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Journal of Bionic Engineering

, Volume 8, Issue 1, pp 56–68 | Cite as

Biomimetic control of mechanical systems equipped with musculotendon actuators

  • Javier Moreno-Valenzuela
  • Adriana Salinas-Avila
Article

Abstract

This paper addresses the problem of modelling, control, and simulation of a mechanical system actuated by an ago- nist-antagonist musculotendon subsystem. Contraction dynamics is given by case I of Zajac’s model. Saturated semi positive proportional-derivative-type controllers with switching as neural excitation inputs are proposed. Stability theory of switched system and SOSTOOLS, which is a sum of squares optimization toolbox of Matlab, are used to determine the stability of the obtained closed-loop system. To corroborate the obtained theoretical results numerical simulations are carried out. As additional contribution, the discussed ideas are applied to the biomimetic control of a DC motor, i.e., the position control is addressed assuming the presence of musculotendon actuators. Real-experiments corroborate the expected results.

Keyword

biomimetic control musculotendon dynamics neural excitation saturation switched systems 

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References

  1. [1]
    Zajac F E. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Critical Reviews in Biomedical Engineering, 1989, 17, 359–411.Google Scholar
  2. [2]
    Hill A V. The heat of shortening and the dynamic constants of muscle. Proceedings of the Royal Society of London B, Biological Sciences, 1938, 126, 136–195.CrossRefGoogle Scholar
  3. [3]
    Huxley A F. Muscle structure and theories of contraction. Progress in Biophysics and Biophysical Chemistry, 1957, 7, 255–318.Google Scholar
  4. [4]
    Epstein M, Herzog W. Theoretical Models of Skeletal Muscle: Biological and Mathematical Considerations, John Wiley & Sons, New York, 1998.Google Scholar
  5. [5]
    He J, Levine W S, Loeb G E. Feedback gains for correcting small perturbations to standing posture. IEEE Transactions on Automatic Control, 1991, 36, 322–332.CrossRefzbMATHGoogle Scholar
  6. [6]
    Martin C F, Schovanec L. Muscle mechanics and dynamics of ocular motion. Journal of Mathematical Systems, Estimation and Control, 1998, 8, 1–15.MathSciNetzbMATHGoogle Scholar
  7. [7]
    Menegaldo L L. Modelagem Biomecânicae Controle Ótimo da Postura Humana Através de Algoritmos Baseados na Teoria das Aproximações Consistentes, PhD, Escola Politécnica da Universidade de São Paulo, Departamento de Engenharia Mecânica, Saõ Paulo, 2001. (in Portuguese)Google Scholar
  8. [8]
    Farahat W, Herr H. Workloop energetics of antagonist muscles. Proceedings of the 28th IEEE EMBS Annual International Conference, New York, USA, 2006, 3640–3643.Google Scholar
  9. [9]
    Winters J M, Stark L. Muscle models: What is gained and what is lost by varying model complexity. Biological Cybernetics, 1987, 55, 403–420.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Thelen D, Blemker S, Anderson C, Delp S. Dynamic Modeling and Simulation of Muscle-Tendon Actuators. Notes of the lecture ME 382: Modeling and Simulation of Human Movement, Stanford University, 2001.Google Scholar
  11. [11]
    Pandy M G, Zajac F E, Sim E, Levine W. An optimal control model for maximum-height human jumping. Journal of Biomechanics, 1990, 23, 1185–1198.CrossRefGoogle Scholar
  12. [12]
    Iqbal K, Roy A. Stabilizing PID controllers for a single-link biomechanical model with position, velocity, and force feedback. Journal of Biomechanical Engineering, 2004, 126, 838–843.CrossRefGoogle Scholar
  13. [13]
    Tahara K, Luo Z W, Arimoto S, Kino H. Sensory-motor control mechanism for reaching movements of a redundant musculo-skeletal arm. Journal of Robotic Systems, 2005, 22, 639–651.CrossRefzbMATHGoogle Scholar
  14. [14]
    Moody C B, Barhorst A A, Schovanec L. A neuro-muscular elasto-dynamic model of the human arm part 2: Musculotendon dynamics and related stress effects. Journal of Bionic Engineering, 2009, 6, 108–119.CrossRefGoogle Scholar
  15. [15]
    Laczko J, Pilissy T, Tibold R. Neuro-mechanical modeling and controlling of human limb movements of spinal cord injured patients. Proceedings of the 2nd International Symposium on Applied Sciences in Biomedical and Communication Technologies, Bratislava, Slovakia, 2009, 1–2.Google Scholar
  16. [16]
    Liberzon D. Switching in System and Control, Birkhäuser, Boston, USA, 2003.CrossRefzbMATHGoogle Scholar
  17. [17]
    Beldiman O, Bushnell L. Stability, linearization and control of switched systems. Proceedings of the American Control Conference, San Diego, USA, 1999, 2950–2954.Google Scholar
  18. [18]
    Prajna S, Papachristodoulou A. Analysis of switched and hybrid systems-beyond piecewise quadratic methods. Pro- ceedings of the 2003 American Control Conference, Denver, USA, 2003, 2779–2784.CrossRefGoogle Scholar
  19. [19]
    Papachristodoulou A, Prajna S. A tutorial on sum of squares techniques for systems analysis. Proceedings of the 2005 American Control Conference, Portland, USA, 2005, 2686–2700.Google Scholar
  20. [20]
    Prajna S, Papachristodoulou A, Seiler P, Parrilo P A. SOSTOOLS: Sum of Squares Optimization Toolbox for MATLAB, [2004-06-01], http://www.mit.edu/parrilo/sostools
  21. [21]
    Bar-Cohen Y, Biomimetics: Biologically Inspired Technologies, CRC Press, Boca Raton, 2006.Google Scholar
  22. [22]
    Gottlieb G L, Agarwal G C. Dynamic relationship between isometric muscles tension and the electromyogram in man. Journal of Applied Physiology, 1971, 30, 345–351.CrossRefGoogle Scholar
  23. [23]
    Liberzon D, Morse S. Basic problems in stability and design of switched systems. IEEE Control Systems Magazine, 1999, 19, 59–70.CrossRefGoogle Scholar
  24. [24]
    Cavallaro E E, Rosen J, Perry J C, Burns S. Real-time myoprocessors for a neural controlled powered exoskeleton arm. IEEE Transactions on Biomedical Engineering, 2006, 53, 2387–2396.CrossRefGoogle Scholar
  25. [25]
    Baratta R, Solomonow M, Zhou B H, Letson D, Chuinard R, D’ Ambrosia R. Muscular Coactivation. The role of the antagonist musculature in maintaining knee stability. American Journal of Sports Medecine, 1988, 16, 113–122.CrossRefGoogle Scholar
  26. [26]
    Solomonow M, Baratta R, Zhou B H, D’ Ambrosia R. Electromyogram coactivation patterns of the elbow antagonist muscles during slow isokinetic movement. Experimental Neurology, 1988, 100, 470–477.CrossRefGoogle Scholar
  27. [27]
    Tsuji T, Tanaka Y, Morasso P, Sanguineti V, Kaneko M. Bio-mimetic trajectory generation of robots via artificial potential field with time base generator. IEEE Transactions on Systems, Man, and Cybernetic Part C: Applications, and Reviews, 2002, 32, 403–420.CrossRefGoogle Scholar
  28. [28]
    Hashimoto S, Narita S, Kasahara H, Takanishi A, Sugano S, Shirai H, Kobayashi T, Takanobu H, Kurata T, Fujiwara K, Matsuno T, Kawasaki T, Hoashi K. Humanoid robot-development of an information assistant robot hadaly. Proceedings of the 8th IEEE International Workshop on Robot and Human Communication, Pisa, Italy, 1997, 106–111.Google Scholar
  29. [29]
    Hirai K, Hirose M, Haikawa Y, Takenaka T. The development of honda humanoid robot. Proceedings of the 1998 IEEE International Conference on Robotics and Automation, Leuven, Belgium, 1998, 1321–1326.Google Scholar

Copyright information

© Jilin University 2011

Authors and Affiliations

  • Javier Moreno-Valenzuela
    • 1
  • Adriana Salinas-Avila
    • 1
  1. 1.Instituto Politécnico Nacional-CITEDIAv. del Parque 1310, Mesa de OtayTijuanaMexico

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