Journal of Computational Neuroscience

, Volume 24, Issue 1, pp 57–68 | Cite as

Optimality, stochasticity, and variability in motor behavior

  • Emmanuel GuigonEmail author
  • Pierre Baraduc
  • Michel Desmurget


Recent theories of motor control have proposed that the nervous system acts as a stochastically optimal controller, i.e. it plans and executes motor behaviors taking into account the nature and statistics of noise. Detrimental effects of noise are converted into a principled way of controlling movements. Attractive aspects of such theories are their ability to explain not only characteristic features of single motor acts, but also statistical properties of repeated actions. Here, we present a critical analysis of stochastic optimality in motor control which reveals several difficulties with this hypothesis. We show that stochastic control may not be necessary to explain the stochastic nature of motor behavior, and we propose an alternative framework, based on the action of a deterministic controller coupled with an optimal state estimator, which relieves drawbacks of stochastic optimality and appropriately explains movement variability.


Motor control Noise Model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Atkeson, C., & Hollerbach, J. (1967). Kinematic features of unrestrained vertical arm movements. Journal of Neuroscience, 5(9), 2318–2330.Google Scholar
  2. Bernstein, N. (1967). The Co-ordination and regulation of movements. Oxford: Pergamon.Google Scholar
  3. Bryson, A. (1999). Dynamic optimization. Englewood Cliffs, NJ: Prentice Hall.Google Scholar
  4. Bryson, A., & Ho, YC. (1975). Applied optimal control – Optimization, estimation, and control. New York: Hemisphere.Google Scholar
  5. Burdet, E., & Milner, T. (1998). Quantization of human motions and learning of accurate movements. Biological Cybernetics, 78(4), 307–318.PubMedCrossRefGoogle Scholar
  6. Chhabra, M., & Jacobs, R. (2006a). Near-optimal human adaptive control across different noise environments. Journal of Neuroscience, 26(42), 10883–10887.PubMedCrossRefGoogle Scholar
  7. Chhabra, M., & Jacobs, R. (2006b). Properties of synergies arising from a theory of optimal motor behavior. Neural Computation, 18(10), 2320–2342.PubMedCrossRefGoogle Scholar
  8. Desmurget, M., & Grafton, S. (2000). Forward modeling allows feedback control for fast reaching movements. Trends in Cognitive Sciences, 4(11), 423–431.PubMedCrossRefGoogle Scholar
  9. Goodwin, G., & Sin, K. (1984). Adaptive filtering prediction and control. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
  10. Gordon, J., Ghilardi, M., Cooper, S., & Ghez, C. (1994a). Accuracy of planar reaching movements. I. Independence of direction and extent variability. Experimental Brain Research, 99(1), 97–111.CrossRefGoogle Scholar
  11. Gordon, J., Ghilardi, M., Cooper, S., & Ghez, C. (1994b). Accuracy of planar reaching movements. II. Systematic extent errors resulting from inertial anisotropy. Experimental Brain Research, 99(1), 112–130.Google Scholar
  12. Guigon, E., Baraduc, P., & Desmurget, M. (2007). Computational motor control: Redundancy and invariance. Journal of Neurophysiology, 97(1), 331–347.PubMedCrossRefGoogle Scholar
  13. Hamilton, A., & Wolpert, D. (2002). Controlling the statistics of action: Obstacle avoidance. Journal of Neurophysiology, 87(5), 2434–2440.PubMedGoogle Scholar
  14. Harris, C., & Wolpert, D. (1998). Signal-dependent noise determines motor planning. Nature, 394, 780–784.PubMedCrossRefGoogle Scholar
  15. Hoff, B. (1994). A model of duration in normal and perturbed reaching movement. Biological Cybernetics, 71(6), 481–488.CrossRefGoogle Scholar
  16. Hoff, B., & Arbib, M. (1993). Models of trajectory formation and temporal interaction of reach and grasp. Journal of Motor Behavior, 25(3), 175–192.PubMedCrossRefGoogle Scholar
  17. Knill, D., & Pouget, A. (2004). The bayesian brain: The role of uncertainty in neural coding and computation. Trends in Neurosciences27(12), 712–719.PubMedCrossRefGoogle Scholar
  18. Li, W. (2006). Optimal control for biological movement systems. Ph.D. thesis, University of California, San Diego.Google Scholar
  19. Meyer, D., Abrams, R., Kornblum, S., Wright, C., & Smith, J. (1988). Optimality in human motor performance: Ideal control of rapid aimed movement. Psychological Review, 95(3), 340–370.PubMedCrossRefGoogle Scholar
  20. Nelson, W. (1983). Physical principles for economies of skilled movements. Biological Cybernetics, 46(2), 135–147.PubMedCrossRefGoogle Scholar
  21. Novak, K., Miller, L., & Houk, J. (2000). Kinematic properties of rapid hand movements in a knob turning task. Experimental Brain Research, 132(4), 419–433.CrossRefGoogle Scholar
  22. Pélisson, D., Prablanc, C., Goodale, M., & Jeannerod, M. (1986). Visual control of reaching movements without vision of the limb. II. Evidence of fast unconscious processes correcting the trajectory of the hand to the final position of a double-step stimulus. Experimental Brain Research, 62(2), 303–311.CrossRefGoogle Scholar
  23. Saunders, J., & Knill, D. (2004) Visual feedback control of hand movements. Journal of Neuroscience, 24(13), 3223–3234.PubMedCrossRefGoogle Scholar
  24. Schaal, S., & Schweighofer, N. (2005). Computational motor control in humans and robots. Current Opinion in Neurobiology, 15(6), 675–682.PubMedCrossRefGoogle Scholar
  25. Scholz, J., & Schöner, G. (1999). The uncontrolled manifold concept: Identifying control variables for a functional task. Experimental Brain Research, 126(3), 289–306.CrossRefGoogle Scholar
  26. Scholz, J., Schöner, G., & Latash, M. (2000). Identifying the control structure of multijoint coordination during pistol shooting. Experimental Brain Research, 135(3), 382–404.CrossRefGoogle Scholar
  27. Stein, R., Gossen, E., & Jones, K. (2005). Neuronal variability: Noise or part of the signal? Nature Reviews Neuroscience, 6(5), 389–397.PubMedCrossRefGoogle Scholar
  28. Todorov, E. (2004). Optimality principles in sensorimotor controls. Nature Neuroscience, 7(9), 907–915.PubMedCrossRefGoogle Scholar
  29. Todorov, E. (2005). Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system. Neural Computation, 17(5), 1084–1108.PubMedCrossRefGoogle Scholar
  30. Todorov, E., & Jordan, M. (2002). Optimal feedback control as a theory of motor coordination. Nature Neuroscience, 5(11), 1226–1235.PubMedCrossRefGoogle Scholar
  31. Todorov, E., & Li, W. (2005). A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems. In: Proc American Control Conference (pp. 300–306).Google Scholar
  32. Torres, E., & Zipser, D. (2004). Simultaneous control of hand displacements and rotations in orientation-matching experiments. Journal of Applied Physiology, 96(5), 1978–1987.PubMedCrossRefGoogle Scholar
  33. Trommershäuser, J., Gepshtein, S., Maloney, L., Landy, M., & Banks, M. (2005). Optimal compensation for changes in task-relevant movement variability. Journal of Neuroscience, 25(31), 7169–7178.PubMedCrossRefGoogle Scholar
  34. van Beers, R., Haggard, P., & Wolpert, D. (2004) The role of execution noise in movement variability. Journal of Neurophysiology, 91(2), 1050–1063.PubMedCrossRefGoogle Scholar
  35. van Beers, R., Sittig, A., & Denier van der Gon, J, (1999). Integration of proprioceptive and visual position-information: An experimentally supported model. Journal of Neurophysiology, 81(3), 1355–1364.PubMedGoogle Scholar
  36. Wolpert, D., & Ghahramani, Z. (2000) Computational principles of movement neuroscience. Nature Neuroscience, 3(Supplement), 1212–1217.PubMedCrossRefGoogle Scholar
  37. Wolpert, D., Ghahramani, Z., & Jordan, M. (1995). An internal model for sensorimotor integration. Science, 269, 1880–1882.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Emmanuel Guigon
    • 1
    Email author
  • Pierre Baraduc
    • 2
  • Michel Desmurget
    • 2
  1. 1.INSERM U742, ANIMUniversité Pierre et Marie Curie (UPMC Paris 6)ParisFrance
  2. 2.Centre de Neurosciences CognitivesCNRS UMR 5229BronFrance

Personalised recommendations