Optimal Locomotion for Limbless Crawlers

TL;DR

This paper models limbless crawling, revealing that optimal movement involves traveling waves similar to biological peristalsis, and provides insights into biological locomotion and bioinspired robot design.

Contribution

It introduces a theoretical model showing that optimal active stress distribution for limbless crawlers is a traveling wave, explaining biological observations and guiding robot design.

Findings

Optimal active stress is a traveling wave pattern.

Scaling law relates crawling speed to body mass.

Biological peristalsis may be an optimal locomotion strategy.

Abstract

Limbless crawling is ubiquitous in biology, from cells to organisms. We develop and analyze a model for the dynamics of one-dimensional elastic crawlers, subject to active stress and deformation-dependent friction with the substrate. We find that the optimal active stress distribution that maximizes the crawler's center of mass displacement given a fixed amount of energy input is a traveling wave. This theoretical optimum corresponds to peristalsis-like extension-contraction waves observed in biological organisms, possibly explaining the prevalence of peristalsis as a convergent gait across species. Our theory elucidates key observations in biological systems connecting the anchoring phase of a crawler to the retrograde and prograde distinction seen in peristaltic waves among various organisms. Using our optimal gait solution, we derive a scaling relation between the crawling speed and body mass, explaining experiments on earthworms with three orders of magnitude body mass variations. Our results offer insights and tools for optimal bioinspired crawling robots design with finite battery capacity.