  Trapped-ion arrays offer interesting possibilities for quantum simulation. We
show that a proper arrangement of elliptical micro-traps combined with the
external driving of the micro-trap frequencies allows, without the need of any
precise fine-tuning, for the robust realization of non-Abelian vibron dynamics.
We show that this non-Abelian nature may be readily probed experimentally in a
simple plaquette arrangement. This study opens interesting perspectives for the
study of non-Abelian spin-orbit coupling with motional excitations in two- and
three-dimensional ion arrays.
