Biological Cybernetics

, Volume 65, Issue 3, pp 147–159 | Cite as

Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment

  • G. Taga
  • Y. Yamaguchi
  • H. Shimizu
Article

Abstract

A new principle of sensorimotor control of legged locomotion in an unpredictable environment is proposed on the basis of neurophysiological knowledge and a theory of nonlinear dynamics. Stable and flexible locomotion is realized as a global limit cycle generated by a global entrainment between the rhythmic activities of a nervous system composed of coupled neural oscillators and the rhythmic movements of a musculo-skeletal system including interaction with its environment. Coordinated movements are generated not by slaving to an explicit representation of the precise trajectories of the movement of each part but by dynamic interactions among the nervous system, the musculo-skeletal system and the environment. The performance of a bipedal model based on the above principle was investigated by computer simulation. Walking movements stable to mechanical perturbations and to environmental changes were obtained. Moreover, the model generated not only the walking movement but also the running movement by changing a single parameter nonspecific to the movement. The transitions between the gait patterns occurred with hysteresis.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersson O, Grillner S (1983) Peripheral control of the cat's step cycle. II Entrainment of the central pattern generators for locomotion by sinusoidal hip movements during “fictive locomotion”. Acta Physiol Scand 118:229–239Google Scholar
  2. Arshavsky YI, Gelfand IM, Orlovsky GN (1984) Cerebellum and rhythmical movements. Springer, Berlin Heidelberg New YorkGoogle Scholar
  3. Bässler U (1986) On the definition of central pattern generator and its sensory control. Biol Cybern 54:65–69Google Scholar
  4. Beuter A, Flashner H, Arabyan A (1986) Phase plane modeling of leg motion. Biol Cybern 53:273–284Google Scholar
  5. Brown TG (1914) On the nature of the fundamental activity of the nervous centeres. J Physiol 48:18–46Google Scholar
  6. Doya K, Yoshizawa S (1989) Adaptive neural oscillator using continuous-time back-propagation learning. Neural Networks 2:375–385Google Scholar
  7. Friesen WO, Stent GS (1977) Generation of a locomotory rhythm by a neural network with recurrent cyclic inhibition. Biol Cybern 28:27–40Google Scholar
  8. Grillner S (1975) Locomotion in vertebrates: central mechanisms and reflex interaction. Physiol Rev 55:247–304Google Scholar
  9. Grillner S (1981) Control of locomotion in bipeds, tetrapods and fish. In: Brooks VB (ed) Handbook of physiology, Sect 1: The nervous system vol II: motor control. Waverly Press, Maryland, pp 1179–1236Google Scholar
  10. Grillner S (1985) Neurobiological bases of rhythmic motor acts in vertebrates. Science 228:143–149Google Scholar
  11. Haken H (1983) Synergetics — An introduction, 3rd edn. Springer, Berlin Heidelberg New YorkGoogle Scholar
  12. Haken H, Kelso JAS, Bunz H (1985) A theoretical model of phase transitions in human hand movements. Biol Cybern 51:347–356Google Scholar
  13. Ito M (1984) The cerebellum and neural control. Raven Press, New YorkGoogle Scholar
  14. Kato I (1983) Biped walking robot — its history and problems. J Robot Soc Jpn 1–3:4–6 (in Japanese)Google Scholar
  15. Kato R, Mori M (1984) Control method of biped locomotion giving asymptotic stability of trajectory. Automatica 20–4:405–414Google Scholar
  16. Kawahara K, Mori S (1982) A two compartment model of the stepping generator: Analysis of the roles of a stage-setter and a rhythm generator. Biol Cybern 43:225–230Google Scholar
  17. Kawato M, Furukawa K, Suzuki R (1987) A hierarchical neural-network model for control and learning of voluntary movement. Biol Cybern 57:169–185Google Scholar
  18. Kelso JAS (1984) Phase transitions and critical behavior in human bimanual coordination. Am J Physiol: Reg Integ Comp 15:R1000-R1004Google Scholar
  19. Kleinfeld D, Sompolinsky H (1988) Associative neural network model for the generation of temporal patterns — theory and application to central pattern generators. Biophys J 54:1039–1051Google Scholar
  20. Matsuoka K (1985) Sustained oscillations generated by mutually inhibiting neurons with adaptation. Biol Cybern 52:367–376Google Scholar
  21. Matsuoka K (1987) Mechanisms of frequency and pattern control in the neural rhythm generators. Biol Cybern 56:345–353Google Scholar
  22. McGeer T (1989) Powered flight, child's play, silly wheels and walking machines. Proceedings of the IEEE International Conference on Robotics and Automation. 1989, pp 1592–1598Google Scholar
  23. Miller S, Scott PD (1977) The spinal locomotor generator. Exp Brain Res 30:387–403Google Scholar
  24. Mochon S, McMahon TA (1980) Ballistic walking. J Biomech 13:49–57Google Scholar
  25. Mori S (1987) Integration of posture and locomotion in acute decerebrate cats and in awake, freely moving cats. Prog Neurobiol 28:161–195Google Scholar
  26. Murray MP (1967) Gait as a total pattern of movement. Am J Phys Med 46:290–333Google Scholar
  27. Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. Wiley, New YorkGoogle Scholar
  28. Nilsson J, Thorstensson A, Halbertsma J (1985) Changes in leg movements and muscle activity with speed of locomotion and mode of progression in humans. Acta Physiol Scand 123:457–475Google Scholar
  29. Pandy M, Berme N (1988) A numerical method for simulating the dynamics of human walking. J Biomech 21–12:1043–1051Google Scholar
  30. Pearlmutter BA (1989) Learning state space trajectories in recurrent neural networks. Neural Comput 1:263–269Google Scholar
  31. Pearson KG (1987) Central pattern generation: a concept under scrutiny. In: Advances in physiological research. Plenum Press, New York, pp 167–185Google Scholar
  32. Raibert MH (1984) Hopping in legged systems — modeling and simulation for the two-dimensional one-legged case. IEEE Transactions on systems, man, and cybernetics SMC-14–3:451–463Google Scholar
  33. Schöner G, Kelso JAS (1988) Dynamic pattern generation in behavioral and neural systems. Science 239:1513–1520Google Scholar
  34. Schöner G, Jiang WY, Kelso JAS (1990) A synergetic theory of quadrupedal gaits and gait transitions. J Theor Biol 142:359–391Google Scholar
  35. Selverston AI (ed) (1985) Model neural networks and behavior. Plenum Press, New YorkGoogle Scholar
  36. Shik ML, Severin FV, Orlovsky GN (1966) Control of walking and running by means of electrical stimulation of the mid-brain. Biophysics 11:756–765Google Scholar
  37. Thelen H (1988) Dynamical approaches to the development of behavior. In: Kelso JAS, Mandell AJ, Shlesinger MF (eds) Dynamic patterns in complex systems, World Scientific, Singapore, pp 348–369Google Scholar
  38. Williams RJ, Zipser D (1989) A learning algorithm for continually running fully recurrent neural networks. Neural Comput 1:270–280Google Scholar
  39. Yuasa H, Ito M (1990) Coordination of many oscillators and generation of locomotory patterns. Biol Cybern 63:177–184Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • G. Taga
    • 1
  • Y. Yamaguchi
    • 1
  • H. Shimizu
    • 1
  1. 1.Faculty of Pharmaceutical SciencesUniversity of Tokyo HongoTokyoJapan

Personalised recommendations