Simulation of snakes using vertical body bending to traverse terrain with large height variation

TL;DR

This study presents a dynamic simulation demonstrating how snakes use vertical body bending to traverse terrains with large height variations, highlighting the importance of contact forces and feedback in propulsion.

Contribution

We developed a novel dynamic simulation model showing how vertical bending enables snakes to generate propulsion on uneven terrain, incorporating force feedback mechanisms.

Findings

Vertical bending generates sufficient propulsion even with low friction.

Snakes push against terrain with pressure five times their body weight.

Force feedback improves propulsion stability under terrain perturbations.

Abstract

Snake moves across various terrains by bending its elongated body. Recent studies discovered that snakes can use vertical bending to traverse terrain of large height variation, such as horizontally oriented cylinders, a wedge (Jurestovsky, Usher, Astley, 2021, J. Exp. Biol.), and uneven terrain (Fu & Li, 2020, Roy. Soc. Open Sci.; Fu, Astley, Li, 2022 Bioinspiration & Biomimetics). Here, to understand how vertical bending generates propulsion, we developed a dynamic simulation of a snake traversing a wedge (height = 0.05 body length, slope = 27 degrees) and a half cylindrical obstacle (height = 0.1 body length). By propagating down the body an internal torque profile with a maximum around the obstacle, the simulated snake moved forward as observed in the animal. Remarkably, even when frictional drag is low (snake-terrain kinetic friction coefficient of 0.20), the body must push against the wedge with a pressure 5 times that from body weight to generate sufficient forward propulsion to move forward. This indicated that snakes are highly capable of bending vertically to push against the environment to generate propulsion. Testing different controllers revealed that contact force feedback further helps generate and maintain propulsion effectively under unknown terrain perturbations.