Skip to main content

Analysis of the Results of Stabiolmetric Tests with a Stepwise Input Action in the Context of the Mechanics of Controlled Systems

Abstract—Problems of optimal control were analyzed for a human motion model for stabilometric tests where the posture changes under a stepwise input action. The presence of a prominent “swing” and an “overshoot” are characteristic of the center-of-pressure trajectories recorded in the test. A one-dimensional inverted pendulum model was used in the study. The solution of the optimal control for the inverted pendulum motion controlled by coupling torque was put in correspondence with the test results. The problems of optimal speed-of-response control and linear–quadratic regulator were considered. The solution of these optimum problems was compared with the stabilometric test results. A modified algorithm was proposed for stabilometric data processing. This motion was shown to reach a stable motor pattern. The swing and overshoot were found to correspond to the acceleration and deceleration stages, respectively.

This is a preview of subscription content, access via your institution.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.


  1. 1

    F. B. Horak and F. J. Hlavacka, J. Neurophysiol. 86, 575 (2001).

    Article  Google Scholar 

  2. 2

    G. A. Pereyaslov and S. S. Sliva, Izv. TRTU 5 (28), 82 (2002).

    Google Scholar 

  3. 3

    B. N. Smetanin, K. E. Popov, and G. V. Kozhina, Neurophysiology 36 (1), 58 (2004).

    Article  Google Scholar 

  4. 4

    V. Yu. Shlykov, T. B. Kireeva, and Yu. S. Levik, Izv. Yuzhn. Fed, Univ., Tekh. Nauki 6 (83), 112 (2008).

    Google Scholar 

  5. 5

    Yu. S. Levik, T. B. Kireeva, and V. Yu. Shlykov, Al’manakh Klin. Med. 17 (2), 217 (2008).

    Google Scholar 

  6. 6

    E. P. Murtazina, Izv. Yuzhn. Fed, Univ., Tekh. Nauki 9 (98), 123 (2009).

    Google Scholar 

  7. 7

    G. S. Kashevarov, O. I. Elkina, and R. R. Kasimova, Lechebn. Fizkul’t. Sport. Med. 4 (130), 36 (2015).

    Google Scholar 

  8. 8

    I. Yu. Gorskaya, L. G. Kharitonova, A. A. Tereshchenko, and O. V. Krizhivetskaya, Sovr. Probl. Nauki Obraz., № 2 (2017). Cited June 26, 2019.

  9. 9

    P. A. Kruchinin and E. A. Kasatkin, Izv. Yuzhn. Fed, Univ., Tekh. Nauki 10 (159), 254 (2014).

    Google Scholar 

  10. 10

    P. A. Kruchinin, Moscow Univ. Mech. Bul., No. 2(71), 45 (2016).

  11. 11

    P. A. Kruchinin, Russ. J. Biomech. 18 (2), 158 (2014).

    Google Scholar 

  12. 12

    M. Athans and P. Falb, Optimal Control: An Introduction to the Theory and Its Applications (McGraw Hill, 1966).

  13. 13

    Ya. N. Roitenberg, Automatic Control (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  14. 14

    A. L. Hof, J. Biomech. 36 (7), 1031 (2003).

    Article  Google Scholar 

  15. 15

    B. J. Thompson, E. D. Ryan, T. J. Herda, et al., J. Electromyogr. Kines. 22 (6), 893 (2012).

    Article  Google Scholar 

  16. 16

    V. V. Aleksandrov, S. I. Zlochevskii, S. S. Lemak, and N. A. Parusnikov, Introduction to the Dynamics of Controled Systems (Moscow State Univ., Moscow, 1993) [in Russian].

    Google Scholar 

  17. 17

    A. D. Kuo, IEEE Trans. Biomed. Eng. 42 (1), 87 (1995).

    ADS  Article  Google Scholar 

  18. 18

    S. G. Carver, T. Kiemel, N. J. Cowan, and J. J. Jeka, Biol. Cyber., No. (2009), 35.

    Google Scholar 

  19. 19

    P. Paoletti and L. Mahadevan, J. R. Soc. Interface 9, 2097 (2012).

    Article  Google Scholar 

  20. 20

    A. L. Hof, Gait & Posture 4 (3), 222 (1996).

    Article  Google Scholar 

  21. 21

    L. I. Sedov, Methods of Similarity and Dimensions in Mechanics (Nauka, Moscow, 1977) [in Russian].

  22. 22

    I. V. Novozhilov, Fractional analysis. Methods of Motion Decomposition (Birkhäuser, NY, 1997).

  23. 23

    A. P. Kruchinina and A. G. Yakushev, Moscow Univ. Mech. Bul., No. 4 (73), 97 (2018).

Download references


This work was supported by the Russian Foundation for Basic Research (project no. 18-00-01590).

Author information



Corresponding author

Correspondence to P. A. Kruchinin.

Ethics declarations

Conflict of interests. The author declares that he has no conflict of interest.

Statement of compliance with standards of research involving humans as subjects. All procedures performed in studies involving human participants were in accordance with the ethical standards of the 1964 Helsinki Declaration and its later amendments. Informed consent was voluntarily provided by all individual participants involved in the study.

Additional information

Translated by T. Tkacheva

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kruchinin, P.A. Analysis of the Results of Stabiolmetric Tests with a Stepwise Input Action in the Context of the Mechanics of Controlled Systems. BIOPHYSICS 64, 818–827 (2019).

Download citation

  • Keywords: change of upright posture
  • stabilometry
  • tests under a stepwise input action
  • optimal control