Optimal crawling: From mechanical to chemical actuation.

Taking inspiration from the crawling motion of biological cells on a substrate, we consider a physical model of self-propulsion where the spatiotemporal driving can involve both a mechanical actuation by active force couples and a chemical actuation through controlled mass turnover. When the material turnover is slow and the mechanical driving dominates, we find that the highest velocity at a given energetic cost is reached when the actuation takes the form of an active force configuration propagating as a traveling wave. As the rate of material turnover increases, and the chemical driving starts to dominate the mechanical one, such a peristalsis-type control progressively loses its efficacy, yielding to a standing-wave-type driving which involves an interplay between the mechanical and chemical actuation. Our analysis suggests a paradigm for the optimal design of crawling biomimetic robots where the conventional purely mechanical driving through distributed force actuators is complemented by a distributed chemical control of the material remodeling inside the force-transmitting machinery.