Snakes combine vertical and lateral bending to traverse uneven terrain

Contact feedback helps snake robots propel against uneven terrain using vertical bending

Snakes can bend their elongate bodies in various forms to traverse various environments. We understand well how snakes use lateral body bending to push against asperities on flat ground for propulsion, and snake robots can do so effectively. However, snakes can also use vertical bending to push against uneven terrain of large height variation for propulsion, and they can adjust this bending to adapt to novel terrain presumably using mechano-sensing feedback control. Although some snake robots can traverse uneven terrain, few have used vertical bending for propulsion, and how to control this process in novel environments is poorly understood. Here we systematically studied a snake robot with force sensors pushing against large bumps using vertical bending to understand the role of sensory feedback control. We compared a feedforward controller and four feedback controllers that use different sensory information and generate distinct bending patterns and body-terrain interaction. We challenged the robot with increasing backward load and novel terrain geometry that break its contact with the terrain. We further varied how much the feedback control modulated body bending to conform to or push against the terrain to test their effects. Feedforward propagation of vertical bending generated large propulsion when the bending shape matched terrain geometry. However, when perturbations caused loss of contact, the robot easily lost propulsion or had motor overload. Contact feedback control resolved these issues by helping the robot regain contact. Yet excessive conformation interrupted shape propagation and excessive pushing stalled motors frequently. Unlike that using lateral bending, for propulsion generation using vertical bending, body weight that can help maintain contact with the environment but may also overload motors. Our results will help snake robots better traverse uneven terrain with large height variation and can inform how snakes use sensory feedback to control vertical body bending for propulsion.

Efficient bending and lifting patterns in snake locomotion

We optimize three-dimensional snake kinematics for locomotor efficiency. We assume a general space-curve representation of the snake backbone with small-to-moderate lifting off the ground and negligible body inertia. The cost of locomotion includes work against friction and internal viscous dissipation. When restricted to planar kinematics, our population-based optimization method finds the same types of optima as a previous Newton-based method. With lifting, a few types of optimal motions prevail. We have an s-shaped body with alternating lifting of the middle and ends at small-to-moderate transverse friction. With large transverse friction, curling and sliding motions are typical at small viscous dissipation, replaced by large-amplitude bending at large viscous dissipation. With small viscous dissipation, we find local optima that resemble sidewinding motions across friction coefficient space. They are always suboptimal to alternating lifting motions, with average input power 10–100% higher.