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The effects of ground compliance on flexible planar passive biped dynamic walking

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Abstract

Passive biped dynamic walking exhibits humanoid gait. Many efforts have been made to implement a flexible and anthropomorphic passive model. However, the couple of flexible passive walker on compliant ground has not been well studied yet. The objective of this paper was to develop multibody dynamics for flexible passive walker on compliant ground, in which the nonlinear spring-damper contact model was used both in normal and tangential directions to represent ground compliance. Inspired by elastic mechanisms in human locomotion, hip stiffness and damping were incorporated in the proposed flexible passive walker. Different from traditional impactmomentum method, one unified set of continuous dynamics based on continuous force method was developed to describe the entire passive walking gait on compliant ground, including the real double support phase. Through numerical simulations, stable period-one gait and double support phase were gained. After investigating the effects of contact parameters on step length, period and velocity, it was found that larger contact stiffness and smaller contact damping lead to a higher step velocity gait. The adjustment of hip stiffness could be used to improve the versatility of the flexible walker on varying compliant grounds.

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References

  1. O. Kwon, K. S. Jeon and J. H. Park, Optimal trajectory generation for biped robots walking up-and-down stairs, Journal of Mechanical Science and Technology, 20 (5) (2006) 612–620.

    Article  Google Scholar 

  2. Z. Xia, J. Xiong and K. Chen, Global navigation for humanoid robots using sampling-based footstep planners, IEEE/ASME Transactions on Mechatronics, 16 (4) (2011) 716–723.

    Article  Google Scholar 

  3. K. Sreenath, H. W. Park and J. W. Grizzle, Design and experimental implementation of a compliant hybrid zero dynamics controller with active force control for running on MABEL, 2012 IEEE International Conference on Robotics and Automation (ICRA), Saint Paul, MN, USA (2012) 51–56.

    Chapter  Google Scholar 

  4. Y. Sakagami, R. Watanabe, C. Aoyama, S. Matsunaga, N. Higaki and K. Fujimura, The intelligent ASIMO: System overview and integration, 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland (2002) 2478–2483.

    Chapter  Google Scholar 

  5. K. Kaneko, F. Kanehiro, M. Morisawa, K. Akachi, G. Miyamori, A. Hayashi and N. Kanehira, Humanoid robot HRP-4 - humanoid robotics platform with lightweight and slim body, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), San Francisco, CA, USA (2011) 4400–4407.

    Google Scholar 

  6. M. Vukobratović and J. Stepanenko, On the stability of anthropomorphic systems, Mathematical Biosciences, 15 (1-2) (1972) 1–37.

    Article  MATH  Google Scholar 

  7. I. R. Manchester, U. Mettin, F. Iida and R. Tedrake, Stable dynamic walking over uneven terrain, The International Journal of Robotics Research, 30 (3) (2011) 265–279.

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  9. R. Q. Van Der Linde, Active leg compliance for passive walking, Proceedings of 1998 IEEE International Conference on Robotics and Automation, Leuven, Belgium (1998) 2339–2344.

    Google Scholar 

  10. Q. Wang, Y. Huang and L. Wang, Passive dynamic walking with flat feet and ankle compliance, Robotica, 28 (3) (2010) 413–425.

    Article  Google Scholar 

  11. B. Whittington, A. Silder, B. Heiderscheit and D. G. Thelen, The contribution of passive-elastic mechanisms to lower extremity joint kinetics during human walking, Gait & Posture, 27 (4) (2008) 628–634.

    Article  Google Scholar 

  12. Y. Or and M. Moravia, Analysis of foot slippage effects on an actuated spring-mass model of dynamic legged locomotion, International Journal of Advanced Robotic Systems, 13 (2) (2016) 69.

    Article  Google Scholar 

  13. T. Narukawa, M. Takahashi and K. Yoshida, Efficient walking with optimization for a planar biped walker with a torso by hip actuators and springs, Robotica, 29 (4) (2011) 641–648.

    Article  Google Scholar 

  14. G. Gilardi and I. Sharf, Literature survey of contact dynamics modelling, Mechanism and Machine Theory, 37 (10) (2002) 1213–1239.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. J. W. Grizzle, C. Chevallereau, R. W. Sinnet and A. D. Ames, Models, feedback control, and open problems of 3D bipedal robotic walking, Automatica, 50 (8) (2014) 1955–1988.

    Article  MathSciNet  MATH  Google Scholar 

  17. K. An, Z. Fang, Y. Li and Q. Chen, Internal features in basin of attraction of the simplest walking model, Journal of Mechanical Science and Technology, 29 (11) (2015) 4913–4921.

    Article  Google Scholar 

  18. M. W. Whittle, Gait analysis, An introduction, Butterworth- Heinemann, Oxford, UK (1991).

    Google Scholar 

  19. I. Takewaki, Probabilistic critical excitation for MDOF elastic-plastic structures on compliant ground, Earthquake Engineering & Structural Dynamics, 30 (9) (2001) 1345–1360.

    Article  Google Scholar 

  20. K. Kojima and I. Takewaki, Closed-form critical earthquake response of elastic-plastic structures on compliant ground under near-fault ground motions, Frontiers in Built Environment, 2 (2016) 1.

    Google Scholar 

  21. F. Plestan, J. W. Grizzle, E. R. Westervelt and G. Abba, Stable walking of a 7-DOF biped robot, IEEE Transactions on Robotics and Automation, 19 (4) (2003) 653–668.

    Article  Google Scholar 

  22. E. R. Westervelt, J. W. Grizzle, C. Chevallereau, J. H. Choi and B. Morris, Feedback control of dynamic bipedal robot locomotion, CRC Press, USA (2007).

    Book  Google Scholar 

  23. P. S. Freeman and D. E. Orin, Efficient dynamic simulation of a quadruped using a decoupled tree-structure approach, The International Journal of Robotics Research, 10 (6) (1991) 619–627.

    Article  Google Scholar 

  24. D. W. Marhefka and D. E. Orin, Simulation of contact using a nonlinear damping model, Proceedings of 1996 IEEE International Conference on Robotics and Automation, Minneapolis, MN, USA (1996) 1662–1668.

    Chapter  Google Scholar 

  25. Y. Wang, J. Ding and X. Xiao, An adaptive feedforward control method for under-actuated bipedal walking on the compliant ground, International Journal of Robotics and Automation, 32 (1) (2017) 63–77.

    Google Scholar 

  26. M. Peasgood, E. Kubica and J. McPhee, Stabilization of a dynamic walking gait simulation, Journal of Computational and Nonlinear Dynamics, 2 (1) (2007) 65–72.

    Article  Google Scholar 

  27. F. Qi, T. Wang and J. Li, The elastic contact influences on passive walking gaits, Robotica, 29 (5) (2011) 787–796.

    Article  Google Scholar 

  28. D. Koop and C. Q. Wu, Passive dynamic biped walking- Part I: Development and validation of an advanced model, Journal of Computational and Nonlinear Dynamics, 8 (4) (2013) 041007.

    Article  Google Scholar 

  29. A. Goswami, B. Thuilot and B. Espiau, A study of the passive gait of a compass-like biped robot: Symmetry and chaos, The International Journal of Robotics Research, 17 (12) (1998) 1282–1301.

    Article  Google Scholar 

  30. K. L. Johnson, Contact mechanics, Cambridge University Press (1987).

    MATH  Google Scholar 

  31. K. H. Hunt and F. R. E. Crossley, Coefficient of restitution interpreted as damping in vibroimpact, Journal of Applied Mechanics, 42 (2) (1975) 440–445.

    Article  Google Scholar 

  32. K. J. Bathe, Finite element procedures in engineering analysis, Prentice-Hall, New Jersey, USA (1982).

    Google Scholar 

  33. P. Eberhard and B. Hu, Advanced contact dynamics, Southeast University Press, Nan-Jing, China (2003).

    Google Scholar 

  34. C. S. Hsu, Cell to cell mapping: A method of global analysis for nonlinear systems, Springer Science+Business Media, New York, USA (1987).

    Book  MATH  Google Scholar 

  35. D. D. Frey and H. Wang, Adaptive one-factor-at-a-time experimentation and expected value of improvement, Technometrics, 48 (3) (2006) 418–431.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

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

    Yao Wu, Daojin Yao & Xiaohui Xiao

Authors
  1. Yao Wu
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  2. Daojin Yao
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  3. Xiaohui Xiao
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Corresponding author

Correspondence to Xiaohui Xiao.

Additional information

Recommended by Associate Editor Hak Yi

Yao Wu obtained his B.S. in Communication Engineering from Beijing Information Science and Technology University, Beijing, in 2012. Obtained his M.S. in Machine Manufacture and Automation from Beijing Technology and Business University, Beijing, in 2015. Currently, he is pursuing the Ph.D. degree in Mechanical Engineering from Wuhan University, Wuhan, China. His research interests include biped robot dynamics and control.

Daojin Yao obtained his B.S. in Mechanical and Electronic Engineering from East China Jiaotong University, Nanchang, in 2012. He obtained his M.S. in Mechanical and Electronic Engineering from Wuhan University of Technology, Wuhan, in 2015. Currently, he is pursuing a Ph.D. in Mechanical Engineering from Wuhan University, Wuhan, China. His research interests include robot control, electronic circuit design, and embedded programming.

Xiaohui Xiao received the B.S. and M.S. degrees in Mechanical Engineering from Wuhan University, Wuhan, China, in 1991 and 1998, respectively, and the Ph.D. degree in mechanical engineering from Huazhong University of Science and Technology, Wuhan, China, in 2005. She joined the Wuhan University, Wuhan, China, in 1998, where she is currently a Full Professor with the Mechanical Engineering Department, School of Power and Mechanical Engineering. She has published over 30 papers in the areas of mobile robots, dynamics and control, sensors and signal procession. Her current research interests include mobile robotics, high-precision positioning control, and signal processing.

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Wu, Y., Yao, D. & Xiao, X. The effects of ground compliance on flexible planar passive biped dynamic walking. J Mech Sci Technol 32, 1793–1804 (2018). https://doi.org/10.1007/s12206-018-0336-0

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  • DOI: https://doi.org/10.1007/s12206-018-0336-0

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