A Novel 3-D Full Body Model of Snake Locomotion in Complex 3-D Terrain

Despite many studies of snake locomotion on 2-D surfaces, our understanding in 3-D terrains remains limited, due to the lack of a full body description of motion. Here we developed a novel model using variational calculus on Lie Groups to enable 3-D full body quantification of snake locomotion and understand body-terrain interaction. To our surprise, although the model simplified the composite, actuated snake body as an elastic rod, it well predicted the entire body form using only a small number of marker constraints (average error of 0.15 ± 0.05 body radius over entire body). Body acceleration and force estimates from an anisotropic friction model using our method showed that, because opposing forces almost always canceled out, the system behaved quasi-statically near equilibrium. For further validation, we performed experiments to measure elastic properties of snake bodies to improve the accuracy of input parameters. Finally, our model allowed us to apply a novel framework of locomotion energy landscapes to understand quasi-static and dynamic stability in complex 3-D terrains. Our model has a broader applicability to quantitatively measure and model 3-D locomotion and manipulation using continuum body or appendages, such as worms, bacteria flagella, and elephant trunks.