Parametrically Excited Dynamic Bipedal Walking
Fumihiko Asano, Dr. Eng.
Keywords: Passive dynamic walking, Biped robots, Legged locomotion, Telescopic leg, Parametric excitation, Parametric sustained vibration, Limit cycle, Mechanical energy, Efficiency


Abstract: Traditionally, an inverted pendulum has been used as a reduced biped locomotion system, whereas we propose a different approach. The essence of dynamic biped gait generation is mechanical energy restoration and the central problem then yields on how to generate a stable dynamic gait guaranteeing the Zero Moment Point (ZMP) condition. Although our virtual gravity approach succeeded realization of energy-effective dynamic gait generation on a level, it was found that there exists a serious trade-off between the control performances and the ZMP condition. A question then arises on how to realize biped gait generation not only effectively but also easily. The answer is to be found in the mechanism of parametric excitation. Our novel approach does not require any rotational actuation and thus enables to walk being free from the ZMP constraint. By this approach, an energy-effective and first biped locomotion can be realized very easily without concerning the ZMP condition.



Selected papers
  1. F. Asano and Z.W. Luo, "Parametrically excited dynamic walking control of telescopic legged robots," J. of the Robotics Society of Japan, Vol. 23, No. 7, pp. 910-918, Oct. 2005. (In Japanese)
  2. F. Asano and Z.W. Luo, "Parametrically excited dynamic bipedal walking," Bioinspiration and Robotics: Walking and Climbing Robots, pp. 1-14, Sept. 2007.
  3. F. Asano, T. Hayashi, Z.W. Luo, S. Hirano and A. Kato, "Parametric excitation approaches to efficient dynamic bipedal walking," Proc. of the IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 2210-2216, Oct. 2007.
  4. Y. Harata, F. Asano, Z.W. Luo, K. Taji and Y. Uno, "Biped gait generation based on parametric excitation by knee-joint actuation," Proc. of the IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, pp. 2198-2203, Oct. 2007.
  5. F. Asano and Z.W. Luo, "Energy-efficient and high-speed dynamic biped locomotion based on principle of parametric excitation," IEEE Transactions on Robotics, Vol. 24, No. 6, pp. 1289-1301, Dec. 2008. [ Download ]
  6. Y. Harata, F. Asano, Z.W. Luo, K. Taji and Y. Uno, "Biped gait generation based on parametric excitation by knee-joint actuation," Robotica, Vol. 27, Issue 7, pp. 1063-1073, Dec. 2009. [ Download ]
  7. T. Hayashi, K. Kaneko, F. Asano and Z.W. Luo, "Experimental study of dynamic bipedal walking based on the principle of parametric excitation with counterweights," Advanced Robotics, Vol. 25, Nos. 1-2, pp. 273-287, 2011. [ Download ]

Movie collections

By performing simple telescopic actuation of swing or stance leg, we can easily generate a stable dynamic bipedal gait. Please watch the video simulations.

Videos in ICRA2005 presentation (revised version)
  1. Parametrically excited dynamic bipedal walking
  2. Parametrically excited dynamic bipedal walking (Slow motion)
Videos in ROBIO2005 workshop presentation
  1. Parametrically excited dynamic bipedal walking where Tset = 0.45, A = 0.07 and gamma = 0.01
  2. Parametrically excited dynamic bipedal walking where Tset = 0.45, A = 0.07 and gamma = 0.04
  3. Parametrically excited dynamic bipedal walking where Tset = 0.45, A = 0.07 and gamma = 0.07
  4. Parametrically excited dynamic bipedal walking where Tset = 0.45, A = 0.07 and gamma = 0.10
Videos in RSJ2005 presentation
  1. Parametric excitation effect of a pendulum system
  2. Parametrically excited dynamic bipedal walking by stance leg actuation
  3. Parametrically excited dynamic bipedal walking by stance leg actuation (Slow motion)
Videos in SICE SI2005 presentation
  1. Parametrically excited dynamic bipedal walking based on up-and-down motion of the hip-mass where R = 0.8 [m]
  2. Parametrically excited dynamic bipedal walking based on up-and-down motion of the hip-mass where R = 0.8 [m] (Slow motion)
  3. Parametrically excited dynamic bipedal walking based on up-and-down motion of the hip-mass where R = 0.5 [m]
  4. Parametrically excited dynamic bipedal walking based on up-and-down motion of the hip-mass where R = 0.5 [m] (Slow motion)



Experimental study

We developed a prototype parametrically excited dynamic bipedal walker, and finally succeeded stable level dynamic walking.
Please visit our new homepage of the experimental case study! [Go] (Open: Feb. 29, 2008)






Acknowledgment
 This research project was sponsored by Bio-Mimetic Control Research Center, The Institute of Physical and Chemical Research (RIKEN) . It is a pleasure to acknowledge the hospitality and encouragement of the members of environment adaptive robotic systems lab., especially Dr. Zhi-Wei Luo, our team leader. It is also deeply indebted to Mr. Takeshi Hayashi, Dr. Shin-ya Hirano and Prof. Atsuo Kato of Bio Mechanism Lab. , Aichi Institute of Technology , for their considerable assistance with the experimental study.


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