Gait Generation for a Hopping Robot Via Iterative Learning Control Based on Variational Symmetry

  • Satoshi Satoh
  • Kenji Fujimoto
  • Sang-Ho Hyon
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 366)


This paper proposes a novel framework to generate optimal gait trajectories for a one-legged hopping robot via iterative learning control. This method generates gait trajectories which are solutions of a class of optimal control problems without using precise knowledge of the plant model. It is expected to produce natural gait movements such as that of a passive walker. Some numerical examples demonstrate the effectiveness of the proposed method.


Cost Function Hamiltonian System Stance Phase Iterative Learning Control Variational Symmetry 
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  1. 1.
    T. McGeer, “Passive dynamic walking,” Int. J. Robotics Research, vol. 9, no. 2, pp. 62–82, 1990.CrossRefGoogle Scholar
  2. 2.
    K. Osuka and K. Kirihara, “Motion analysis and experiments of passive walking robot quartet ii,” in Proc. the 2000 IEEE Int. Conf. on Robotics and Automation, 2000, pp. 3052–3056.Google Scholar
  3. 3.
    A. Sano, Y. Ikemata, and H. Fujimoto, “Analysis of dynamics of passive walking from storage energy and supply rate,” in Proc. the 2003 IEEE Int. Conf. on Robotics and Automation, 2003, pp. 2478–2483.Google Scholar
  4. 4.
    A. Goswami, B. Espiau, and A. Keramane, “Limit cycles in a passive compass gait biped and passivity-mimicking control laws,” Autonomous Robots, vol. 4, no. 3, pp. 273–286, 1997.CrossRefGoogle Scholar
  5. 5.
    M. W. Spong, “Passivity-based control of the compass gait biped,” in Proc. of IFAC World Congress, 1999, pp. 19–23.Google Scholar
  6. 6.
    F. Asano, M. Yamakita, N. Kamamichi, and Z. W. Luo, “A novel gait generation for biped walking robots based on mechanical energy constraints,” IEEE Trans. Robotics and Automation, vol. 20, no. 3, pp. 565–573, 2004.CrossRefGoogle Scholar
  7. 7.
    M. Ahmadi and M. Buehler, “Stable control of a simulated one-legged running robot with hip and leg compliance,” IEEE Trans. Robotics and Automation, vol. 13, no. 1, pp. 96–104, 1997.CrossRefGoogle Scholar
  8. 8.
    S. Hyon and T. Emura, “Energy-preserving control of passive one-legged running robot,” Advanced Robotics, vol. 18, no. 4, pp. 357–381, 2004.CrossRefGoogle Scholar
  9. 9.
    K. Fujimoto and T. Sugie, “Iterative learning control of Hamiltonian systems: I/O based optimal control approach,” IEEE Trans. Autom. Contr. vol. 48, no. 10, pp. 1756–1761, 2003.CrossRefMathSciNetGoogle Scholar
  10. 10.
    K. Fujimoto, T. Horiuchi, and T. Sugie, “Optimal control of Hamiltonian systems with input constraints via iterative learning,” in Proc. 42nd IEEE Conf. on Decision and Control, 2003, pp. 4387–4392.Google Scholar
  11. 11.
    S. Hyon, “Hamiltonian-based running control of dynamic legged robots,” Systems. Control and Information, vol. 49, no. 7, pp. 260–265, 2005, (in Japanese).Google Scholar
  12. 12.
    S. Satoh, K. Fujimoto, and S. Hyon, “Gait generation for passive running via iterative learning control,” in Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems, 2006, pp. 5907–5912.Google Scholar
  13. 13.
    “Biped gait generation via iterative learning control including discrete state transitions,” 2007, submitted.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Satoshi Satoh
    • 1
  • Kenji Fujimoto
    • 2
  • Sang-Ho Hyon
    • 3
  1. 1.Department of Mechanical Science and Engineering, Graduate School of EngineeringNagoya UniversityNagoyaJapan
  2. 2.Department of Mechanical Science and Engineering, Graduate School of EngineeringNagoya UniversityNagoyaJapan
  3. 3.Computational Neuroscience LaboratoriesATRKyotoJapan

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