Journal of Bionic Engineering

, Volume 9, Issue 2, pp 143–155 | Cite as

Planning and Control for Passive Dynamics Based Walking of 3D Biped Robots

  • Xiang Luo
  • Wenlong Xu


Efficient walking is one of the main goals of research on biped robots. Passive Dynamics Based Walking (PDBW) has been proven to be an efficient pattern in numerous previous approaches to 2D biped walking. The goal of this study is to develop a feasible method for the application of PDBW to 3D robots. First a hybrid control method is presented, where a previously proposed two-point-foot walking pattern is employed to generate a PDBW gait in the sagittal plane and, in the frontal plane, a systematic balance control algorithm is applied including online planning of the landing point of the swing leg and feedback control of the stance foot. Then a multi-space planning structure is proposed to implement the proposed method on a 13-link 3D robot. Related kinematics and planning details of the robot are presented. Furthermore, a simulation of the 13-link biped robot verifies that stable and highly efficient walking can be achieved by the proposed control method. In addition, a number of features of the biped walking, including the transient powers and torques of the joints are explored.


3D biped robot passive dynamics based walking balance control multi-space planning simulation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Sakagami Y, Watanabe R, Aoyama C, Matsunaga S, Higaki N and Fujimura K. The intelligent ASIMO: System overview and integration. IEEE/RSJ International Conference on Intelligent Robots and System, Lausanne, Switzerland, 2002, 2478–2483.CrossRefGoogle Scholar
  2. [2]
    McGeer T. Passive dynamic walking. International Journal of Robotics Research, 1990, 9, 62–82.CrossRefGoogle Scholar
  3. [3]
    McGeer T. Dynamics and control of bipedal locomotion. Journal of Theoretical Biology, 1993, 163, 277–314.CrossRefGoogle Scholar
  4. [4]
    Collins S, Ruina A, Tedrake R, Wisse M. Efficient bipedal robots based on passive-dynamic walkers. Science, 2005, 307, 1082–1085.CrossRefGoogle Scholar
  5. [5]
    Coleman M, Ruina A. An uncontrolled toy that can walk but cannot stand still. Physical Review Letters, 1998, 80, 3658–3661.CrossRefGoogle Scholar
  6. [6]
    Collins S H, Ruina A. A bipedal walking robot with efficient and human-like gait. Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain, 2005, 1983–1988.Google Scholar
  7. [7]
    Wisse M, Schwab A L, van der Linde R Q, van der Helm F C T. How to keep from falling forward: Elementary swing leg action for passive dynamic walkers. IEEE Transactions on Robotics, 2005, 21, 393–401.CrossRefGoogle Scholar
  8. [8]
    Tedrake R, Zhang T W, Fong M, Seung H S. Actuating a simple 3D passive dynamic walker. Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and System, New Orleans, USA, 2004, 4656–4661.Google Scholar
  9. [9]
    Pratt J E. Exploiting Inherent Robustness and Natural Dynamics in the Control of Bipedal Walking Robots, PhD thesis, Computer Science Department, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA, 2000.Google Scholar
  10. [10]
    Huang Q, Nakamura Y, Inamura T. Humanoids walk with feed forward dynamic pattern and feedback sensory reflection. Proceedings of IEEE International Conference on Robotics and Automation, Seoul, Korea, 2001, 4220–4225.Google Scholar
  11. [11]
    Sugihara T, Nakamura Y, Inoue H. Realtime humanoid motion generation through zmp manipulation based on inverted pendulum control. Proceedings of IEEE International Conference on Robotics and Automation, Washington DC, USA, 2002, 1404–1409.Google Scholar
  12. [12]
    Grizzle J W, Abba G, Plestan F. Asymptotically stable walking for biped robots: Analysis via systems with impulse effects. IEEE Transaction on Automatic Control, 2001, 46, 51–64.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Chevallereau C, Abba G, Aoustin Y, Plestan E, Westervelt F, Canduas-de Wit C, Grizzle J. RABBIT: A test bed for advanced control theory. IEEE Control Systems Magazine, 2003, 23, 57–79.CrossRefGoogle Scholar
  14. [14]
    Westervelt E, Grizzle J, Koditschek D. Hybrid zero dynamics of planar biped walkers. IEEE Transaction on Automatic Control, 2003, 48, 42–56.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Chevallereau C, Djoudi D, Grizzle J. Stable bipedal walking with foot rotation through direct regulation of the zero moment point. IEEE Transactions on Robotics, 2008, 24, 390–401.CrossRefGoogle Scholar
  16. [16]
    Bauby C E, Kuo A D. Active control of lateral balance in human walking. Journal of Biomechanics, 2000, 33, 1433–1440.CrossRefGoogle Scholar
  17. [17]
    Chevallereau C, Grizzle J, Shin C L. Asymptotically stable walking of a five-link underactuated 3D bipedal robot. IEEE Transactions on Robotics, 2009, 25, 37–50.CrossRefGoogle Scholar
  18. [18]
    Wang T, Chevallereau C. A new control law for a 3D biped robot based on regulation of the zero moment point and joint path. IEEE-RAS International Conference on Humanoid Robots, Nashville, USA, 2010, 27–32.Google Scholar
  19. [19]
    Ames A D, Gregg R D. Stably extending two-dimensional bipedal walking to three dimensions. Proceedings of the American Control Conference, New York, USA, 2007, 2848–2854.Google Scholar
  20. [20]
    Luo X, Guo R, Zhu C. An orbit based control for biomimetic biped walking. Proceedings of IEEE International Conference on Robotics and Biomimetics, Guilin, China, 2009, 19–23.Google Scholar
  21. [21]
    Luo X, Li W, Zhu C. Planning and control of COP-switch-based planar biped walking. Journal Bionic Engineering, 2011, 8, 33–48.CrossRefGoogle Scholar
  22. [22]
    Bruneau O, Ouezdou F B. Distributed ground/walking robot interaction. Robotica, 1999, 17, 313–323.CrossRefGoogle Scholar

Copyright information

© Jilin University 2012

Authors and Affiliations

  1. 1.School of Mechanical EngineeringSoutheast UniversityNanjingP. R. China

Personalised recommendations