  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.
