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.
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Bernstein, N.I. The Coordination and Regulation of Movements (Pergamon, Oxford, 1967).
Scholz, J.P. & Schoner, G. The uncontrolled manifold concept: identifying control variables for a functional task. Exp. Brain Res. 126, 289–306 (1999).
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).
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).
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).
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).
Winter, D.A. in Perspectives on the Coordination of Movement (ed. Wallace, S. A.) 329–363 (Elsevier, Amsterdam, 1989).
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).
Wright, C.E. in Attention and Performance XIII: Motor Representation and Control (ed. Jeannerod, M.) 294–320 (Lawrence Erlbaum, Hillsdale, New Jersey, 1990).
Haggard, P., Hutchinson, K. & Stein, J. Patterns of coordinated multi-joint movement. Exp. Brain Res. 107, 254–266 (1995).
Cole, K.J. & Abbs, J.H. Coordination of three-joint digit movements for rapid finger-thumb grasp. J. Neurophysiol. 55, 1407–1423 (1986).
Gracco, V.L. & Abbs, J.H. Variant and invariant characteristics of speech movements. Exp. Brain Res. 65, 156–166 (1986).
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).
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).
Cole, K.J. & Abbs, J.H. Kinematic and electromyographic responses to perturbation of a rapid grasp. J. Neurophysiol. 57, 1498–1510 (1987).
Robertson, E.M. & Miall, R.C. Multi-joint limbs permit a flexible response to unpredictable events. Exp. Brain Res. 117, 148–152 (1997).
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).
Nelson, W.L. Physical principles for economies of skilled movements. Biol. Cybern. 46, 135–147 (1983).
Bizzi, E., Accornero, N., Chapple, W. & Hogan, N. Posture control and trajectory formation during arm movement. J. Neurosci. 4, 2738–2744 (1984).
Flash, T. & Hogan, N. The coordination of arm movements: an experimentally confirmed mathematical model. J. Neurosci. 5, 1688–1703 (1985).
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).
Harris, C.M. & Wolpert, D.M. Signal-dependent noise determines motor planning. Nature 394, 780–784 (1998).
Thoroughman, K.A. & Shadmehr, R. Learning of action through adaptive combination of motor primitives. Nature 407, 742–747 (2000).
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).
Hinton, G.E. Parallel computations for controlling an arm. J. Motor Behav. 16, 171–194 (1984).
D'Avella, A. & Bizzi, E. Low dimensionality of supraspinally induced force fields. Proc. Natl. Acad. Sci. USA 95, 7711–7714 (1998).
Santello, M. & Soechting, J.F. Force synergies for multifingered grasping. Exp. Brain Res. 133, 457–467 (2000).
Davis, M.H.A. & Vinter, R.B. Stochastic Modelling and Control (Chapman and Hall, London, 1985).
Sutton, R.S. & Barto, A.G. Reinforcement Learning: An Introduction (MIT Press, Cambridge, Massachusetts, 1998).
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).
Loeb, G.E., Levine, W.S. & He, J. Understanding sensorimotor feedback through optimal control. Cold Spring Harbor Symp. Quant. Biol. 55, 791–803 (1990).
Jordan, M.I. in Attention and Performance XIII: Motor Representation and Control (ed. Jeannerod, M.) 796–836 (Lawrence Erlbaum, Hillsdale, New Jersey, 1990).
Hoff, B. A Computational Description of the Organization of Human Reaching and Prehension. Ph.D. Thesis, University of Southern California (1992).
Kuo, A.D. An optimal control model for analyzing human postural balance. IEEE Trans. Biomed. Eng. 42, 87–101 (1995).
Todorov, E. Studies of goal-directed movements. Ph.D. Thesis, Massachusetts Institute of Technology (1998).
Turvey, M.T. Coordination. Am. Psychol. 45, 938–953 (1990).
Kelso, J.A.S. Dynamic Patterns: The Self-Organization of Brain and Behavior (MIT Press, Cambridge, Massachusetts, 1995).
Marr, D. Vision (Freeman, San Francisco, 1982).
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).
Todorov, E. Cosine tuning minimizes motor errors. Neural Comput. 14, 1233–1260 (2002).
Kawato, M. Internal models for motor control and trajectory planning. Curr. Opin. Neurobiol. 9, 718–727 (1999).
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).
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).
Komilis, E., Pelisson, D. & Prablanc, C. Error processing in pointing at randmoly feedback-induced double-step stimuli. J. Motor Behav. 25, 299–308 (1993).
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).
Flanagan, J.R. & Lolley, S. The inertial anisotropy of the arm is accurately predicted during movement planning. J. Neurosci. 21, 1361–1369 (2001).
Sabes, P.N., Jordan, M.I. & Wolpert, D.M. The role of inertial sensitivity in motor planning. J. Neurosci. 18, 5948–5957 (1998).
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).
Gottlieb, G.L. On the voluntary movement of compliant (inertial-viscoelastic) loads by parcellated control mechanisms. J. Neurophysiol. 76, 3207–3228 (1996).
Newell, K.M. & Vaillancourt, D.E. Dimensional change in motor learning. Hum. Mov. Sci. 20, 695–715 (2001).
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.
The authors declare no competing financial interests.
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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
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