  Aims: for the first time the astrometric capabilities of the Multi-Conjugate
Adaptive Optics (MCAO) facility GeMS with the GSAOI camera on Gemini-South are
tested to quantify the accuracy in determining stellar proper motions in the
Galactic globular cluster NGC 6681. Methods: proper motions from HST/ACS for a
sample of its stars are already available, and this allows us to construct a
distortion-free reference at the epoch of GeMS observations that is used to
measure and correct the temporally changing distortions for each GeMS exposure.
In this way, we are able to compare the corrected GeMS images with a
first-epoch of HST/ACS images to recover the relative proper motion of the
Sagittarius dwarf spheroidal galaxy with respect to NGC 6681. Results: we find
this to be (\mu_{\alpha}cos\delta, \mu_{\delta}) = (4.09,-3.41) mas/yr, which
matches previous HST/ACS measurements with a very good accuracy of 0.03 mas/yr
and with a comparable precision (r.m.s of 0.43 mas/yr). Conclusions: this study
successfully demonstrates that high-quality proper motions can be measured for
quite large fields of view (85 arcsec X 85 arcsec) with MCAO-assisted,
ground-based cameras and provides a first, successful test of the performances
of GeMS on multi-epoch data.
