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Hierarchical control of two-dimensional gaze saccades

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Abstract

Coordinating the movements of different body parts is a challenging process for the central nervous system because of several problems. Four of these main difficulties are: first, moving one part can move others; second, the parts can have different dynamics; third, some parts can have different motor goals; and fourth, some parts may be perturbed by outside forces. Here, we propose a novel approach for the control of linked systems with feedback loops for each part. The proximal parts have separate goals, but critically the most distal part has only the common goal. We apply this new control policy to eye-head coordination in two-dimensions, specifically head-unrestrained gaze saccades. Paradoxically, the hierarchical structure has controllers for the gaze and the head, but not for the eye (the most distal part). Our simulations demonstrate that the proposed control structure reproduces much of the published empirical data about gaze movements, e.g., it compensates for perturbations, accurately reaches goals for gaze and head from arbitrary initial positions, simulates the nine relationships of the head-unrestrained main sequence, and reproduces observations from lesion and single-unit recording experiments. We conclude by showing how our model can be easily extended to control structures with more linked segments, such as the control of coordinated eye on head on trunk movements.

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Notes

  1. One simplification here is that we ignore internal noise in the system, e.g., Harris and Wolpert (1998) showed that optimal control of a system with signal-dependent noise can reproduce the speed-accuracy trade-off for saccades. As we are dealing with rejection of perturbations in linked systems, internal noise is not our primary concern.

  2. To cancel its VOR, the monkey looked at a head-fixed target while sitting on a rotating chair that oscillated sinusoidally

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Acknowledgments

We are especially grateful to Dr. N. J. Gandhi for kindly providing the data points used to make our Fig. 5 and 6.

Drs. Optican and Daye were supported by the Intramural Research Program of the National Eye Institute.

Dr. Blohm has been supported by the National Science and Engineering Research Council (Canada), the Ontario Research Fund (Canada), the Canadian Foundation for Innovation (Canada) and the Botterell Foundation (Queens University, Kingston, ON, Canada).

Dr. Lefevre has been supported by Fonds National de la Recherche Scientifique, Action de Recherche Concertée (Belgium). This paper presents research results of the Belgian Network Dynamical Systems, Control and Optimization, funded by the Interuniversity Attraction Poles Programmes, initiated by the Belgian State, Science Policy Office.

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The authors declare that they have no conflict of interest

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Authors and Affiliations

  1. NIH, NEI, Laboratory of Sensorimotor Research, 49 Convent Drive, Room 2A50, Bethesda, MD, 20892-4435, USA

    Pierre M. Daye & Lance M. Optican

  2. Centre for Neuroscience Studies, Queen’s University, Botterell Hall, Room 229, 18 Stuart Street, Kingston, ON, K7L 3N6, Canada

    Gunnar Blohm

  3. UCLouvain, ICTeam, IoNS, Euler building, 4 avenue Georges Lemaitre, 1348, Louvain-la-Neuve, Belgium

    Philippe Lefèvre

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  1. Pierre M. Daye
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  2. Lance M. Optican
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  4. Philippe Lefèvre
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Correspondence to Pierre M. Daye.

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Daye, P.M., Optican, L.M., Blohm, G. et al. Hierarchical control of two-dimensional gaze saccades. J Comput Neurosci 36, 355–382 (2014). https://doi.org/10.1007/s10827-013-0477-1

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