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

Abstract

We study the asymptotic stability of periodic solutions for sweeping processes defined by a polyhedron with translationally moving faces. Previous results are improved by obtaining a stronger $W^{1,2}$ convergence. Then we present an application to a model of crawling locomotion. Our stronger convergence 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 convergence.

References in corpus (6)

• Existence and stability of a limit cycle in the model of a planar passive biped walking down a slope
• Stasis domains and slip surfaces in the locomotion of a bio-inspired two-segment crawler
• The role of symmetry and dissipation in biolocomotion
• A vanishing inertia analysis for finite dimensional rate-independent systems with nonautonomous dissipation, and an application to soft crawlers
• Rate-independent soft crawlers
• On the genesis of directional friction through bristle-like mediating elements