Psychological Research

, Volume 55, Issue 2, pp 99–106 | Cite as

The problem of redundancy in movement control: The adaptive model theory approach

  • Peter D. Neilson


The problem of redundancy in movement control is encountered when one attempts to answer the question: How does the central nervous system (CNS) determine the pattern of neural activity required in some 5,000,000 descending motor fibres to control only 100–150 biomechanical degrees of freedom of movement? Mathematically this is equivalent to solving a set of simultaneous equations with many more unknowns than equations. This system of equations is redundant because it has an infinite number of possible solutions. The problem is solved by the neuronal circuitry hypothesized in Adaptive Model Theory (AMT). According to AMT, the CNS includes neuronal circuitry able to compute and maintain adaptively the accuracy of internal models of the reciprocal multivariable relationships between outgoing motor commands and their resulting sensory consequences. To identify these input-output relationships by means of regression analysis, correlations between the input signals have to be taken into account. For example, if the inputs are perfectly correlated, the model reduces to a virtual one-input system. In general, the number of inputs modelled equals the number of degrees of freedom encoded by the signals; that is, the number of independently varying (orthogonal) signals. The adaptive modelling circuitry proposed in AMT automatically tunes itself to extract independently varying sensory and motor signals before computing the dynamic relationships between them. Inverse models are employed during response execution to translate movements preplanned as desired trajectories of these high-level sensory-feature signals into appropriately co-ordinated motor commands to send to the muscles. Since movement is preplanned in terms of a number of orthogonalized sensory-feature signals equal to the number of degrees of freedom in the desired response, the problem of redundancy is solved and the correlation or co-ordination between motor-command signals is automatically introduced by the adaptive models.


Neural Activity Movement Control Internal Model Inverse Model Simultaneous Equation 
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. Astrom, K. J., & Wittenmark, B. (1989). Adaptive control. Reading, MA: Addison-Wesley.Google Scholar
  2. Box, G. E. P., & Jenkins, G. M. (1976). Time series analysis: Forecasting and control. San Francisco: Holden-Day.Google Scholar
  3. Goodwin, G. C., & Sin, K. S. (1984). Adaptive filtering prediction and control. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  4. Haykin, S. (1986). Adaptive filter theory. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  5. Johnson, C. R., Jr. (1988). Lectures on adaptive parameter estimation. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  6. Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (1991). Principles of neuroscience. New York: Elsevier.Google Scholar
  7. Ljung, L. (1987). System identification. Theory for the user. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  8. Neilson, M. D., & Neilson, P. D. (1987). Speech motor control and stuttering: A computational model of adaptive sensory-motor processing. Speech Communication, 6, 325–333.Google Scholar
  9. Neilson, P. D., Neilson, M. D., & O'Dwyer, N. J. (1988). Internal models and intermittency: A theoretical account of human tracking behavior. Biological Cybernetics, 58, 101–112.Google Scholar
  10. Neilson, P. D., Neilson, M. D., & O'Dwyer, N. J. (1992). Adaptive Model Theory: Application to disorders of Motor Control. In J. J. Summers (Ed.), Approaches to the study of motor control and learning (Advances in Psychology, pp. 495–548). Amsterdam: North-Holland.Google Scholar
  11. Proakis, J. G., & Manolakis, D. G. (1989). Introduction to digital signal processing. New York: Macmillian Publishing Co.Google Scholar
  12. Widrow, B., & Stearns, S. D. (1985). Adaptive signal processing. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Peter D. Neilson
    • 1
    • 2
  1. 1.Department of Systems and Control, School of Electrical EngineeringUniversity of New South WalesSydneyAustralia
  2. 2.Cerebral Palsy Research Unit, Institute of Neurological SciencesThe Prince Henry HospitalSydneyAustralia

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