Optimizing snake locomotion in the plane. I. Computations

TL;DR

This paper develops a numerical method to identify optimal planar snake motions for locomotion efficiency across different frictional conditions, revealing distinct optimal strategies depending on the transverse friction coefficient.

Contribution

It introduces a computational scheme to determine optimal snake locomotion patterns over a range of friction parameters, including new findings on wave types and scaling laws.

Findings

Retrograde waves are optimal at high transverse friction.

Optimal deflection scales as the -1/4 power of transverse friction.

Triangular waves are optimal at zero transverse friction.

Abstract

We develop a numerical scheme to determine which planar snake motions are optimal for locomotory efficiency, across a wide range of frictional parameter space. For a large coefficient of transverse friction, we find that retrograde traveling waves are optimal. The optimal snake deflection scales as the -1/4 power of the coefficient of transverse friction, in agreement with an asymptotic analysis. At the other extreme, zero coefficient of transverse friction, we propose a triangular direct wave which is optimal. Between these two extremes, a variety of complex, locally optimal motions are found. Some of these can be classified as standing waves (or ratcheting motions).