  Orbital monitoring of exoplanetary and stellar systems is fundamental for
analysing their architecture, dynamical stability and evolution, and mechanisms
of formation. Current high-contrast extreme-adaptive optics imagers like
SPHERE, GPI, and SCExAO+CHARIS explore the population of giant exoplanets and
brown dwarf and stellar companions beyond typically 10 au, covering generally a
small fraction of the orbit (<20%) leading to degeneracies and biases in the
orbital parameters. Precise and robust measurements over time of the position
of the companions are critical, which require good knowledge of the
instrumental limitations and dedicated observing strategies. The homogeneous
dedicated calibration strategy for astrometry implemented for SPHERE has
facilitated high-precision studies by its users since its start of operation in
2014. As the precision of exoplanet imaging instruments is now reaching
milliarcseconds and is expected to improve with the upcoming facilities, we
initiated a community effort, triggered by the SPHERE experience, to share
lessons learned for high-precision astrometry in direct imaging. A homogeneous
strategy would strongly benefit the VLT community, in synergy with VLTI
instruments like GRAVITY/GRAVITY+, future instruments like ERIS and MAVIS, and
in preparation for the exploitation of the ELT's first instruments MICADO,
HARMONI, and METIS.
