Rate-independent soft crawlers

TL;DR

This paper models bio-mimetic soft crawler locomotion using rate-independent systems, proving well-posedness and illustrating strategies like friction anisotropy and shape changes within a mathematical framework.

Contribution

It introduces a novel application of rate-independent system theory to soft crawler locomotion, including proofs of existence and uniqueness of solutions.

Findings

Well-posedness of the model established

Strategies like friction anisotropy effectively described

Existence and uniqueness proven under certain conditions

Abstract

This paper applies the theory of rate-independent systems to model the locomotion of bio-mimetic soft crawlers. We prove the well-posedness of the approach and illustrate how 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. Compared to other rate-independent systems, locomotion models do not present any Dirichlet boundary condition, so that all rigid translations are admissible displacements, resulting in a non-coercivity of the energy term. We prove that existence and uniqueness of solution are guaranteed under suitable assumptions on the dissipation potential. Such results are then extended to the case of time-dependent dissipation.