An Improved Model to Estimate Muscle-Tendon Mechanics and Energetics During Walking with a Passive Ankle Exoskeleton

  • Nianfeng Wang
  • Yihong ZhongEmail author
  • Xianmin Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11740)


One experiment has shown that wearing an elastic ankle exoskeleton can reduce the metabolic cost of walking by \(7.2\pm 2.6\%\), and the best exoskeleton stiffness is 180 Nm/rad. A model has evaluated the plantar flexor muscle-tendon mechanics and energetics during walking with this unpowered exoskeleton, but the optimal stiffness value is twice that of the experiment, so the simulated muscle-tendon mechanics and energetics may be somewhat biased. The purpose of this paper is to develop a model to match the simulation results to the experimental results and to better explore the muscle-tendon mechanics and energetics. The main improvements of this study are: (1) adding the modeling of dorsiflexor to match the work efficiency of plantar flexor and dorsiflexor, (2) analyzing the distribution of moments when the assistant moment is too large, and (3) updating the calculation process. By the improved model, the error of the optimal stiffness is reduced to 3.3%, and the error of the reduction rate of metabolic cost is reduced to nearly 0%.


Ankle joint Human walking Muscle-tendon dynamics Metabolic energy cost Passive elastic exoskeleton 



The authors would like to gratefully acknowledge the reviewers comments. This work is supported by National Natural Science Foundation of China (Grant Nos. U1713207), Science and Technology Planning Project of Guangdong Province (2017A010102005), Key Program of Guangzhou Technology Plan (Grant No. 201904020020).


  1. 1.
    Sankai, Y.: Leading edge of cybernics: robot suit HAL. In: 2006 SICE-ICASE International Joint Conference, pp. P–1. IEEE (2006)Google Scholar
  2. 2.
    Walsh, C.J., Endo, K., Herr, H.: A quasi-passive leg exoskeleton for load-carrying augmentation. Int. J. Humanoid Rob. 4(03), 487–506 (2007)CrossRefGoogle Scholar
  3. 3.
    Mooney, L.M., Rouse, E.J., Herr, H.M.: Autonomous exoskeleton reduces metabolic cost of human walking during load carriage. J. Neuroeng. Rehabil. 11(1), 80 (2014)CrossRefGoogle Scholar
  4. 4.
    Panizzolo, F.A., et al.: A biologically-inspired multi-joint soft exosuit that can reduce the energy cost of loaded walking. J. Neuroeng. Rehabil. 13(1), 43 (2016)CrossRefGoogle Scholar
  5. 5.
    Collins, S.H., Wiggin, M.B., Sawicki, G.S.: Reducing the energy cost of human walking using an unpowered exoskeleton. Nature 522(7555), 212 (2015)CrossRefGoogle Scholar
  6. 6.
    Rajagopal, A., Dembia, C.L., DeMers, M.S., Delp, D.D., Hicks, J.L., Delp, S.L.: Full-body musculoskeletal model for muscle-driven simulation of human gait. IEEE Trans. Biomed. Eng. 63(10), 2068–2079 (2016)CrossRefGoogle Scholar
  7. 7.
    Uchida, T.K., Seth, A., Pouya, S., Dembia, C.L., Hicks, J.L., Delp, S.L.: Simulating ideal assistive devices to reduce the metabolic cost of running. PLoS ONE 11(9), e0163417 (2016)CrossRefGoogle Scholar
  8. 8.
    Sawicki, G.S., Khan, N.S.: A simple model to estimate plantarflexor muscle-tendon mechanics and energetics during walking with elastic ankle exoskeletons. IEEE Trans. Biomed. Eng. 63(5), 914–923 (2016)CrossRefGoogle Scholar
  9. 9.
    Zajac, F.E.: Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Crit. Rev. Biomed. Eng. 17(4), 359–411 (1989)Google Scholar
  10. 10.
    Brand, R.A., Crowninshield, R.D., Wittstock, C., Pedersen, D., Clark, C.R., Van Krieken, F.: A model of lower extremity muscular anatomy. J. Biomech. Eng. 104(4), 304–310 (1982)CrossRefGoogle Scholar
  11. 11.
    Arnold, E.M., Ward, S.R., Lieber, R.L., Delp, S.L.: A model of the lower limb for analysis of human movement. Ann. Biomed. Eng. 38(2), 269–279 (2010)CrossRefGoogle Scholar
  12. 12.
    Geyer, H., Herr, H.: A muscle-reflex model that encodes principles of legged mechanics produces human walking dynamics and muscle activities. IEEE Trans. Neural Syst. Rehabil. Eng. 18(3), 263–273 (2010)CrossRefGoogle Scholar
  13. 13.
    Maganaris, C.N.: In vivo measurement-based estimations of the moment arm in the human tibialis anterior muscle-tendon unit. J. Biomech. 33(3), 375–379 (2000)CrossRefGoogle Scholar
  14. 14.
    Maganaris, C.N., Baltzopoulos, V., Sargeant, A.J.: In vivo measurement-based estimations of the human achilles tendon moment arm. Eur. J. Appl. Physiol. 83(4–5), 363–369 (2000)CrossRefGoogle Scholar
  15. 15.
    Wu, S., Chen, W., Xiong, C.: A simplified musculoskeletal hip model for replicating the natural human walking behavior. In: 2018 3rd International Conference on Advanced Robotics and Mechatronics (ICARM), pp. 426–430. IEEE (2018)Google Scholar
  16. 16.
    Chleboun, G.S., Busic, A.B., Graham, K.K., Stuckey, H.A.: Fascicle length change of the human tibialis anterior and vastus lateralis during walking. J. Orthop. Sport. Phys. Ther. 37(7), 372–379 (2007)CrossRefGoogle Scholar
  17. 17.
    Thelen, D.G., Anderson, F.C.: Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. J. Biomech. 39(6), 1107–1115 (2006)CrossRefGoogle Scholar
  18. 18.
    Rubenson, J., Pires, N.J., Loi, H.O., Pinniger, G.J., Shannon, D.G.: On the ascent: the soleus operating length is conserved to the ascending limb of the force-length curve across gait mechanics in humans. J. Exp. Biol. 215(20), 3539–3551 (2012)CrossRefGoogle Scholar
  19. 19.
    Alexander, R.M.: Optimum muscle design for oscillatory movements. J. Theor. Biol. 184(3), 253–259 (1997)CrossRefGoogle Scholar
  20. 20.
    Umberger, B.R., Rubenson, J.: Understanding muscle energetics in locomotion: new modeling and experimental approaches. Exerc. Sport Sci. Rev. 39(2), 59–67 (2011)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Guangdong Provincial Key Laboratory of Precision Equipment and Manufacturing Technology, School of Mechanical and Automotive EngineeringSouth China University of TechnologyGuangzhouChina

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