  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.
