Modeling the Dynamics of an Exoskeleton with Control Torques in the Joints and a Variable Length of the Links Using the Recurrent Method for Constructing Differential Equations of Motion

  • A. V. Borisov
  • G. M. Rozenblat


The process of modeling the dynamics of an exoskeleton is considered (from a description of the model and the formulation of differential equations of motion to numerical calculations with the given control torques). For the first time, a new recurrent method for constructing the differential equations of motion of an exoskeleton that makes it possible to reduce labor and time costs is proposed and described. A comparison with well-known methods is carried out. The novelty of the approach is to take into account the variation in the lengths of the links of the exoskeleton. The problem of determining the control torques is solved experimentally. The urgency of the research lies in the possibility of restoring the motor functions of a person using an exoskeleton based on an empirical solution of the inverse problem of dynamics. The problem of determining the angles of rotation, angular velocities, angular accelerations of the links, and coordinates of the center of mass of the exoskeleton with a given control is solved. Only the plane motion is considered.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Yu. Pogorelov, “Contemporary algorithms for computer synthesis of equations of motion of multibody systems,” J. Comput. Syst. Sci. Int. 44, 503 (2005).zbMATHGoogle Scholar
  2. 2.
    Yu. F. Golubev and D. Yu. Pogorelov, “Computer added simulation of walking robots,” Fundam. Prikl. Mat. 4, 525–534 (1998).MathSciNetzbMATHGoogle Scholar
  3. 3.
    V. V. Velichenko, Matrix-Geometric Methods in Mechanics with Applications to Robot-Engineering Problems (Nauka, Moscow, 1988) [in Russian].zbMATHGoogle Scholar
  4. 4.
    G. V. Korenev, Introduction in Human Mechanics (Nauka, Moscow, 1977) [in Russian].Google Scholar
  5. 5.
    A. M. Formal’skii, The Movement of Anthropomorphic Mechanisms (Nauka, Moscow, 1982) [in Russian].Google Scholar
  6. 6.
    A. V. Borisov and G. M. Rozenblat, “Matrix method of generation of differential equations of motion and control of the exoskeleton,” Prikl. Mat. Mekh. 81, 511–522 (2017).Google Scholar
  7. 7.
    R. G. Mukharlyamov, “Reduction of the equations of dynamics of systems with constraints to a given structure,” J. Appl. Math. Mech. 71, 361–370 (2007).MathSciNetCrossRefGoogle Scholar
  8. 8.
    R. G. Mukharlyamov, “Differential-algebraic equations of programmed motions of lagrangian dynamical systems,” Mech. Solids 46, 534 (2011).CrossRefGoogle Scholar
  9. 9.
    F. L. Chernous’ko, I. M. Ananievski, and S. A. Reshmin, Control of Nonlinear Dynamical Systems: Methods and Applications (Fizmatlit, Moscow, 2006; Springer, New York, 2008).CrossRefzbMATHGoogle Scholar
  10. 10.
    Yu. F. Golubev, “Appel’s function in the dynamics of rigid body systems,” KIAM Preprint No. 58 (Keldysh Inst. Appl. Math., Moscow, 2014). Scholar
  11. 11.
    A. V. Borisov, Dynamics of Endo-and Exoskeleton (Smolensk. Gor. Tipografiya, Smolensk, 2012) [in Russian].Google Scholar
  12. 12.
    V. V. Beletskii, Two-Legged Walking—Model Problems of Dynamics and Control (Nauka, Moscow, 1984) [in Russian].Google Scholar
  13. 13.
    M. Vukobratovic, Legged Locomotion Robots and Anthropomorphic Mechanisms (Mihailo Pupin Inst., Beograd, 1975).Google Scholar
  14. 14.
    A. V. Chigarev and A. V. Borisov, “Simulation of an antropomorphous robot motion on the plaine with the use of Mathematica package,” Informatika, No. 2, 5–10 (2013).Google Scholar
  15. 15.
    R. G. Mukharlyamov, “Simulation of control processes, stability and stabilization of systems with program constraints,” J. Comput. Syst. Sci. Int. 54, 13 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    R. G. Mukharlyamov, “Stabilization of the motions of mechanical systems in prescribed phase-space manifolds,” J. Appl. Math. Mech. 70, 210–222 (2006).MathSciNetCrossRefGoogle Scholar
  17. 17.
    R. G. Mukharlyamov and E. A. Gorshkov, “Control of bounded system dynamics and inverse dynamics problems,” Vestn. Ross. Univ. Druzhby Narodov, Ser. Mat., Inform., Fiz., No. 1, 73–82 (2015).Google Scholar
  18. 18.
    E. K. Lavrovskii and E. V. Pis’mennaya, “Control algorithms exoskeleton of lower limb single support phase mode and walk on flat and stairs surfaces,” Mekhatron. Avtomatiz. Upravl., No. 1, 44–51 (2014).Google Scholar
  19. 19.
    V. V. Lapshin, Mechanics and Control of Walking Machines Motion (MGTU, Moscow, 2012) [in Russian].Google Scholar
  20. 20.
    A. M. Formal’skii, “On one method of exosceleton control,” in Proceedings of the Lomonosov Readings (Mosk. Gos. Univ., Moscow, 2012), pp. 151–152.Google Scholar
  21. 21.
    V. E. Pavlovskii, “For elaboration of walking machines,” KIAM Preprint No. 101 (Keldysh Inst. Appl. Math., Moscow, 2013). Scholar
  22. 22.
    A. P. Aliseichik, I. A. Orlov, V. E. Pavlovskii, V. V. Pavlovskii, and A. K. Platonov, “Mechanics and control of exosceletons of lower extremities for neurorehabilitation of spinal patients,” in Proceedings of the 11th All-Russia Workshop on Fundamental Problems of Theoretical and Applied Mechanics (Akad. Nauk RT, Kazan’, 2015).Google Scholar
  23. 23.
    N. A. Bernshtein, Selected Works on Biomechanics and Cybernetics (SportAkademPress, Moscow, 2001) [in Russian].Google Scholar
  24. 24.
    V. I. Dubrovskii and V. N. Fedorova, Biomechanics (Vlados-Press, Moscow, 2003) [in Russian].Google Scholar
  25. 25.
    V. M. Zatsiorskii, A. S. Aruin, and V. N. Seluyanov, Biomechanics of Human Locomotor System (Fizkul’tura Sport, Moscow, 1981) [in Russian].Google Scholar
  26. 26.
    A. Yu. Mishanov and P. A. Kruchinin, “Estimation measures in problem of optical motion capture systems lost data recovery with ground reaction force measurements,” Ross. Zh. Biomekh. 12 (3), 58–73 (2008).Google Scholar
  27. 27.
    Yu. I. Nyashin and V. A. Lokhov, Principles of Biomechanics (Perm. Gos. Tekh. Univ., Perm’, 2007) [in Russian].Google Scholar
  28. 28.
    W. Blajer and A. Czaplicki, “An alternative scheme for determination of joint reaction forces in human multibody models,” J. Theor. Appl. Mech. 43, 813–824 (2006).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Smolensk BranchMoscow Power Engineering InstituteSmolenskRussia
  2. 2.Moscow Automobile and Road Construction State Technical UniversityMoscowRussia

Personalised recommendations