Proceedings of the Steklov Institute of Mathematics

, Volume 291, Issue 1, pp 118–126 | Cite as

Application of optimal control to a biomechanics model

Article

Abstract

A model of sport biomechanics describing short-distance running (sprinting) is developed by applying methods of optimal control. In the considered model, the motion of a sportsman is described by a second-order ordinary differential equation. Two interconnected optimal control problems are formulated and solved: the minimum energy and time-optimal control problems. Based on the comparison with real data, it is shown that the proposed approach to sprint modeling provides realistic results.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Bellman, Dynamic Programming (Princeton Univ. Press, Princeton, NJ, 1957).MATHGoogle Scholar
  2. 2.
    H. K. Eriksen, J. R. Kristiansen, Ø. Langangen, and I. K. Wehus, “How fast could Usain Bolt have run? A dynamical study,” Am. J. Phys. 77 (3), 224–228 (2009).CrossRefGoogle Scholar
  3. 3.
    S. Gaudet, “A physical model of sprinting,” J. Biomech. 47 (12), 2933–2940 (2014).CrossRefGoogle Scholar
  4. 4.
    P. Hartman, Ordinary Differential Equations (J. Wiley & Sons, New York, 1964).MATHGoogle Scholar
  5. 5.
    O. Helene and M. T. Yamashita, “The force, power, and energy of the 100 meter sprint,” Am. J. Phys. 78 (3), 307–309 (2010).CrossRefGoogle Scholar
  6. 6.
    J. J. Hernández Gómez, V. Marquina, and R. W. Gómez, “On the performance of Usain Bolt in the 100 m sprint,” Eur. J. Phys. 34 (5), 1227–1233 (2013).CrossRefGoogle Scholar
  7. 7.
    J. B. Keller, “A theory of competitive running,” Phys. Today 26 (9), 43–47 (1973).CrossRefGoogle Scholar
  8. 8.
    N. N. Krasovskii, Theory of Motion Control: Linear Systems (Nauka, Moscow, 1968) [in Russian].Google Scholar
  9. 9.
    R. H. Miller, B. R. Umberger, J. Hamill, and G. E. Caldwell, “Evaluation of the minimum energy hypothesis and other potential optimality criteria for human running,” Proc. R. Soc. London B: Biol. Sci. 279, 1498–1505 (2012).CrossRefGoogle Scholar
  10. 10.
    J. R. Mureika, “A realistic quasi-physical model of the 100 m dash,” Can. J. Phys. 79 (4), 697–713 (2001).CrossRefGoogle Scholar
  11. 11.
    L. S. Pontryagin, Ordinary Differential Equations (Nauka, Moscow, 1961; Pergamon, London, 1962).MATHGoogle Scholar
  12. 12.
    L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Fizmatgiz, Moscow, 1961; Interscience, New York, 1962).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.International Institute for Applied Systems AnalysisLaxenburgAustria

Personalised recommendations