Inspired by the locomotion of terrestrial limbless animals, we study
the motion of a lubricated rod of a hydrogel on a soft substrate. We
show that it is possible to mimic observed biological gaits by
vibrating the substrate and by using a variety of mechanisms to
break longitudinal and lateral symmetry. Our simple theory and
experiments provide a unified view of the creeping, undulating,
and inchworming gaits observed in limbless locomotion on land, all
of which originate as symmetry-breaking bifurcations of a simple
base state associated with periodic longitudinal oscillations of a
slender gel. These ideas are therefore also applicable to technological situations that involve moving small, soft solids on
substrates.