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Morphology and the gradient of a symmetric potential predicts gait transitions of dogs

Wilshin, S D; Haynes, G C; Porteous, J; Koditschek, D; Revzen, S; Spence, A J


S D Wilshin

G C Haynes

J Porteous

D Koditschek

S Revzen

A J Spence


Gaits and gait transitions play a central role in the movement of animals. Symmetry is thought to govern the structure of the nervous system, and constrain the limb motions of quadrupeds. We quantify the symmetry of dog gaits with respect to combinations of bilateral, fore-aft, and spatio-temporal symmetry groups. We tested the ability of symmetries to model motion capture data of dogs walking, trotting and transitioning between those gaits. Fully symmetric models performed comparably to asymmetric with only a 22% increase in the residual sum of squares and only one-quarter of the parameters. This required adding a spatio-temporal shift representing a lag between fore and hind limbs. Without this shift, the symmetric model residual sum of squares was 1700% larger. This shift is related to (linear regression, n = 5, p = 0.0328) dog morphology. That this symmetry is respected throughout the gaits and transitions indicates that it generalizes outside a single gait. We propose that relative phasing of limb motions can be described by an interaction potential with a symmetric structure. This approach can be extended to the study of interaction of neurodynamic and kinematic variables, providing a system-level model that couples neuronal central pattern generator networks and mechanical models.


Wilshin, S. D., Haynes, G. C., Porteous, J., Koditschek, D., Revzen, S., & Spence, A. J. (2017). Morphology and the gradient of a symmetric potential predicts gait transitions of dogs. Biological Cybernetics, 111(3-4), 269-277.

Journal Article Type Other
Acceptance Date Jun 6, 2017
Publication Date Jun 19, 2017
Deposit Date Jun 8, 2017
Publicly Available Date Jun 8, 2017
Journal Biological Cybernetics
Print ISSN 0340-1200
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 111
Issue 3-4
Pages 269-277
Keywords Gaits; Dogs; Symmetry; Gait transitions; Dynamical systems
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