Humanoid Robot Gait Generation Based on Limit Cycle Stability

  • Mingguo Zhao
  • Ji Zhang
  • Hao Dong
  • Yu Liu
  • Liguo Li
  • Xuemin Su
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5399)


This paper presents the gait generation and mechanical design of a humanoid robot based on a limit cycle walking method-Virtual Slope Control. This method is inspired by Passive Dynamic Walking. By shortening the swing leg, the robot walking on level ground can be considered as on a virtual slope. Parallel double crank mechanisms and elastic feet are introduced to the 5 DoF robot leg, to make the heelstrike of the swing leg equivalent to the point-foot collision used in Virtual Slope Control. In practical walking, the gait is generated by connecting the two key frames in the sagittal and lateral plane with sinusoids. With the addition of leg rotational movement, the robot achieves a fast forward walking of 2.0leg/s and accomplishes omnidirectional walking favorably.


Humanoid Robot Swing Phase Limit Cycle Stability Complementary Energy Robot Walking 
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.


  1. 1.
    Vukobratovic, M., Juricic, D.: Contribution to the synthesis of biped gait. In: Proc. IFAC Symp. Technical and Biological Problem on Control, Erevan, USSR (1968)Google Scholar
  2. 2.
    Juricic, D., Vukobratovic, M.: Mathematical Modeling of Biped Walking Systems (ASME Publ., 1972) 72-WA/BHF-13 (1972)Google Scholar
  3. 3.
    Vukobratovic, M., Stepanenko, Y.: Mathematical models of general anthropomorphic systems. Mathematical Biosciences 17, 191–242 (1973)CrossRefzbMATHGoogle Scholar
  4. 4.
    Vukobratovic, M.: How to control the artificial anthropomorphic systems. IEEE Trans. System, Man and Cybernetics SMC-3, 497–507 (1973)CrossRefzbMATHGoogle Scholar
  5. 5.
    Hirose, M., Haikawa, Y., Takenaka, T., et al.: Development of humanoid robot ASIMO. In: Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems, Workshop 2, Maui, HI, USA, October 29 (2001)Google Scholar
  6. 6.
    Kaneko, K., Kanehiro, F., Kajita, S., et al.: Humanoid robot HRP-2. In: Proc. IEEE International Conference on Robotics and Automation (ICRA), New Orleans, LA, USA, April 26 - May 1, pp. 1083–1090 (2004)Google Scholar
  7. 7.
    Nagasaka, K., Kuroki, Y., Suzuki, S., et al.: Integrated motion control for walking, jumping and running on a small bipedal entertainment robot. In: Proc. IEEE International Conference on Robotics and Automation (ICRA), New Orleans, LA, USA, April 26 - May 1, vol. 4, pp. 3189–3194 (2004)Google Scholar
  8. 8.
    Friedmann, M., Kiener, J., Petters, S., et al.: Versatile, high-quality motions and behavior control of humanoid soccer robots. In: Proc. 2006 IEEE-RAS International Conference on Humanoid Robots, Genoa, Italy, December 4, pp. 9–16 (2006)Google Scholar
  9. 9.
    Hemker, T., Sakamoto, H., Stelzer, M., et al.: Hardware-in-the-Loop Optimization of the Walking Speed of a Humanoid Robot. In: Proc. CLAWAR 2006, Brussels, Belgium, September 12-14 (2006)Google Scholar
  10. 10.
    Vukobratovic, M., Frank, A., Juricic, D.: On the Stability of Biped Locomotion. IEEE Transactions on Biomedical Engineering 17(1) (1970)Google Scholar
  11. 11.
    Hobbelen, D., Wisse, M.: Limit Cycle Walking. In: Humanoid Robots: Human-like Machines, ch. 14, p. 642. I-Tech Education and Publishing, Vienna (2007)Google Scholar
  12. 12.
    Collins, S., Ruina, A., Tedrake, R., et al.: Efficient Bipedal Passive-Dynamic Walkers. Science 307(5712), 1082–1085 (2005)CrossRefGoogle Scholar
  13. 13.
    Hurmuzlu, Y., Moskowitz, G.: Role of Impact in the Stability of Bipedal Locomotion. International Journal of Dynamics and Stability of Systems 1(3), 217–234 (1986)CrossRefzbMATHGoogle Scholar
  14. 14.
    McGeer, T.: Passive Dynamic Walking. International Journal of Robotics Research 9, 62–82 (1990)CrossRefGoogle Scholar
  15. 15.
    Garcia, M.: Stability, Scaling, and Chaos in Passive Dynamic Gait Models. PhD Thesis, Cornell University, Ithaca, NY (1999)Google Scholar
  16. 16.
    Wisse, M.: Essentials of Dynamic Walking: Analysis and design of two-legged robots. PhD Thesis, Delft University of Technology, Netherlands (2004)Google Scholar
  17. 17.
    Tedrake, R.: Applied Optimal Control for Dynamically Stable Legged Locomotion. PhD Thesis, MIT, MA (2004)Google Scholar
  18. 18.
    Pratt, J., Chew, C.-M., Torres, A., et al.: Virtual Model Control: An Intuitive Approach for Bipedal Locomotion. The International Journal of Robotics Research 20(2), 129–143 (2001)CrossRefGoogle Scholar
  19. 19.
    Chevallereau, C., Abba, G., Aoustin, Y., et al.: RABBIT: a testbed for advanced control theory. IEEE Control Systems Magazine 23(5), 57–79 (2003)CrossRefGoogle Scholar
  20. 20.
    Geng, T., Porr, B., Wörgötter, F.: Fast Biped Walking with a Sensor-driven Neuronal Controller and Real-Time Online Learning. The International Journal of Robotics Research 25(3), 243–259 (2006)CrossRefGoogle Scholar
  21. 21.
    Morimoto, J., Cheng, G., Atkeson, C.G., et al.: A simple reinforcement learning algorithm for biped walking. In: Proceedings of IEEE International Conference on Robotics and Automation, vol. 3 (2004)Google Scholar
  22. 22.
    Kulvanit, P., Stryk, O.: RoboCup Soccer Humanoid League Rules and Setup for the, competition in Suzhou, China (2008),

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mingguo Zhao
    • 1
  • Ji Zhang
    • 1
  • Hao Dong
    • 1
  • Yu Liu
    • 1
  • Liguo Li
    • 1
  • Xuemin Su
    • 1
  1. 1.Department of AutomationTsinghua UniversityBeijingP.R. China

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