Skip to main content

Advertisement

SpringerLink
Log in

Direct Methods for Predicting Movement Biomechanics Based Upon Optimal Control Theory with Implementation in OpenSim

  • Published:
Annals of Biomedical Engineering Aims and scope Submit manuscript

Abstract

The aim of this study was to compare the computational performances of two direct methods for solving large-scale, nonlinear, optimal control problems in human movement. Direct shooting and direct collocation were implemented on an 8-segment, 48-muscle model of the body (24 muscles on each side) to compute the optimal control solution for maximum-height jumping. Both algorithms were executed on a freely-available musculoskeletal modeling platform called OpenSim. Direct collocation converged to essentially the same optimal solution up to 249 times faster than direct shooting when the same initial guess was assumed (3.4 h of CPU time for direct collocation vs. 35.3 days for direct shooting). The model predictions were in good agreement with the time histories of joint angles, ground reaction forces and muscle activation patterns measured for subjects jumping to their maximum achievable heights. Both methods converged to essentially the same solution when started from the same initial guess, but computation time was sensitive to the initial guess assumed. Direct collocation demonstrates exceptional computational performance and is well suited to performing predictive simulations of movement using large-scale musculoskeletal models.

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

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8

Similar content being viewed by others

References

  1. Ackermann, M., and A. J. van den Bogert. Optimality principles for model-based prediction of human gait. J. Biomech. 43:1055–1060, 2010.

    Article  PubMed  PubMed Central  Google Scholar 

  2. Ackermann, M., and A. J. van den Bogert. Predictive simulation of gait at low gravity reveals skipping as the preferred locomotion strategy. J. Biomech. 45:1293–1298, 2012.

    Article  PubMed  PubMed Central  Google Scholar 

  3. Anderson, F. C., and M. G. Pandy. Storage and utilization of elastic strain energy during jumping. J. Biomech. 26:1413–1427, 1993.

    Article  CAS  PubMed  Google Scholar 

  4. Anderson, F. C., and M. G. Pandy. A dynamic optimization solution for vertical jumping in three dimensions. Comput. Methods Biomech. Biomed. Eng. 2:201–231, 1999.

    Article  Google Scholar 

  5. Anderson, F. C., and M. G. Pandy. Dynamic optimization of human walking. J. Biomech. Eng. 123:381–390, 2001.

    Article  CAS  PubMed  Google Scholar 

  6. Betts, J. T. Survey of numerical methods for trajectory optimization. J. Guid. Control. Dyn. 21:193–207, 1998.

    Article  Google Scholar 

  7. Bryson, A. E. Applied Optimal Control: Optimization, Estimation and Control. New York: CRC Press, 1975.

    Google Scholar 

  8. Celik, H., and S. J. Piazza. Simulation of aperiodic bipedal sprinting. J. Biomech. Eng. 135:081008–081008, 2013.

    Article  Google Scholar 

  9. Crowninshield, R. D. Use of optimization techniques to predict muscle forces. J. Biomech. Eng. 100:88–92, 1978.

    Article  Google Scholar 

  10. Davy, D. T., and M. L. Audu. A dynamic optimization technique for predicting muscle forces in the swing phase of gait. J. Biomech. 20:187–201, 1987.

    Article  CAS  PubMed  Google Scholar 

  11. Delp, S. L., F. C. Anderson, A. S. Arnold, P. Loan, A. Habib, C. T. John, E. Guendelman, and D. G. Thelen. OpenSim: open-source software to create and analyze dynamic simulations of movement. IEEE Trans. Biomed. Eng. 54:1940–1950, 2007.

    Article  PubMed  Google Scholar 

  12. Eriksson, A. Optimization in target movement simulations. Comput. Methods Appl. Mech. Eng. 197:4207–4215, 2008.

    Article  Google Scholar 

  13. Hatze, H. The complete optimization of a human motion. Math. Biosci. 28:99–135, 1976.

    Article  Google Scholar 

  14. Hull, D. G. Conversion of optimal control problems into parameter optimization problems. J. Guid. Control Dyn. 20:57–60, 1997.

    Article  Google Scholar 

  15. Hunt, K., and F. Crossley. Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. 42:440–445, 1975.

    Article  Google Scholar 

  16. Johnson, K. Contact Mechanics. Cambridge: Cambridge University Press, 1985.

    Book  Google Scholar 

  17. Kaplan, M. L., and J. H. Heegaard. Predictive algorithms for neuromuscular control of human locomotion. J. Biomech. 34:1077–1083, 2001.

    Article  CAS  PubMed  Google Scholar 

  18. Kistemaker, D. A., J. D. Wong, and P. L. Gribble. The cost of moving optimally: kinematic path selection. J. Neurophysiol. 112:1815–1824, 2014.

    Article  PubMed  PubMed Central  Google Scholar 

  19. Miller, R. H., S. C. Brandon, and K. J. Deluzio. Predicting sagittal plane biomechanics that minimize the axial knee joint contact force during walking. J. Biomech. Eng. 135:011007, 2013.

    Article  PubMed  Google Scholar 

  20. Miller R. H., and J. Hamill. Optimal footfall patterns for cost minimization in running. J. Biomech. 2015.

  21. Miller, R. H., B. R. Umberger, and G. E. Caldwell. Limitations to maximum sprinting speed imposed by muscle mechanical properties. J. Biomech. 45:1092–1097, 2012.

    Article  PubMed  Google Scholar 

  22. Pandy, M. G. Computer modeling and simulation of human movement. Ann. Rev. Biomed. Eng. 3:245–273, 2001.

    Article  CAS  Google Scholar 

  23. Pandy, M. G., F. C. Anderson, and D. G. Hull. A parameter optimization approach for the optimal control of large-scale musculoskeletal systems. J. Biomech. Eng. 114:450–460, 1992.

    Article  CAS  PubMed  Google Scholar 

  24. Pandy, M. G., and F. E. Zajac. Optimal muscular coordination strategies for jumping. J. Biomech. 24:1–10, 1991.

    Article  CAS  PubMed  Google Scholar 

  25. Pandy, M. G., F. E. Zajac, E. Sim, and W. S. Levine. An optimal control model for maximum-height human jumping. J. Biomech. 23:1185–1198, 1990.

    Article  CAS  PubMed  Google Scholar 

  26. Seth, A., and M. G. Pandy. A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement. J. Biomech. 40:356–366, 2007.

    Article  PubMed  Google Scholar 

  27. Stelzer, M., and O. Von Stryk. Efficient forward dynamics simulation and optimization of human body dynamics. ZAMM J. Appl. Math. Mech. 86:828–840, 2006.

    Article  Google Scholar 

  28. Thelen, D. G., and F. C. Anderson. Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. J. Biomech. 39:1107–1115, 2006.

    Article  PubMed  Google Scholar 

  29. van den Bogert, A. J. D. Blana and Heinrich. Implicit methods for efficient musculoskeletal simulation and optimal control. Proc. IUTAM 2:297–316, 2011.

    Article  Google Scholar 

  30. Van den Bogert A. J., M. Hupperets, H. Schlarb and B. Krabbe. Predictive musculoskeletal simulation using optimal control: Effects of added limb mass on energy cost and kinematics of walking and running. Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology 1754337112440644, 2012.

  31. Zajac, F. E., and M. E. Gordon. Determining muscle’s force and action in multi-articular movement. Exerc. Sport Sci. Rev. 17:187–230, 1989.

    CAS  PubMed  Google Scholar 

Download references

Acknowledgments

This work was supported by a VESKI Innovation Fellowship awarded to MGP. A University of Melbourne Postgraduate Scholarship to SP is also gratefully acknowledged.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Melbourne, Parkville, VIC, 3010, Australia

    Sina Porsa, Yi-Chung Lin & Marcus G. Pandy

Authors
  1. Sina Porsa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi-Chung Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marcus G. Pandy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcus G. Pandy.

Additional information

Associate Editor Michael Torry oversaw the review of this article.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (PDF 644 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Porsa, S., Lin, YC. & Pandy, M.G. Direct Methods for Predicting Movement Biomechanics Based Upon Optimal Control Theory with Implementation in OpenSim. Ann Biomed Eng 44, 2542–2557 (2016). https://doi.org/10.1007/s10439-015-1538-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10439-015-1538-6

Keywords

Search

Navigation