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Limbless crawling is ubiquitous in biology, from cells to organisms. Wedevelop and analyze a model for the dynamics of one-dimensional elasticcrawlers, subject to active stress and deformation-dependent friction with thesubstrate. We find that the optimal active stress distribution that maximizesthe crawler's center of mass displacement given a fixed amount of energy inputis a traveling wave. This theoretical optimum corresponds to peristalsis-likeextension-contraction waves observed in biological organisms, possiblyexplaining the prevalence of peristalsis as a convergent gait across species.Our theory elucidates key observations in biological systems connecting theanchoring phase of a crawler to the retrograde and prograde distinction seen inperistaltic waves among various organisms. Using our optimal gait solution, wederive a scaling relation between the crawling speed and body mass, explainingexperiments on earthworms with three orders of magnitude body mass variations.Our results offer insights and tools for optimal bioinspired crawling robotsdesign with finite battery capacity.

Optimal Locomotion for Limbless Crawlers