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Modeling of a bipedal robot using mutually coupled Rayleigh oscillators

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Abstract.

The objective of the work presented here was the modeling of a bipedal robot using a central pattern generator (CPG) formed by a set of mutually coupled Rayleigh oscillators. We analyzed a 2D model, with the three most important determinants of gait, that performs only motions parallel to the sagittal plane. Using oscillators with integer relation of frequency, we determined the transient motion and the stable limit cycles of the network formed by the three oscillators, showing the behavior of the knee angles and the hip angle. A comparison of the plotted graphs revealed that the system provided excellent results when compared to experimental analysis. Based on the results of the study, we come to the conclusion that the use of mutually coupled Rayleigh oscillators can represent an excellent method of signal generation, allowing their application for feedback control of a walking machine.

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References

  1. Angeles J, DeLuca A, Hiller M, Kecskeméthy A, Roth B (1994) Kinematics and dynamics of multi-body mechanical systems. CISM Lecture Notes, International Centre for Mechanical Sciences (CISM), Udine, Italy

  2. Bay JS, Hemami H (1987) Modelling of a neural pattern generator with coupled nonlinear oscillators. IEEE Trans Biomed Eng 34:297–306

    Google Scholar 

  3. Braune W, Fischer O (1987) The human gait. Springer, Berlin Heidelburg, New York. Translated from Der Gang des Menschen, Teubner BG (1895–1904)

  4. Calancie B, Needham-Shropshire B, Jacobs P, Willer K, Zych G, Green BA (1994) Involuntary stepping after chronic spinal cord injury. Evidence for a central rhythm generator for locomotion in man. Brain 117(Pt 5):1143–1159

    Google Scholar 

  5. Collins JJ, Richmond SA (1994) Hard-wired central pattern generators for quadrupedal locomotion. Biol Cybern 71:375–385

    Google Scholar 

  6. Collins JJ, Stewart I (1993) Hexapodal gaits and coupled nonlinear oscillators models. Biol Cybern 68:287–298

    Google Scholar 

  7. Dimitrijevic MR, Gerasimenko Y, Pinter MM (1998) Evidence for a spinal central pattern generator in humans. Ann NY Acad Sci 860:360–376

    Google Scholar 

  8. Dutra MS, Pina Filho ACde, Romano VF (2003) Modeling of a bipedal locomotor using coupled nonlinear oscillators of Van der Pol. Biol Cybern 88(4):286–292

  9. Dutra MS (1995) Bewegungskoordination und Steuerung einer zweibeinigen Gehmaschine. Shaker, Aachen

  10. Dutra MS (1997) Modeling of a bipedal locomotor using nonlinear oscillators. Int J Intell Mechatron Des Prod 2(2): 88–97

    Google Scholar 

  11. Eberhart HD (1976) Physical principles for locomotion. In: Herman RM et al (eds) Neural control of locomotion. Plenum, New York

  12. Grillner S (1981) Control of locomotion in bipeds, tetrapods and fish. In: Handbook of physiology. American Physical Society, College Park, MD, pp 1179–1236

  13. Grillner S (1985) Neurobiological bases of rhythmic motor acts in vertebrates. Science 228:143–149

    Google Scholar 

  14. Johnsson A (1978) Zur Biophysik biologischer Oszillatoren. In: Biophisik. Springer, Berlin Heidelberg New York

  15. Mackay-Lyons M (2002) Central pattern generation of locomotion: a review of the evidence. Phys Ther 82(1):69–83

    Google Scholar 

  16. McMahon TA (1984) Muscles, reflexes and locomotion. Princeton University Press, Princeton, NJ

  17. Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Wiley, New York, pp 59–61

  18. Pavlidis T (1973) Biological oscillators. Academic, New York

  19. Pearson KG (1993) Common principles of motor control in vertebrates and invertebrates. Annu Rev Neurosci 16:265–297

    Google Scholar 

  20. Pina Filho ACde (2004) Study of mutually coupled nonlinear oscillators applied in the locomotion of a bipedal robot (in Portuguese). D.Sc. Qualifying Examination, Universidade Federal do Rio de Janeiro, COPPE/PEM, Brazil

  21. Pinter MM, Dimitrijevic MR (1999) Gait after spinal cord injury and the central pattern generator for locomotion. Spinal Cord 37(8):531–537

    Google Scholar 

  22. Raptopoulos LSC, D’Angelo MD, Dutra MS (2001) Kinematics analisys of human locomotion (in Portuguese). In: 16th Brazilian congress of mechanical engineering (COBEM), Minas Gerais, Brazil

  23. Saunders JB, Inman V, Eberhart HD (1953) The major determinants in normal and pathological gait. J Bone Joint Surg 35A:543–558

    Google Scholar 

  24. Winter D (1983) Biomechanical motor patterns in normal walking. J Mot Behav 15(4):302–330

    Google Scholar 

  25. Zielinska T (1996) Coupled oscillators utilised as gait rhythm generators of a two-legged walking machine. Biol Cybern 74:263–273

    Google Scholar 

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Correspondence to Armando C. de Pina Filho.

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Acknowledgements The authors would like to express their gratitude to CNPq and CAPES for the financial support provided during the course of this research.

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Filho, A., Dutra, M. & Raptopoulos, L. Modeling of a bipedal robot using mutually coupled Rayleigh oscillators. Biol Cybern 92, 1–7 (2005). https://doi.org/10.1007/s00422-004-0531-1

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  • DOI: https://doi.org/10.1007/s00422-004-0531-1

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