Skip to main content
SpringerLink
Log in

Forward dynamics simulation of a simplified neuromuscular-skeletal-exoskeletal model based on the CMA-ES optimization algorithm: framework and case studies

  • Research
  • Published:
Multibody System Dynamics Aims and scope Submit manuscript

Abstract

The modeling and simulation of coupled neuromusculoskeletal-exoskeletal systems play a crucial role in human biomechanical analysis, as well as in the design and control of exoskeletons. This study incorporates the integration of exoskeleton models into a reflex-based gait model, emphasizing human-exoskeleton interaction. Specifically, we introduce an optimization-based dynamic simulation framework that integrates a neuromusculoskeletal feedback loop, multibody dynamics, human-exoskeleton interaction, and foot-ground contact. The framework advances in human-exoskeleton interaction and muscle reflex model refinement. Without relying on experimental measurements or empirical data, our framework employs a stepwise optimization process to determine muscle reflex parameters, taking into account multidimensional criteria. This allows the framework to generate a full range of kinematic and biomechanical signals, including muscle activations, muscle forces, joint torques, etc., which are typically challenging to measure experimentally. To evaluate the validity of the framework, we compare the simulated results with experimental data obtained from a healthy subject wearing an exoskeleton while walking at different speeds (0.9, 1.0, and 1.1 m/s) and terrains (flat and uphill). The results demonstrate that our framework can capture the qualitative differences in muscle activity associated with different functions, as well as the evolutionary patterns of muscle activity and kinematic signals with respect to varying walking conditions, with the Pearson correlation coefficient R > 0.7. Simulations of the human walking with the exoskeleton in both passive mode and assisting mode at a peak torque of 20 N⋅m are further conducted to investigate the effect of exoskeleton assistance on human biomechanics. The simulation framework we propose has the potential to facilitate gait analysis and performance evaluation of coupled human-exoskeleton systems, as well as enable efficient and cost-effective testing of novel exoskeleton designs and control strategies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data Availability

No datasets were generated or analysed during the current study.

References

  1. Dollar, A.M., Herr, H.: Lower extremity exoskeletons and active orthoses: challenges and state-of-the-art. IEEE Trans. Robot. 24, 144–158 (2008). https://doi.org/10.1109/TRO.2008.915453

    Article  Google Scholar 

  2. Harant, M., Näf, M.B., Mombaur, K.: Multibody dynamics and optimal control for optimizing spinal exoskeleton design and support. Multibody Syst. Dyn. 57, 389–411 (2023). https://doi.org/10.1007/s11044-023-09877-w

    Article  MathSciNet  Google Scholar 

  3. Nasr, A., Bell, S., McPhee, J.: Optimal design of active-passive shoulder exoskeletons: a computational modeling of human-robot interaction. Multibody Syst. Dyn. 57, 73–106 (2023). https://doi.org/10.1007/s11044-022-09855-8

    Article  MathSciNet  Google Scholar 

  4. Nam, K.Y., Kim, H.J., Kwon, B.S., Park, J.W., Lee, H.J., Yoo, A.: Robot-assisted gait training (Lokomat) improves walking function and activity in people with spinal cord injury: a systematic review. J. NeuroEng. Rehabil. 14, 1–13 (2017). https://doi.org/10.1186/s12984-017-0232-3

    Article  Google Scholar 

  5. de Looze, M.P., Bosch, T., Krause, F., Stadler, K.S., O’Sullivan, L.W.: Exoskeletons for industrial application and their potential effects on physical work load. Ergonomics 59, 671–681 (2016). https://doi.org/10.1080/00140139.2015.1081988

    Article  Google Scholar 

  6. Collins, S.H., Bruce Wiggin, M., Sawicki, G.S.: Reducing the energy cost of human walking using an unpowered exoskeleton. Nature 522, 212–215 (2015). https://doi.org/10.1038/nature14288

    Article  Google Scholar 

  7. Ishmael, M.K., Archangeli, D., Lenzi, T.: Powered hip exoskeleton improves walking economy in individuals with above-knee amputation. Nat. Med. 27, 1783–1788 (2021). https://doi.org/10.1038/s41591-021-01515-2

    Article  Google Scholar 

  8. Park, K.W., Choi, J., Kong, K.: Iterative learning of human behavior for adaptive gait pattern adjustment of a powered exoskeleton. IEEE Trans. Robot. 38, 1395–1409 (2022). https://doi.org/10.1109/TRO.2022.3144955

    Article  Google Scholar 

  9. Ishmael, M.K., Archangeli, D., Lenzi, T.: A powered hip exoskeleton with high torque density for walking, running, and stair ascent. IEEE/ASME Trans. Mechatron. 27, 4561–4572 (2022). https://doi.org/10.1109/TMECH.2022.3159506

    Article  Google Scholar 

  10. Sarkisian, S.V., Ishmael, M.K., Lenzi, T.: Self-aligning mechanism improves comfort and performance with a powered knee exoskeleton. IEEE Trans. Neural Syst. Rehabil. Eng. 29, 629–640 (2021). https://doi.org/10.1109/TNSRE.2021.3064463

    Article  Google Scholar 

  11. Zoss, A.B., Kazerooni, H., Chu, A.: Biomechanical design of the Berkeley Lower Extremity Exoskeleton (BLEEX). IEEE/ASME Trans. Mechatron. 11, 128–138 (2006). https://doi.org/10.1109/TMECH.2006.871087

    Article  Google Scholar 

  12. Martini, E., Crea, S., Parri, A., Bastiani, L., Faraguna, U., McKinney, Z., Molino-Lova, R., Pratali, L., Vitiello, N.: Gait training using a robotic hip exoskeleton improves metabolic gait efficiency in the elderly. Sci. Rep. 9, 7157 (2019). https://doi.org/10.1038/s41598-019-43628-2

    Article  Google Scholar 

  13. Mo, F., Zhang, Q., Zhang, H., Long, J., Wang, Y., Chen, G., Ye, J.: A simulation-based framework with a proprioceptive musculoskeletal model for evaluating the rehabilitation exoskeleton system. Comput. Methods Programs Biomed. 208, 106270 (2021). https://doi.org/10.1016/j.cmpb.2021.106270

    Article  Google Scholar 

  14. Padmanabha, G.A., Ramalingasetty, S.T., Vetrivel, B., Mukherjee, I., Omkar, S.N., Sivakumar, R.: Computational modelling of musculoskeletal to predict the human response with exoskeleton suit. Int. J. Biomechatronics Biomed. Robot. 3, 169 (2020). https://doi.org/10.1504/ijbbr.2020.108441

    Article  Google Scholar 

  15. Gordon, D.F.N., McGreavy, C., Christou, A., Vijayakumar, S.: Human-in-the-loop optimization of exoskeleton assistance via online simulation of metabolic cost. IEEE Trans. Robot. 38, 1410–1429 (2022). https://doi.org/10.1109/TRO.2021.3133137

    Article  Google Scholar 

  16. Ezati, M., Ghannadi, B., McPhee, J.: A review of simulation methods for human movement dynamics with emphasis on gait. Multibody Syst. Dyn. 47, 265–292 (2019). https://doi.org/10.1007/s11044-019-09685-1

    Article  MathSciNet  Google Scholar 

  17. Bianco, N.A., Franks, P.W., Hicks, J.L., Delp, S.L.: Coupled exoskeleton assistance simplifies control and maintains metabolic benefits: a simulation study. PLoS ONE 17, 1–18 (2022). https://doi.org/10.1371/journal.pone.0261318

    Article  Google Scholar 

  18. Li, X., Chen, J., Wang, W., Zhang, F., Han, H., Zhang, J.: Using predictive simulation methods to design suitable assistance modes for human walking on slopes. 2020 3rd Int. Conf. Control Robot. ICCR 2020, 169–175 (2020). https://doi.org/10.1109/ICCR51572.2020.9344320

    Article  Google Scholar 

  19. Uhlrich, S.D., Uchida, T.K., Lee, M.R., Delp, S.L.: Ten steps to becoming a musculoskeletal simulation expert: a half-century of progress and outlook for the future. J. Biomech. 154, 1–41 (2023). https://doi.org/10.1016/j.jbiomech.2023.111623

    Article  Google Scholar 

  20. Yu, J., Zhang, S., Wang, A., Li, W.: Human gait analysis based on OpenSim. In: International Conference on Advanced Mechatronic Systems, ICAMechS, pp. 278–281 (2020)

    Google Scholar 

  21. 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, 263–273 (2010). https://doi.org/10.1109/TNSRE.2010.2047592

    Article  Google Scholar 

  22. Sinica, A.M.: A forward-inverse dynamics modeling framework for a forward-inverse dynamics modeling framework for human musculoskeletal multibody system (2022)

  23. Ignasiak, D.: A novel method for prediction of postoperative global sagittal alignment based on full-body musculoskeletal modeling and posture optimization. J. Biomech. 102, 109324 (2020). https://doi.org/10.1016/j.jbiomech.2019.109324

    Article  Google Scholar 

  24. Karatsidis, A., Jung, M., Schepers, H.M., Bellusci, G., de Zee, M., Veltink, P.H., Andersen, M.S.: Musculoskeletal model-based inverse dynamic analysis under ambulatory conditions using inertial motion capture. Med. Eng. Phys. 65, 68–77 (2019). https://doi.org/10.1016/j.medengphy.2018.12.021

    Article  Google Scholar 

  25. Mathai, B., Gupta, S.: Numerical predictions of hip joint and muscle forces during daily activities: a comparison of musculoskeletal models. Proc. Inst. Mech. Eng., H J. Eng. Med. 233, 636–647 (2019). https://doi.org/10.1177/0954411919840524

    Article  Google Scholar 

  26. Millard, M., Emonds, A.L., Harant, M., Mombaur, K.: A reduced muscle model and planar musculoskeletal model fit for the simulation of whole-body movements. J. Biomech. 89, 11–20 (2019). https://doi.org/10.1016/j.jbiomech.2019.04.004

    Article  Google Scholar 

  27. Weng, J., Hashemi, E., Arami, A.: Adaptive reference inverse optimal control for natural walking with musculoskeletal models. IEEE Trans. Neural Syst. Rehabil. Eng. 30, 1567–1575 (2022). https://doi.org/10.1109/TNSRE.2022.3180690

    Article  Google Scholar 

  28. Willson, A.M., Anderson, A.J., Richburg, C.A., Muir, B.C., Czerniecki, J., Steele, K.M., Aubin, P.M.: Full body musculoskeletal model for simulations of gait in persons with transtibial amputation. Comput. Methods Biomech. Biomed. Eng. 26, 412–423 (2023). https://doi.org/10.1080/10255842.2022.2065630

    Article  Google Scholar 

  29. Quental, C., Simões, F., Sequeira, M., Ambrósio, J., Vilas-Boas, J.P., Nakashima, M.: A multibody methodological approach to the biomechanics of swimmers including hydrodynamic forces. Multibody Syst. Dyn. 57, 413–426 (2023). https://doi.org/10.1007/s11044-022-09865-6

    Article  MathSciNet  Google Scholar 

  30. Engelhardt, L., Melzner, M., Havelkova, L., Fiala, P., Christen, P., Dendorfer, S., Simon, U.: A new musculoskeletal AnyBodyTM detailed hand model. Comput. Methods Biomech. Biomed. Eng. 24, 777–787 (2020). https://doi.org/10.1080/10255842.2020.1851367

    Article  Google Scholar 

  31. Fonk, R., Schneeweiss, S., Simon, U., Engelhardt, L.: Hand motion capture from a 3d leap motion controller for a musculoskeletal dynamic simulation. Sensors 21, 1199 (2021). https://doi.org/10.3390/s21041199

    Article  Google Scholar 

  32. Michnik, R., ZadoŃ, H., Nowakowska-Lipiec, K., Jochymczyk-WoŹniak, K., MyŚliwiec, A., Mitas, A.W.: The effect of the pelvis position in the sagittal plane on loads in the human musculoskeletal system. Acta Bioeng. Biomech. 22, 33–42 (2020). https://doi.org/10.37190/ABB-01606-2020-02

    Article  Google Scholar 

  33. Trinler, U., Schwameder, H., Baker, R., Alexander, N.: Muscle force estimation in clinical gait analysis using AnyBody and OpenSim. J. Biomech. 86, 55–63 (2019). https://doi.org/10.1016/j.jbiomech.2019.01.045

    Article  Google Scholar 

  34. Ackermann, M., van den Bogert, A.J.: Optimality principles for model-based prediction of human gait. J. Biomech. 43, 1055–1060 (2010). https://doi.org/10.1016/j.jbiomech.2009.12.012

    Article  Google Scholar 

  35. Caruntu, D.I., Moreno, R.: Human knee inverse dynamics model of vertical jump exercise. J. Comput. Nonlinear Dyn. 14, 101005 (2019). https://doi.org/10.1115/1.4044246

    Article  Google Scholar 

  36. Zhao, Y., Li, Z., Zhang, Z., Qian, K., Xie, S.: An EMG-driven musculoskeletal model for estimation of wrist kinematics using mirrored bilateral movement. Biomed. Signal Process. Control 81, 104480 (2023). https://doi.org/10.1016/j.bspc.2022.104480

    Article  Google Scholar 

  37. Yao, S., Zhuang, Y., Li, Z., Song, R.: Adaptive admittance control for an ankle exoskeleton using an EMG-driven musculoskeletal model. Front. Neurorobot. 12 (2018). https://doi.org/10.3389/fnbot.2018.00016

  38. Sun, L., An, H., Ma, H., Wei, Q.: Research on assistance evaluation and online optimization method of lower limb exoskeleton based on musculoskeletal model. In: Proceedings of the 31st Chinese Control and Decision Conference, CCDC 2019, pp. 4974–4979. IEEE Press, New York (2019)

    Google Scholar 

  39. Moya-Esteban, A., van der Kooij, H., Sartori, M.: Robust estimation of lumbar joint forces in symmetric and asymmetric lifting tasks via large-scale electromyography-driven musculoskeletal models. J. Biomech. 144, 111307 (2022). https://doi.org/10.1016/j.jbiomech.2022.111307

    Article  Google Scholar 

  40. Bélaise, C., Dal Maso, F., Michaud, B., Mombaur, K., Begon, M.: An EMG-marker tracking optimisation method for estimating muscle forces. Multibody Syst. Dyn. 42, 119–143 (2018). https://doi.org/10.1007/s11044-017-9587-2

    Article  Google Scholar 

  41. Guo, J., Chen, J., Wang, J., Ren, G., Tian, Q., Guo, C.: EMG-assisted forward dynamics simulation of subject-specific mandible musculoskeletal system. J. Biomech. 139, 111143 (2022). https://doi.org/10.1016/j.jbiomech.2022.111143

    Article  Google Scholar 

  42. Song, S., Geyer, H.: A neural circuitry that emphasizes spinal feedback generates diverse behaviours of human locomotion. J. Physiol. 593, 3493–3511 (2015). https://doi.org/10.1113/JP270228

    Article  Google Scholar 

  43. Van Wouwe, T., Ting, L.H., De Groote, F.: An approximate stochastic optimal control framework to simulate nonlinear neuromusculoskeletal models in the presence of noise. PLoS Comput. Biol. 18, 1–30 (2022). https://doi.org/10.1371/journal.pcbi.1009338

    Article  Google Scholar 

  44. Dorschky, E., Nitschke, M., Seifer, A.K., van den Bogert, A.J., Eskofier, B.M.: Estimation of gait kinematics and kinetics from inertial sensor data using optimal control of musculoskeletal models. J. Biomech. 95, 109278 (2019). https://doi.org/10.1016/j.jbiomech.2019.07.022

    Article  Google Scholar 

  45. Falisse, A., Serrancolí, G., Dembia, C.L., Gillis, J., Jonkers, I., De Groote, F.: Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies. J. R. Soc. Interface 16, 20190402 (2019). https://doi.org/10.1098/rsif.2019.0402

    Article  Google Scholar 

  46. Shourijeh, M.S., McPhee, J.: Forward dynamic optimization of human gait simulations: a global parameterization approach. J. Comput. Nonlinear Dyn. 9, 031018 (2014). https://doi.org/10.1115/1.4026266

    Article  Google Scholar 

  47. Hansen, N.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evol. Comput. 11, 1–18 (2003)

    Article  Google Scholar 

  48. Wang, X., Chen, J., Qiao, H.: Motion learning and rapid generalization for musculoskeletal systems based on recurrent neural network modulated by initial states. IEEE Trans. Cogn. Dev. Syst. 14, 1691–1704 (2022). https://doi.org/10.1109/TCDS.2021.3136854

    Article  Google Scholar 

  49. Chen, J., Qiao, H.: Muscle-synergies-based neuromuscular control for motion learning and generalization of a musculoskeletal system. IEEE Trans. Syst. Man Cybern. Syst. 51, 3993–4006 (2021). https://doi.org/10.1109/TSMC.2020.2966818

    Article  Google Scholar 

  50. Wang, X., Guo, J., Tian, Q.: A forward-inverse dynamics modeling framework for human musculoskeletal multibody system. Acta Mech. Sin. Xuebao 38, 522140 (2022). https://doi.org/10.1007/s10409-022-22140-x

    Article  MathSciNet  Google Scholar 

  51. Diao, H., Xin, H., Dong, J., He, X., Li, D., Jin, Z.: Prediction of cervical spinal joint loading and secondary motion using a musculoskeletal multibody dynamics model via force-dependent kinematics approach. Spine 42(24), E1403–E1409 (2017). https://doi.org/10.1097/BRS.0000000000002176

    Article  Google Scholar 

  52. Andersen, M.S., De Zee, M., Damsgaard, M., Nolte, D., Rasmussen, J.: Introduction to force-dependent kinematics: theory and application to mandible modeling. J. Biomech. Eng. 139, 091001 (2017). https://doi.org/10.1115/1.4037100

    Article  Google Scholar 

  53. Thelen, D.G., Anderson, F.C.: Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. J. Biomech. 39, 1107–1115 (2006). https://doi.org/10.1016/j.jbiomech.2005.02.010

    Article  Google Scholar 

  54. Thelen, D.G., Anderson, F.C., Delp, S.L.: Generating dynamic simulations of movement using computed muscle control. J. Biomech. 36, 321–328 (2003). https://doi.org/10.1016/S0021-9290(02)00432-3

    Article  Google Scholar 

  55. Shourijeh, M.S., Smale, K.B., Potvin, B.M., Benoit, D.L.: A forward-muscular inverse-skeletal dynamics framework for human musculoskeletal simulations. J. Biomech. 49, 1718–1723 (2016). https://doi.org/10.1016/j.jbiomech.2016.04.007

    Article  Google Scholar 

  56. Whittle, M.W.: Gait and Analysis an Introduction (2007)

    Google Scholar 

  57. Whittle, M.W.: Gait Analysis: An Introduction. Butterworth-Heinemann, UK (2003)

    Google Scholar 

  58. Geyer, H., Seyfarth, A., Blickhan, R.: Positive force feedback in bouncing gaits? Proc. R. Soc. Lond. B, Biol. Sci. 270, 2173–2183 (2003). https://doi.org/10.1098/rspb.2003.2454

    Article  Google Scholar 

  59. Geijtenbeek, T., Van De Panne, M., Van Der Stappen, A.F.: Flexible muscle-based locomotion for bipedal creatures. ACM Trans. Graph. 32 (2013). https://doi.org/10.1145/2508363.2508399

  60. Rockenfeller, R., Günther, M., Schmitt, S., Götz, T.: Comparative sensitivity analysis of muscle activation dynamics. Comput. Math. Methods Med. 2015 (2015). https://doi.org/10.1155/2017/6752731

  61. Guo, J., Huang, H., Yu, Y., Liang, Z., Ambrósio, J., Zhao, Z., Ren, G., Ao, Y.: Modeling muscle wrapping and mass flow using a mass-variable multibody formulation. Multibody Syst. Dyn. 49, 315–336 (2020). https://doi.org/10.1007/s11044-020-09733-1

    Article  MathSciNet  Google Scholar 

  62. Guo, J., Sun, Y., Hao, Y., Cui, L., Ren, G.: A mass-flowing muscle model with shape restrictive soft tissues: correlation with sonoelastography. Biomech. Model. Mechanobiol. 19, 911–926 (2020). https://doi.org/10.1007/s10237-019-01260-z

    Article  Google Scholar 

  63. Millard, M., Uchida, T., Seth, A., Delp, S.L.: Flexing computational muscle: modeling and simulation of musculotendon dynamics. J. Biomech. Eng. 135, 021005 (2013). https://doi.org/10.1115/1.4023390

    Article  Google Scholar 

  64. Charles, J.P., Cappellari, O., Spence, A.J., Hutchinson, J.R., Wells, D.J.: Musculoskeletal geometry, muscle architecture and functional specialisations of the mouse hindlimb. PLoS ONE 11, e0147669 (2016). https://doi.org/10.1371/journal.pone.0147669

    Article  Google Scholar 

  65. Geijtenbeek, T.: SCONE: open source software for predictive simulation of biological motion. J. Open Sour. Softw. 4, 1421 (2019). https://doi.org/10.21105/joss.01421

    Article  Google Scholar 

  66. Jin, W., Fang, H.: Design and preliminary evaluation of a lightweight, cable-driven hip exoskeleton for walking assistance. In: 2022 IEEE International Conference on Robotics and Biomimetics, ROBIO 2022, pp. 291–296. IEEE Press, New York (2022)

    Google Scholar 

  67. Mitchell, H.H., Hamilton, T.S., Steggerda, F.R., Bean, H.W.: The chemical composition of the adult human body and its bearing on the biochemistry of growth. J. Biol. Chem. 158, 625–637 (1945)

    Article  Google Scholar 

  68. Anderson, F.C., Pandy, M.G.: A dynamic optimization solution for vertical jumping in three dimensions. Comput. Methods Biomech. Biomed. Eng. 2, 201–231 (1999). https://doi.org/10.1080/10255849908907988

    Article  Google Scholar 

  69. Langlois, K., Rodriguez-Cianca, D., Serrien, B., De Winter, J., Verstraten, T., Rodriguez-Guerrero, C., Vanderborght, B., Lefeber, D.: Investigating the effects of strapping pressure on human-robot interface dynamics using a soft robotic cuff. IEEE Trans. Med. Robot. Bionics. 3, 146–155 (2020). https://doi.org/10.1109/TMRB.2020.3042255

    Article  Google Scholar 

  70. Ka, D.M., Hong, C., Toan, T.H., Qiu, J.: Minimizing human-exoskeleton interaction force by using global fast sliding mode control. Int. J. Control. Autom. Syst. 14, 1064–1073 (2016). https://doi.org/10.1007/s12555-014-0395-7

    Article  Google Scholar 

  71. Hunt, K., Crossley, E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. (1975)

  72. Simbody (2023). HuntCrossleyForce class reference, simbody.github.io/3.7.0/classSimTK_1_1HuntCrossleyForce.html

  73. Wang, J.M., Hamner, S.R., Delp, S.L., Koltun, V.: Optimizing locomotion controllers using biologically-based actuators and objectives. In: ACM Transactions on Graphics (2012)

    Google Scholar 

  74. Hansen, N.: The CMA evolution strategy: a comparing review. Stud. Fuzziness Soft Comput. 192, 75–102 (2006). https://doi.org/10.1007/11007937_4

    Article  Google Scholar 

  75. Buchanan, T.S., Lloyd, D.G., Manal, K., Besier, T.F.: Neuromusculoskeletal modeling: estimation of muscle forces and joint moments and movements from measurements of neural command. J. Appl. Biomech. 20, 367–395 (2004)

    Article  Google Scholar 

  76. Saito, A., Tomita, A., Ando, R., Watanabe, K., Akima, H.: Similarity of muscle synergies extracted from the lower limb including the deep muscles between level and uphill treadmill walking. Gait Posture 59, 134–139 (2018). https://doi.org/10.1016/j.gaitpost.2017.10.007

    Article  Google Scholar 

  77. Wren, T.A.L., Do Patrick, K., Rethlefsen, S.A., Healy, B.: Cross-correlation as a method for comparing dynamic electromyography signals during gait. J. Biomech. 39, 2714–2718 (2006). https://doi.org/10.1016/j.jbiomech.2005.09.006

    Article  Google Scholar 

  78. Asbeck, A.T., De Rossi, S.M.M., Holt, K.G., Walsh, C.J.: A biologically inspired soft exosuit for walking assistance. Int. J. Robot. Res. 34, 744–762 (2014)

    Article  Google Scholar 

  79. Franz, J.R., Kram, R.: The efect of grade and speed during walking. Gait Posture 35, 143–147 (2013). https://doi.org/10.1016/j.gaitpost.2011.08.025

    Article  Google Scholar 

  80. Schmitz, A., Silder, A., Heiderscheit, B., Mahoney, J., Thelen, D.G.: Differences in lower-extremity muscular activation during walking between healthy older and young adults. J. Electromyogr. Kinesiol. 19, 1085–1091 (2009). https://doi.org/10.1016/j.jelekin.2008.10.008

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the Reviewers for their detailed, insightful, and constructive comments, which have greatly contributed to the quality of this manuscript. The authors would also like to thank Mr. Chenghang Ye for his help in producing the supplementary videos.

Funding

This research was supported by the National Natural Science Foundation of China (Grants No. 12272096) and the Shanghai Pilot Program for Basic Research - Fudan University 21TQ1400100-22TQ009.

Author information

Authors and Affiliations

  1. Institute of AI and Robotics, State Key Laboratory of Medical Neurobiology, MOE Engineering Research Center of AI & Robotics, Fudan University, Shanghai, 200433, China

    Wei Jin, Qiwei Zhang, Xiaoxu Zhang & Hongbin Fang

  2. Yiwu Research Institute, Fudan University, Yiwu, Zhejiang Province, 322000, China

    Wei Jin, Qiwei Zhang, Xiaoxu Zhang & Hongbin Fang

  3. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Jiaqi Liu & Jian Xu

  4. College of Engineering, Peking University, Beijing, 100871, China

    Qining Wang

Authors
  1. Wei Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiaqi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiwei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaoxu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Qining Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jian Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Hongbin Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Wei Jin and Jiaqi Liu contributed equally to this work. Wei Jin: Data curation; Formal analysis; Investigation; Methodology; Software; Visualization; Writing – original draft. Jiaqi Liu: Data curation; Formal analysis; Investigation; Methodology; Software; Visualization; Writing – original draft. Qiwei Zhang: Investigation; Visualization. Xiaoxu Zhang: Software; Visualization. Qining Wang: Writing – review & editing; Resources; Project administration. Jian Xu: Writing – review & editing; Resources; Supervision. Hongbin Fang: Conceptualization; Formal Analysis; Methodology; Validation; Writing – review & editing; Resources; Project administration; Funding acquisition; Supervision.

Corresponding author

Correspondence to Hongbin Fang.

Ethics declarations

Ethical approval

The protocol received approval from the Ethical Committee of Fudan University (protocol code FE21124, approved on 16 August 2021).

Consent to participate

Written informed consent was obtained from the subject involved in the study.

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below are the links to the electronic supplementary material.

(PDF 831 kB)

(MP4 6.5 MB)

(MP4 7.1 MB)

(MP4 6.1 MB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jin, W., Liu, J., Zhang, Q. et al. Forward dynamics simulation of a simplified neuromuscular-skeletal-exoskeletal model based on the CMA-ES optimization algorithm: framework and case studies. Multibody Syst Dyn (2024). https://doi.org/10.1007/s11044-024-09982-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11044-024-09982-4

Keywords

Search

Navigation