: Finding resonance: Adaptive frequency oscillators for dynamic legged locomotion (submitted)Google Scholar
  4. 4.
    Buchli, J., Ijspeert, A.J.: Distributed Central Pattern Generator Model for Robotics Application Based on Phase Sensitivity Analysis. In: Ijspeert, A.J., Murata, M., Wakamiya, N. (eds.) BioADIT 2004. LNCS, vol. 3141, pp. 333–349. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Buchli, J., Ijspeert, A.J.: A simple, adaptive locomotion toy-system. In: Schaal, S., Ijspeert, A.J., Billard, A., Vijayakumar, S., Hallam, J., Meyer, J.A. (eds.) From Animals to Animats 8. Proceedings of the Eighth International Conference on the Simulation of Adaptive Behavior (SAB 2004), pp. 153–162. MIT Press, Cambridge (2004)Google Scholar
  6. 6.
    Buchli, J., Righetti, L., Ijspeert, A.J.: A Dynamical Systems Approach to Learning: A Frequency-Adaptive Hopper Robot. In: Capcarrère, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J. (eds.) ECAL 2005. LNCS (LNAI), vol. 3630, pp. 210–220. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Cohen, A.H., Boothe, D.L.: Sensorimotor interactions during locomotion: principles derived from biological systems. Autonomous Robots 7(3), 239–245 (1999)CrossRefGoogle Scholar
  8. 8.
    Fukuoka, Y., Kimura, H., Cohen, A.H.: Adaptive dynamic walking of a quadruped robot on irregular terrain based on biological concepts. The International Journal of Robotics Research 3-4, 187–202 (2003)CrossRefGoogle Scholar
  9. 9.
    Grillner, S.: Control of locomotion in bipeds, tetrapods and fish. In: Brooks, V.B. (ed.) Handbook of Physiology, The Nervous System, Motor Control, vol. 2, pp. 1179–1236. American Physiology Society, Bethesda (1981)Google Scholar
  10. 10.
    Honerkamp, J.: The heart as a system of coupled nonlinear oscillators. J. Math. Biol. 18(1), 69–88 (1983)Google Scholar
  11. 11.
    Hopf, E.: Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems. In: Ber. Math.-Phys., Sächs. Akad. d. Wissenschaften, Leipzig, pp. 1–22 (1942)Google Scholar
  12. 12.
    McGeer, T.: Passive dynamic walking. International Journal of Robotics Research 9, 62–82 (1990)CrossRefGoogle Scholar
  13. 13.
    Michel, O.: Webots: Professional mobile robot simulation. International Journal of Advanced Robotic Systems 1(1), 39–42 (2004)Google Scholar
  14. 14.
    Smith, R., et al.: Open Dynamics Engine, Available online at: http://ode.org
  15. 15.
    Righetti, L., Buchli, J., Ijspeert, A.J.: Dynamic hebbian learning in adaptive frequency oscillators. Physica D 216(2), 269–281 (2006)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Strogatz, S.: Nonlinear Dynamics and Chaos. With applications to Physics, Biology, Chemistry, and Engineering. Addison Wesley Publishing Company, Reading (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Giorgio Brambilla
    • 1
  • Jonas Buchli
    • 1
  • Auke Jan Ijspeert
    • 1
  1. 1.Biologically Inspired Robotic Group (BIRG)Ecole Polytechnique Fédérale de Lausanne (EPFL, Station 14)LausanneSwitzerland

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