Efficient bending and lifting patterns in snake locomotion

TL;DR

This paper optimizes 3D snake locomotion patterns to identify energy-efficient movements, revealing dominant gaits depending on friction and dissipation conditions, with implications for bio-inspired robotics.

Contribution

It introduces a population-based optimization method for 3D snake kinematics, extending previous work and identifying key optimal locomotion patterns under various friction and dissipation regimes.

Findings

S-shaped body with alternating lifting is optimal at moderate friction.

Curling and sliding are typical at high transverse friction with low dissipation.

Alternating lifting motions are more energy-efficient than sidewinding-like motions.

Abstract

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. A few types of optimal motions prevail. We find an s-shaped body with alternating lifting of the middle and ends for small-to-moderate transverse friction. For large transverse friction, curling and sliding motions are typical with small viscous dissipation, replaced by large-amplitude bending with 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.