Geometric Swimmer on Granular Material

Abstract

Chionactis occipitalis (the Mojave Shovel-nose snake) lives in a desert habitat where it uses body undulations to move effectively across the sandy terrain. Animal experiments have shown that Chionactis (N=10) travelling on granular substrates exhibits a particular set of waveforms which can be approximated by a sinusoidal variation in curvature - a serpenoid curve. Furthermore, all snakes tested used only a narrow subset of all available waveform parameters--measured as the relative curvature of the waveform, κλs=5.0±0.3, and number of waves on the body ξ=1.8±0.1. We hypothesize that a particular choice of parameters to describe the serpenoid curve produces a waveform that offers distinct locomotive benefit. To test this hypothesis, we used a physical model (a snake robot) to empirically explore the space of serpenoid motions at different curvature amplitudes. As expected from geometric locomotion theory, the amplitude of the gait cycle had a significant influence on the performance of locomotion. Two key results from these experiments are (1) displacement per cycle increases with amplitude at small amplitudes, but reaches a peak value of 0.55 body-lengths at relative curvature κλs=6.0, and (2) the peak mechanical cost of transport of these motions (speed at a given power, or power to move at a given speed) is at a slightly lower amplitude than the maximum-displacement gait, which reflects the extra effort required to capture all of the available displacement, vs repeating more cycles of a slightly less efficacious gait in the same time period.