Skip to main content

Advertisement

SpringerLink
Log in

3D-Simulation of human walking by parameter optimization

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The simulation of human gait is a complex dynamical problem that requires accounting for energy consumption as well as dealing with a redundantly actuated multibody system. If muscle forces and generalized coordinates are parameterized, optimization techniques allow the simulation of the muscle forces and of the walking motion. An optimization framework is presented for non-symmetrical gait cycles found in the presence of one-sided gait disorders. The motion of each leg is independently parameterized for a whole walking cycle. The non-linear constraints used to fulfill the equations of motion and the kinematical constraints of the different walking phases are implemented in an efficient way. Fifth-order splines are used for the parameterization to reduce the oscillatory behavior coming from non-periodicity conditions. To achieve the computational performance required for three-dimensional simulations, the spline interpolation problem has been split in two parts, one is performed in a preprocessing stage and the other during the optimization. Numerical differentiation via finite differences is avoided by implementing analytical derivatives of the splines functions and of the contractile element force law. The results show good numerical performance, and the computational efficiency for 3D-simulations with one-sided gait disorders is highlighted.

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

Similar content being viewed by others

References

  1. Ackermann, M.: Dynamics and Energetics of Walking with Prostheses. PhD thesis, Institut für Technische und Numerische Mechanik, Stuttgart (2007)

  2. Ackermann, M., Gros, H.: Measurements of Human Gaits. Technical Report of Zwischenbericht ZB-144, Institute of Engineering and Computational Mechanics, University of Stuttgart, 70550 Stuttgart (2005)

  3. Ackermann M., Schiehlen W.: Dynamic analysis of human gait disorder and metabolical cost estimation. Arch. Appl. Mech. 75(10–12), 569–594 (2006)

    Article  MATH  Google Scholar 

  4. Al Nazer R., Rantalainen T., Heinonen A., Sievänen H., Mikkola A.: Flexible multibody simulation approach in the analysis of tibial strain during walking. J. Biomech. 41, 1036–1043 (2008)

    Article  Google Scholar 

  5. Allard, P., Cappozzo, A., Lundberg, A., Vaughan, C.L. (eds.): Three-Dimensional Analysis of Human Locomotion. Wiley, Chichester (1998)

  6. Anderson F., Pandy M.: A dynamic optimization solution for vertical jumping in three dimensions. Comput. Methods Biomech. Biomed. Eng. 2, 201–231 (1999)

    Article  Google Scholar 

  7. Anderson F., Pandy M.: Dynamic optimization of human walking. J. Biomech. Eng. 123, 381–390 (2001)

    Article  Google Scholar 

  8. Bessonnet G., Seguin P., Sardain P.: A parametric optimization approach to walking pattern synthesis. Int. J. Robotics Res. 24(7), 523–536 (2005)

    Article  Google Scholar 

  9. Brand R., Pedersen D., Friederich J.: The sensitivity of muscle force predictions to changes in physiologic cross-sectional area. J. Biomech. 19(8), 589–596 (1986)

    Article  Google Scholar 

  10. Cole G., van den Bogert A., Herzog W., Gerritsen K.: Modeling of force production in skeletal muscle undergoing stretch. J. Biomech. 29, 1091–1104 (1996)

    Article  Google Scholar 

  11. Delp S., Loan J.: A graphics-based software system to develop and analyze models of musculoskeletal structures. Comput. Biol. Med. 25(1), 21–34 (1995)

    Article  Google Scholar 

  12. Kim H., Wang Q., Rahmatalla S., Swan C., Arora J., Abdel-Malek K., Assouline J.: Dynamic motion planning of 3D human locomotion using gradient-based optimization. J. Biomech. Eng. 130, 03100201–03100214 (2008)

    Google Scholar 

  13. Kurz T., Eberhard P., Henninger C., Schiehlen W.: From Neweul to Neweul-M2: symbolical equations of motion for multibody system analysis and synthesis. Multib. Syst. Dyn. 24, 1 (2010)

    Article  Google Scholar 

  14. Menegaldo L., Fleury A., Weber H.: Biomechanical modeling and optimal control of human posture. J. Biomech. 36, 1701–1712 (2003)

    Article  Google Scholar 

  15. Menegaldo L., Fleury A., Weber H.: Moment arms and musculotendon lengths estimtion for a three-dimensional lower-limb model. J. Biomech. 37, 1447–1453 (2004)

    Article  Google Scholar 

  16. Nagano A., Gerritsen K.: Effects of neuromuscular strength training on vertical jumping performance—a computer simulation study. J. Appl. Biomech. 17, 113–128 (2001)

    Google Scholar 

  17. Pandy M.: Computer modeling and simulation of human walking. Annu. Rev. Biomed. Eng. 3, 245–273 (2001)

    Article  Google Scholar 

  18. Peasgood, M., McPhee, J., Kubica, E.: Stabilization and energy optimization of a dynamic walking gait simulation. In: Proceedings of the ASME 2005 International Design Engineering Technical Conferences & Computers and Information in Engineering. Long Beach (Sept 24–28 2005)

  19. Riener R., Edrich T.: Identification of passive elastic joint moments in the lower extremities. J. Biomech. 32, 539–544 (1999)

    Article  Google Scholar 

  20. Rodrgigo S., Ambrosio J., Da Silva M., Penisi O.: Analysys of human gait based on multibody formulations and optimization tools. Mech. Based Des. Struct Mach. 36(4), 446–477 (2008)

    Article  Google Scholar 

  21. Schiehlen W.: Multibody system dynamics: roots and perspectives. Multib. Syst. Dyn. 1, 149–188 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  22. Stein R., Zehr E., Lebiedowska M., Popovic D., Scheiner A., Chizeck H.: Estimating mechanical parameters of leg segments in individuals with and without physical disabilities. IEEE Trans. Rehabil. Eng. 4(3), 201–211 (1996)

    Article  Google Scholar 

  23. Strang G.: Linear Algebra and Its Applications. 2nd edn. Academic Press, New York (1980)

    Google Scholar 

  24. Umberger B.: Effects of suppressing arm swing on kinematics, kinetics and energetics of human walking. J. Biomech. 41, 2575–2580 (2008)

    Article  Google Scholar 

  25. Umberger B., Gerritsen K., Martin P.: A model of human muscle energy expendidure. Comput. Methods Biomech. Biomed. Eng. 6(2), 99–111 (2003)

    Article  Google Scholar 

  26. van Soest A., Bobbert M.: The contribution of muscle properties in the control of explosive movements. Biol. Cybern. 69, 195–204 (1993)

    Article  Google Scholar 

  27. Winter D.: The Biomechanics and Motor Control of Human Gait: Normal Elderly and Pathological. University of Waterloo Press, Waterloo (1991)

    Google Scholar 

  28. Wojtyra M.: Multibody simulation of human walking. Mech. Based Des. Struct. Mach. 31(3), 357–379 (2003)

    Article  Google Scholar 

  29. Zatsiorsky V.: Kinematics of Human Motion. Human Kinetics, Champaign, Illinois (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, University of Seville, Camino de los descubrimientos s/n, 41092, Seville, Spain

    Daniel García-Vallejo

  2. Institute of Engineering and Computational Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569, Stuttgart, Germany

    Werner Schiehlen

Authors
  1. Daniel García-Vallejo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Werner Schiehlen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel García-Vallejo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

García-Vallejo, D., Schiehlen, W. 3D-Simulation of human walking by parameter optimization. Arch Appl Mech 82, 533–556 (2012). https://doi.org/10.1007/s00419-011-0571-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-011-0571-7

Keywords

Search

Navigation