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Signal-dependent noise determines motor planning

Nature volume 394, pages 780–784 (1998)Cite this article

Abstract

When we make saccadic eye movements or goal-directed arm movements, there is an infinite number of possible trajectories that the eye or arm could take to reach the target1,2. However, humans show highly stereotyped trajectories in which velocity profiles of both the eye and hand are smooth and symmetric for brief movements3,4. Here we present a unifying theory of eye and arm movements based on the single physiological assumption that the neural control signals are corrupted by noise whose variance increases with the size of the control signal. We propose that in the presence of such signal-dependent noise, the shape of a trajectory is selected to minimize the variance of the final eye or arm position. This minimum-variance theory accurately predicts the trajectories of both saccades and arm movements and the speed–accuracy trade-off described by Fitt's law5. These profiles are robust to changes in the dynamics of the eye or arm, as found empirically6,7. Moreover, the relation between path curvature and hand velocity during drawing movements reproduces the empirical ‘two-thirds power law’8,9. This theory provides a simple and powerful unifying perspective for both eye and arm movement control.

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Figure 1: A comparison of bang-bang (dashed line) and minimum-variance (solid line) control for a 10 degree saccade with a duration of 50 ms.
Figure 2: Comparison of empirical and predicted saccade trajectories.
Figure 3: Comparison of empirical and theoretical arm velocity profiles.
Figure 4: Comparison of empirical and predicted arm movement durations.
Figure 5: Comparison of empirical and predicted trajectories for a two-joint arm.

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Acknowledgements

We thank S. Goodbody, Z. Ghahramani and M. Pembrey for comments on the manuscript. This project was supported by the MRC, the Wellcome Trust, Help a Child to See charity, the IRIS fund, the Child Health Research Appeal Trust and the Royal Society.

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Authors and Affiliations

  1. Department of Ophthalmology and Visual Sciences Unit, Great Ormond Street Hospital for Children NHS Trust, and Institute of Child Health, University College London, London, WC1N 3JH, UK

    Christopher M. Harris

  2. Sobell Department of Neurophysiology, Institute of Neurology, Queen Square, University College London, London, WC1N 3BG, UK

    Daniel M. Wolpert

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  1. Christopher M. Harris
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  2. Daniel M. Wolpert
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Harris, C., Wolpert, D. Signal-dependent noise determines motor planning. Nature 394, 780–784 (1998). https://doi.org/10.1038/29528

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