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Periodic Stability for 2-D Biped Dynamic Walking on Compliant Ground

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Intelligent Robotics and Applications (ICIRA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9245))

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Abstract

The improvement of stability for dynamic biped walking is motivated by the potential use of humanoid robot in complex environment. This paper focuses on the effect of ground compliance on the periodic stability of dynamic walking. Firstly, the compliant ground is equivalent to a spring-damper system, and the coupling dynamics model of robot-ground system is modelled as a rigid planar kinematic chains in contact with a stiffness-damping system. Based on it, two differential equations are obtained to describe the dynamic walking process in one cycle which is separated into a swing phase followed by an impact phase. Subsequently, a stable gait is planned under rigid assumption and transplanted to the walking under compliant ground condition. The effect of ground compliance on the gait during the swing phases is analyzed under 15 kinds of ground conditions, respectively and effect on it during impact phase is analyzed under 12 kinds of ground conditions. Finally, the periodic stability under the effect of ground compliance is analyzed with 6 kinds of ground conditions, and the effect of ground compliance on the periodic stability of dynamic walking is concluded.

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References

  1. McGeer, T.: Passive dynamic walking. The International Journal of Robotics Research 9(2), 62–82 (1990)

    Article  Google Scholar 

  2. Griffin, B., Grizzle, J.: Walking gait optimization for accommodation of unknown terrain height variations. In: American Control Conference (2015) (Submitted on 25 September 2014)

    Google Scholar 

  3. Dai, H. Tedrake, R.: Optimizing robust limit cycles for legged locomotion on unknown terrain. In: CDC, pp. 1207–1213 (2012)

    Google Scholar 

  4. Byl, K., Tedrake, R.: Metastable walking machines. International Journal of Robotics Research 28(8), 1040–1064 (2008)

    Article  Google Scholar 

  5. Zhao, H., Powell, M.J., Ames, A.D.: Human-inspired motion primitives and transitions for bipedal robotic locomotion in diverse terrain. Optimal Control Applications and Methods 35(6), 730–755 (2014)

    Article  Google Scholar 

  6. Ames, A.D., Cousineau, E.A., Powell, M.J.: Dynamically stable bipedal robotic walking with NAO via human-inspired hybrid zero dynamics. In: Proceedings of the 15th ACM International Conference on Hybrid Systems: Computation and Control, pp. 135–144 (2012)

    Google Scholar 

  7. Spong, M.W., Bullo, F.: Controlled symmetries and passive walking. IEEE Transactions on Automatic Control 50(7), 1025–1031 (2005)

    Article  MathSciNet  Google Scholar 

  8. Hu, Y., Yan, G., Lin, Z.: Stable walking for a compass-like biped robot in complex environments. In: American Control Conference (ACC), pp. 6048–6053 (2010)

    Google Scholar 

  9. Hurmuzlu, Y., Marghitu, D.B.: Rigid body collisions of planar kinematic chains with multiple contact points. The international journal of robotics research 13(1), 82–92 (1994)

    Article  Google Scholar 

  10. Bicchi, A., Kumar, V.: Robotic grasping and contact: A review. In: ICRA, pp. 348–353 (2000)

    Google Scholar 

  11. Lens, T., Radkhah, K., von Stryk, O.: Simulation of dynamics and realistic contact forces for manipulators and legged robots with high joint elasticity. In: IEEE International Conference on Advanced Robotics (ICAR), pp. 34–41 (2011)

    Google Scholar 

  12. Stronge, W.J., James, R., Ravani, B.: Oblique impact with friction and tangential compliance. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 359(1789), 2447–2465 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. Stronge, W.J.: Rigid body collisions with friction. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 431(1881), 169–181 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  14. Marhefka, D.W., Orin, D.E.: Simulation of contact using a nonlinear damping model. In: Proceedings of IEEE International Conference on Robotics and Automation, 1996, vol. 2, pp. 1662–1668 (1996)

    Google Scholar 

  15. Chevallereau, C., Grizzle, J.W., Shih, C.L.: Asymptotically stable walking of a five-link underactuated 3-D bipedal robot. IEEE Transactions on Robotics 25(1), 37–50 (2009)

    Article  Google Scholar 

  16. Grizzle, J.W., Abba, G., Plestan, F.: Asymptotically stable walking for biped robots: Analysis via systems with impulse effects. IEEE Transactions on Automatic Control 46(1), 51–64 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Power and Mechanical Engineering, Wuhan University, Wuhan, 430072, China

    Yang Wang, Jiatao Ding & Xiaohui Xiao

Authors
  1. Yang Wang
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  2. Jiatao Ding
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  3. Xiaohui Xiao
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Corresponding author

Correspondence to Xiaohui Xiao .

Editor information

Editors and Affiliations

  1. University of Portsmouth, Portsmouth, United Kingdom

    Honghai Liu

  2. Tokyo Metropolitan University, Tokyo, Japan

    Naoyuki Kubota

  3. Shanghai Jiao Tong University, Shanghai, China

    Xiangyang Zhu

  4. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Rüdiger Dillmann

  5. University of Portsmouth, Portsmouth, United Kingdom

    Dalin Zhou

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© 2015 Springer International Publishing Switzerland

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Wang, Y., Ding, J., Xiao, X. (2015). Periodic Stability for 2-D Biped Dynamic Walking on Compliant Ground. In: Liu, H., Kubota, N., Zhu, X., Dillmann, R., Zhou, D. (eds) Intelligent Robotics and Applications. ICIRA 2015. Lecture Notes in Computer Science(), vol 9245. Springer, Cham. https://doi.org/10.1007/978-3-319-22876-1_32

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  • DOI: https://doi.org/10.1007/978-3-319-22876-1_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22875-4

  • Online ISBN: 978-3-319-22876-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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