PAOLO GIDONI - Czech Academy of Sciences - AN INTRODUCTION TO THE MODELLING OF SOFT CRAWLING LOCOMOTORS -
The inclusion of elastic components in the modelling and design of biomimetic crawlers endows these systems with new compliance capabilities, but at the same time raises additional challenges to the analysis of their locomotion properties.
The mathematical theory of rate-independent systems and sweeping processes provides an effective framework to address such issues. Indeed, the various strategies adopted by crawlers to achieve locomotion, such as friction anisotropy, complex shape changes and control on the friction coefficients, can be effectively described in terms of stasis domains.
The aim of this talk is to provide, with the aid of representative toy models, an essential introduction to the modelling of rate-independent soft crawlers. On one hand we show how Calculus of Variations provides a useful toolkit to the analysis of such systems; on the other hand we highlight how the differences between a mechanical systems guided by active external forces and soft self-propelled locomotors raise new mathematical challenges.