  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.
