The slow-actuation limit for a rate-independent model of crawling locomotion

Paolo Gidoni (Czech Academy of Sciences)

Abstract: The quasi-static limit is a classical approximation in the modelling of several mechanical phenomena, in which, intuitively, the system evolves so slowly that it is assumed to be at equilibrium at all times. A well-studied abstract family of quasi-static evolutions is that of the so-called rate-independent systems, with several applications in solid mechanics. In this talk we study a family of finite-dimensional rate-independent models of crawling locomotion.  Our aim is to illustrate how the quasi-static regime can be effectively used in the study of certain biological and robotic locomotion strategies, and to justify it not only by a physical, but also by a rigorous analytical derivation as a slow-actuation limit of the dynamic evolution. We conclude with a brief survey of related open problems.