Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction

We study the asymptotic stability of periodic solutions for sweep- ing processes defined by a polyhedron with translationally moving faces. Pre- vious results are improved by obtaining a stronger W1,2 convergence. Then we present an application to a model of crawling locomotion. Our stronger conver- gence allows us to prove the stabilization of the system to a running-periodic (or derivo-periodic, or relative-periodic) solution and the well-posedness of an average asymptotic velocity depending only on the gait adopted by the crawler. Finally, we discuss some examples of finite-time versus asymptotic-only con- vergence.