Biological Cybernetics

, Volume 57, Issue 3, pp 169–185 | Cite as

A hierarchical neural-network model for control and learning of voluntary movement

  • M. Kawato
  • Kazunori Furukawa
  • R. Suzuki


In order to control voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: the determination of a desired trajectory in the visual coordinates, the transformation of its coordinates to the body coordinates and the generation of motor command. Based on physiological knowledge and previous models, we propose a hierarchical neural network model which accounts for the generation of motor command. In our model the association cortex provides the motor cortex with the desired trajectory in the body coordinates, where the motor command is then calculated by means of long-loop sensory feedback. Within the spinocerebellum — magnocellular red nucleus system, an internal neural model of the dynamics of the musculoskeletal system is acquired with practice, because of the heterosynaptic plasticity, while monitoring the motor command and the results of movement. Internal feedback control with this dynamical model updates the motor command by predicting a possible error of movement. Within the cerebrocerebellum — parvocellular red nucleus system, an internal neural model of the inverse-dynamics of the musculo-skeletal system is acquired while monitoring the desired trajectory and the motor command. The inverse-dynamics model substitutes for other brain regions in the complex computation of the motor command. The dynamics and the inverse-dynamics models are realized by a parallel distributed neural network, which comprises many sub-systems computing various nonlinear transformations of input signals and a neuron with heterosynaptic plasticity (that is, changes of synaptic weights are assumed proportional to a product of two kinds of synaptic inputs). Control and learning performance of the model was investigated by computer simulation, in which a robotic manipulator was used as a controlled system, with the following results: (1) Both the dynamics and the inverse-dynamics models were acquired during control of movements. (2) As motor learning proceeded, the inverse-dynamics model gradually took the place of external feedback as the main controller. Concomitantly, overall control performance became much better. (3) Once the neural network model learned to control some movement, it could control quite different and faster movements. (4) The neural netowrk model worked well even when only very limited information about the fundamental dynamical structure of the controlled system was available. Consequently, the model not only accounts for the learning and control capability of the CNS, but also provides a promising parallel-distributed control scheme for a large-scale complex object whose dynamics are only partially known.


Neural Network Model Motor Learning Voluntary Movement Motor Command Sensory Feedback 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Albus JS (1971) A theory of cerebellar functions. Math Biosci 10:25–61Google Scholar
  2. Albus JS (1975) A new approach to manipulator control: the cerebellar model articulation controller (CMAC). J Dyn Syst Meas Control 97:270–277Google Scholar
  3. Allen GI, Tsukahara N (1974) Cerebrocerebellar communication systems. Physiol Rev 54:957–1006Google Scholar
  4. Amari S (1977) Neural theory of association and conceptformation. Biol Cybern 26:175–185Google Scholar
  5. Arbib MA (1981) Perceptual structures and distributed motor control. In: Brooks VB (ed) Handbook of physiology, sect 1: vol 11, part 2. American Physiol Soc, Bethesda, pp 1449–1480Google Scholar
  6. Arimoto S, Kawamura S, Miyazaki F (1984a) Bettering operation of dynamic systems by learning: a new control theory for sevomechanism or mechatronics systems. 23rd IEEE Conf Des Control 2:1064–1069Google Scholar
  7. Arimoto S, Kawamura S, Miyazaki F (1984b) Can mechanical robots learn by themselves; Proceedings of 2nd International Symposium on Robotics Research, Kyoto, JapanGoogle Scholar
  8. Cheney PD, Fetz EE (1980) Functional classes of primate corticomotoneuronal cells and their relation to active force. J Neurophysiol 44:773–791Google Scholar
  9. Dubowsky S, DesForges DT (1979) The application of model reference adaptive control to robotic manipulators. J Dyn Syst Meas Control 101:193–200Google Scholar
  10. Eccles JC: Introductory remarks In: Massion J, Sasaki K (eds) Cerebro-cerebellar interactions, pp 1–18. North-Holland Elsevier, Amsterdam Oxford New York, pp 1–18Google Scholar
  11. Evarts EV (1981) Role of motor cortex in voluntary movements in primates. In: Brooks VB (ed) Handbook of physiology, sect 1: vol 11, part 2. American Physiol Soc, Bethesda, pp 1083–1120Google Scholar
  12. Geman S (1979) Some averaging and stability results for random differential equations. SIAM J Appl Math 36:86–105Google Scholar
  13. Ghez C, Fahn S (1985) The cerebellum. In: Kandel ER, Schwartz JH (eds) Principles of neural science. Elsevier, New York, pp 502–522Google Scholar
  14. Bilbert PFC, Thach WT (1977) Purkinje cell activity during motor learning. Brain Res 128:309–328Google Scholar
  15. Flash T, Hogan N (1985) The coordination of arm movements; an experimentally confirmed mathematical model. J Neurosci 5:1688–1703Google Scholar
  16. Fujita M (1982a) Adaptive filter model of the cerebellum. Biol Cybern 45:195–206Google Scholar
  17. Fujita M (1982b) Simulation of adaptive modification of the vestibulo-ocular reflex with an adaptive filter model of the cerebellum. Biol Cybern 45:207–214Google Scholar
  18. Furukawa K (1984) Identification of a robotic manipulator by a neural model. Osaka Univ, Bachelor's ThesisGoogle Scholar
  19. Hollerbach JM (1980) A recursive Lagrangian formulation of manipulator dynamics and a comparative study of dynamics formulation complexity. IEEE Trans SMC-10:730–736Google Scholar
  20. Hollerbach JM (1982) Computers, brains and the control of movement. Trends Neuro Sci 5:189–192Google Scholar
  21. Ito M (1970) Neurophysiological aspects of the cerebellar motor control system. Int J Neurol 7:162–176Google Scholar
  22. Ito M (1984) The cerebellum and neural control. Raven Press, New YorkGoogle Scholar
  23. Ito M, Shiida T, Yagi N, Yamamoto M (1974) The cerebellar modification of rabbit's horizontal vestibulo-ocular reflex induced by sustained head rotation combined with visual stimulation. Proc Jpn Acad 50:85–89Google Scholar
  24. Ito M, Jastreboff PJ, Miyashita Y (1982) Specific effects of unilateral lesions in the flocculus upon eye movements in albino rabbits. Exp Brain Res 45:233–242Google Scholar
  25. Ito M, Sakurai M, Tongroach P (1982) Climbing fibre induced depression of both mossy fibre responsiveness and gultamate sensitivity of cerebellar Purkinje cells. J Physiol 324:113–134Google Scholar
  26. Kawato M, Hamaguchi T, Murakami F, Tsukahara N (1984) Quantitative analysis of electrical properties of dendritic spines. Biol Cybern 50:447–454Google Scholar
  27. Llinás R, Walton K, Hillman D, Sotelo C (1975) Inferior olive: its role in motor learning. Science 190:1230–1231Google Scholar
  28. Luh JYS, Walker MW, Paul RPC (1980) On-line computational scheme for mechanical manipulations. J Dyn Syst Meas Control 102:69–76Google Scholar
  29. Marr D (1969) A theory of cerebellar cortex. J Physiol 202:437–470Google Scholar
  30. Marr D (1982) Vision. Freeman, New YorkGoogle Scholar
  31. Miyamoto H (1985) A motor learning model based on synaptic plasticity. Osaka University, Bachelor's ThesisGoogle Scholar
  32. Miyamoto H, Kawato M, Suzuki R (1987) Hierarchical learning control of an industrial manipulator using a model of the central nervous system, Japan IEICE Technical Report, MBE-86-81:25–32Google Scholar
  33. Poggio T, Torre V (1981) A theory of synaptic interactions. In: Reichardt WE, Poggio T (eds) Theoretical approaches in neurobiology. MIT Press, Cambridge, pp 28–46Google Scholar
  34. Poirier LJ, Bouvier G, Bédard P, Bouchard R, Larochelle L, Olivier A, Singh P (1969) Essai sur les cirvuits neuronaux mipliqués dans le tremblement postural et l'hypokinesie. Rev Neurol 120:15–40Google Scholar
  35. Raibert MH (1978) A model for sensorimotor control and learning. Biol Cybern 29:29–36Google Scholar
  36. Sasaki K, Gemba H (1982) Development and change of cortical field potentials during learning processes of visually initiated hand movements in the monkey. Exp Brain Res 48:429–437Google Scholar
  37. Sasaki K, Gemba H, Mizuno N (1982) Cortical field potentials preceding visually initiated hand movements and cerebellar actions in the monkey. Exp Brain Res 46:29–36Google Scholar
  38. Setoyama T (1987) Symbolic calculation of subsystems of the neural inverse-dynamics model for a 6 degrees of freedom manipulator using REDUCE. Osaka University, Bachelor's ThesisGoogle Scholar
  39. Tsukahara N (1981) Synaptic plasticity in the mammalian central nervous system. Annu Rev Neurosci 4:351–379Google Scholar
  40. Tsukahara N, Kawato M (1982) Dynamic and plastic properties of the brain stem neuronal networks as the possible neuronal basis of learning and memory. In: Amari S, Arbib MA (eds) Competition and cooperation in neural nets. Springer, Berlin Heidelberg New York, pp 430–441Google Scholar
  41. Tsukahara N, Oda Y, Notsu T (1981) Classical conditioning mediated by the red nucleus in the cat. J Neurosci 1:72–79Google Scholar
  42. Uno Y, Kawato M, Suzuki R (1987) Formation of optimum trajectory in control of arm movement — minimum torquechange model — Japan IEICE Technical Report MBE 86-79:9–16Google Scholar
  43. Widrow B, McCool JM, Larimore MG, Johnson CR (1976) Stationary and nonstationary learning characteristics of the LMS adaptive filter. Proc IEEE 64:1151–1162Google Scholar
  44. Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12:1–24Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • M. Kawato
    • 1
  • Kazunori Furukawa
    • 1
  • R. Suzuki
    • 1
  1. 1.Department of Biophysical Engineering, Faculty of Engineering ScienceOsaka UniversityToyonaka, OsakaJapan

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