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We study the asymptotic stability of periodic solutions for sweepingprocesses defined by a polyhedron with translationally moving faces. Previousresults are improved by obtaining a stronger $W^{1,2}$ convergence. Then wepresent an application to a model of crawling locomotion. Our strongerconvergence allows us to prove the stabilization of the system to arunning-periodic (or derivo-periodic, or relative-periodic) solution and thewell-posedness of an average asymptotic velocity depending only on the gaitadopted by the crawler. Finally, we discuss some examples of finite-time versusasymptotic-only convergence.

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