Attitude is Everything: Extending Models of Fish Kinematics to Maneuvers

Heidi Verheggen, Liusha Geng

Abstract


A primary component of studying fish locomotion is identifying characteristics of locomotor kinematics for a wide variety of undulatory swimming behaviors among various fish species. Identifying such characteristics requires obtaining a quantitative description of the harmonic structure of these kinematics. In this study, we seek to obtain this description by improving on an existing model to better capture the periodic components of various forms of locomotion. Both the old and new models were based on video data reduced to midline position for various species: hagfish, lamprey, and shark, in various locomotive states, including constant-velocity swimming and turning. To improve tailbeat frequency estimation, a statistical technique involving the Hilbert transform was devised to extract a fundamental frequency associated with data for a given video clip. Applying this technique yielded a more general and consistent estimate of the period of midline motion, addressing a central challenge of modeling unsteady swimming. The frequency estimates were notably consistent along the body in all trials, and surprisingly showed the least variation for a turning shark. Thus the Hilbert transform adapted our model to handle maneuvers. In addition to this advancement, the model of midline kinematics was greatly simplified: by using attitude data, essentially data on the angle of body segments, the number of fitting parameters was reduced by nearly a factor of one half, and the data was more appropriately fitted using least absolute residual regression rather than least-squares. Thus, with the reconstruction techniques we have developed, the analytical process presented here yields an accurate, quantitative description enabling a better understanding of locomotor kinematics.

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