VOOZH about

URL: https://www.nature.com/articles/nn963?error=cookies_not_supported&code=7a7378f8-7c64-4314-978b-1ebd74eaa598

⇱ Optimal feedback control as a theory of motor coordination | Nature Neuroscience

Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Abstract

A central problem in motor control is understanding how the many biomechanical degrees of freedom are coordinated to achieve a common goal. An especially puzzling aspect of coordination is that behavioral goals are achieved reliably and repeatedly with movements rarely reproducible in their detail. Existing theoretical frameworks emphasize either goal achievement or the richness of motor variability, but fail to reconcile the two. Here we propose an alternative theory based on stochastic optimal feedback control. We show that the optimal strategy in the face of uncertainty is to allow variability in redundant (task-irrelevant) dimensions. This strategy does not enforce a desired trajectory, but uses feedback more intelligently, correcting only those deviations that interfere with task goals. From this framework, task-constrained variability, goal-directed corrections, motor synergies, controlled parameters, simplifying rules and discrete coordination modes emerge naturally. We present experimental results from a range of motor tasks to support this theory.

This is a preview of subscription content, access via your institution

Access options

Subscribe to this journal

Receive 12 print issues and online access

$259.00 per year

only $21.58 per issue

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Redundancy exploitation.
Figure 2: Final state variability.
Figure 3: Trajectory variability.
Figure 4: Hitting and throwing.
Figure 5: Hand manipulation.
Figure 6: Telescopic 'arm' model.

Similar content being viewed by others

References

  1. Bernstein, N.I. The Coordination and Regulation of Movements (Pergamon, Oxford, 1967).

    Google Scholar 

  2. Scholz, J.P. & Schoner, G. The uncontrolled manifold concept: identifying control variables for a functional task. Exp. Brain Res. 126, 289–306 (1999).

    Article  CAS  Google Scholar 

  3. Scholz, J.P., Schoner, G. & Latash, M.L. Identifying the control structure of multijoint coordination during pistol shooting. Exp. Brain Res. 135, 382–404 (2000).

    Article  CAS  Google Scholar 

  4. Tseng, Y.W., Scholz, J.P. & Schoner, G. Goal-equivalent joint coordination in pointing: affect of vision and arm dominance. Motor Control 6, 183–207 (2002).

    Article  Google Scholar 

  5. Domkin, D., Laczko, J., Jaric, S., Johansson, H. & Latash, M.L. Structure of joint variability in bimanual pointing tasks. Exp. Brain Res. 143, 11–23 (2002).

    Article  Google Scholar 

  6. Balasubramaniam, R., Riley, M.A. & Turvey, M.T. Specificity of postural sway to the demands of a precision task. Gait Posture 11, 12–24 (2000).

    Article  CAS  Google Scholar 

  7. Winter, D.A. in Perspectives on the Coordination of Movement (ed. Wallace, S. A.) 329–363 (Elsevier, Amsterdam, 1989).

    Book  Google Scholar 

  8. Vereijken, B., van Emmerik, R.E.A., Whiting, H. & Newel, K.M. Free(z)ing degrees of freedom in skill acquisition. J. Motor Behav. 24, 133–142 (1992).

    Article  Google Scholar 

  9. Wright, C.E. in Attention and Performance XIII: Motor Representation and Control (ed. Jeannerod, M.) 294–320 (Lawrence Erlbaum, Hillsdale, New Jersey, 1990).

    Google Scholar 

  10. Haggard, P., Hutchinson, K. & Stein, J. Patterns of coordinated multi-joint movement. Exp. Brain Res. 107, 254–266 (1995).

    Article  CAS  Google Scholar 

  11. Cole, K.J. & Abbs, J.H. Coordination of three-joint digit movements for rapid finger-thumb grasp. J. Neurophysiol. 55, 1407–1423 (1986).

    Article  CAS  Google Scholar 

  12. Gracco, V.L. & Abbs, J.H. Variant and invariant characteristics of speech movements. Exp. Brain Res. 65, 156–166 (1986).

    Article  CAS  Google Scholar 

  13. Li, Z.M., Latash, M.L. & Zatsiorsky, V.M. Force sharing among fingers as a model of the redundancy problem. Exp. Brain Res. 119, 276–286 (1998).

    Article  CAS  Google Scholar 

  14. Gracco, V.L. & Abbs, J.H. Dynamic control of the perioral system during speech: kinematic analyses of autogenic and nonautogenic sensorimotor processes. J. Neurophysiol. 54, 418–432 (1985).

    Article  CAS  Google Scholar 

  15. Cole, K.J. & Abbs, J.H. Kinematic and electromyographic responses to perturbation of a rapid grasp. J. Neurophysiol. 57, 1498–1510 (1987).

    Article  CAS  Google Scholar 

  16. Robertson, E.M. & Miall, R.C. Multi-joint limbs permit a flexible response to unpredictable events. Exp. Brain Res. 117, 148–152 (1997).

    Article  CAS  Google Scholar 

  17. Sporns, O. & Edelman, G.M. Solving Bernstein's problem: a proposal for the development of coordinated movement by selection. Child Dev. 64, 960–981 (1993).

    Article  CAS  Google Scholar 

  18. Nelson, W.L. Physical principles for economies of skilled movements. Biol. Cybern. 46, 135–147 (1983).

    Article  CAS  Google Scholar 

  19. Bizzi, E., Accornero, N., Chapple, W. & Hogan, N. Posture control and trajectory formation during arm movement. J. Neurosci. 4, 2738–2744 (1984).

    Article  CAS  Google Scholar 

  20. Flash, T. & Hogan, N. The coordination of arm movements: an experimentally confirmed mathematical model. J. Neurosci. 5, 1688–1703 (1985).

    Article  CAS  Google Scholar 

  21. Uno, Y., Kawato, M. & Suzuki, R. Formation and control of optimal trajectory in human multijoint arm movement: minimum torque-change model. Biol. Cybern. 61, 89–101 (1989).

    Article  CAS  Google Scholar 

  22. Harris, C.M. & Wolpert, D.M. Signal-dependent noise determines motor planning. Nature 394, 780–784 (1998).

    Article  CAS  Google Scholar 

  23. Thoroughman, K.A. & Shadmehr, R. Learning of action through adaptive combination of motor primitives. Nature 407, 742–747 (2000).

    Article  CAS  Google Scholar 

  24. Gelfand, I., Gurfinkel, V., Tsetlin, M. & Shik, M. in Models of the Structural-Functional Organization of Certain Biological Systems (eds. Gelfand, I., Gurfinkel, V., Fomin, S. & Tsetlin, M.) 329–345 (MIT Press, Cambridge, Massachusetts, 1971).

    Google Scholar 

  25. Hinton, G.E. Parallel computations for controlling an arm. J. Motor Behav. 16, 171–194 (1984).

    Article  CAS  Google Scholar 

  26. D'Avella, A. & Bizzi, E. Low dimensionality of supraspinally induced force fields. Proc. Natl. Acad. Sci. USA 95, 7711–7714 (1998).

    Article  CAS  Google Scholar 

  27. Santello, M. & Soechting, J.F. Force synergies for multifingered grasping. Exp. Brain Res. 133, 457–467 (2000).

    Article  CAS  Google Scholar 

  28. Davis, M.H.A. & Vinter, R.B. Stochastic Modelling and Control (Chapman and Hall, London, 1985).

    Book  Google Scholar 

  29. Sutton, R.S. & Barto, A.G. Reinforcement Learning: An Introduction (MIT Press, Cambridge, Massachusetts, 1998).

    Google Scholar 

  30. Meyer, D.E., Abrams, R.A., Kornblum, S., Wright, C.E. & Smith, J.E.K. Optimality in human motor performance: ideal control of rapid aimed movements. Psychol. Rev. 95, 340–370 (1988).

    Article  CAS  Google Scholar 

  31. Loeb, G.E., Levine, W.S. & He, J. Understanding sensorimotor feedback through optimal control. Cold Spring Harbor Symp. Quant. Biol. 55, 791–803 (1990).

    Article  CAS  Google Scholar 

  32. Jordan, M.I. in Attention and Performance XIII: Motor Representation and Control (ed. Jeannerod, M.) 796–836 (Lawrence Erlbaum, Hillsdale, New Jersey, 1990).

    Google Scholar 

  33. Hoff, B. A Computational Description of the Organization of Human Reaching and Prehension. Ph.D. Thesis, University of Southern California (1992).

  34. Kuo, A.D. An optimal control model for analyzing human postural balance. IEEE Trans. Biomed. Eng. 42, 87–101 (1995).

    Article  CAS  Google Scholar 

  35. Todorov, E. Studies of goal-directed movements. Ph.D. Thesis, Massachusetts Institute of Technology (1998).

  36. Turvey, M.T. Coordination. Am. Psychol. 45, 938–953 (1990).

    Article  CAS  Google Scholar 

  37. Kelso, J.A.S. Dynamic Patterns: The Self-Organization of Brain and Behavior (MIT Press, Cambridge, Massachusetts, 1995).

    Google Scholar 

  38. Marr, D. Vision (Freeman, San Francisco, 1982).

    Google Scholar 

  39. Schmidt, R.A., Zelaznik, H., Hawkins, B., Frank, J.S. & Quinn, J.T. Jr. Motor-output variability: a theory for the accuracy of rapid notor acts. Psychol. Rev. 86, 415–451 (1979).

    Article  Google Scholar 

  40. Todorov, E. Cosine tuning minimizes motor errors. Neural Comput. 14, 1233–1260 (2002).

    Article  Google Scholar 

  41. Kawato, M. Internal models for motor control and trajectory planning. Curr. Opin. Neurobiol. 9, 718–727 (1999).

    Article  CAS  Google Scholar 

  42. Todorov, E. & Jordan, M.I. Smoothness maximization along a predefined path accurately predicts the speed profiles of complex arm movements. J. Neurophysiol. 80, 696–714 (1998).

    Article  CAS  Google Scholar 

  43. Todorov, E., Shadmehr, R. & Bizzi, E. Augmented feedback presented in a virtual environment accelerates learning of a difficult motor task. J. Motor Behav. 29, 147–158 (1997).

    Article  CAS  Google Scholar 

  44. Komilis, E., Pelisson, D. & Prablanc, C. Error processing in pointing at randmoly feedback-induced double-step stimuli. J. Motor Behav. 25, 299–308 (1993).

    Article  CAS  Google Scholar 

  45. Gordon, J., Ghilardi, M.F., Cooper, S. & Ghez, C. Accuracy of planar reaching movements. II. Systematic extent errors resulting from inertial anisotropy. Exp. Brain Res. 99, 112–130 (1994).

    Article  CAS  Google Scholar 

  46. Flanagan, J.R. & Lolley, S. The inertial anisotropy of the arm is accurately predicted during movement planning. J. Neurosci. 21, 1361–1369 (2001).

    Article  CAS  Google Scholar 

  47. Sabes, P.N., Jordan, M.I. & Wolpert, D.M. The role of inertial sensitivity in motor planning. J. Neurosci. 18, 5948–5957 (1998).

    Article  CAS  Google Scholar 

  48. Wolpert, D.M., Ghahramani, Z. & Jordan, M.I. Are arm trajectories planned in kinematic or dynamic coordinates—an adaptation study. Exp. Brain Res. 103, 460–470 (1995).

    Article  CAS  Google Scholar 

  49. Gottlieb, G.L. On the voluntary movement of compliant (inertial-viscoelastic) loads by parcellated control mechanisms. J. Neurophysiol. 76, 3207–3228 (1996).

    Article  CAS  Google Scholar 

  50. Newell, K.M. & Vaillancourt, D.E. Dimensional change in motor learning. Hum. Mov. Sci. 20, 695–715 (2001).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank P. Dayan, Z. Ghahramani, G. Hinton and G. Loeb for discussions and comments on the manuscript. E.T. was supported by the Howard Hughes Medical Institute, the Gatsby Charitable Foundation and the Alfred Mann Institute for Biomedical Engineering. M.I.J. was supported by ONR/MURI grant N00014-01-1-0890.

Author information

Authors and Affiliations

  1. Department of Cognitive Science, University of California, San Diego, 9500 Gilman Dr., La Jolla, 92093-0515, California, USA

    Emanuel Todorov

  2. Division of Computer Science and Department of Statistics, University of California, Berkeley, 731 Soda Hall #1776, Berkeley, 94720-1776, California, USA

    Michael I. Jordan

Authors
  1. Emanuel Todorov
  2. Michael I. Jordan

Corresponding author

Correspondence to Emanuel Todorov.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

About this article

Cite this article

Todorov, E., Jordan, M. Optimal feedback control as a theory of motor coordination. Nat Neurosci 5, 1226–1235 (2002). https://doi.org/10.1038/nn963

Download citation

  • Issue date:

  • DOI: https://doi.org/10.1038/nn963

Search

Advanced search

Quick links

👁 Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing