  Context. The precise determinations of stellar mass at $\sim$1% provide
important constraints on stellar evolution models. Accurate parallax
measurements can also serve as independent benchmarks for the next Gaia data
release. Aims. We aim at measuring the masses and distance of binary systems
with a precision level better than 1% using a fully geometrical and empirical
method. Methods. We obtained the first interferometric observations for the
eclipsing systems AI Phe, AL Dor, KW Hya, NN Del, $\psi$ Cen and V4090 Sgr with
the VLTI/PIONIER combiner, which we combined with radial velocity measurements
to derive their three-dimensional orbit, masses, and distance. Results. We
determined very precise stellar masses for all systems, ranging from 0.04% to
3.3 % precision level. We combined these measurements with stellar effective
temperature and linear radius to fit stellar isochrones models and determined
the age of the systems. We also derived the distance to the systems with a
precision level as high as 0.4%. Conclusions. The comparison of theoretical
models with stellar parameters shows that stellar models are still deficient in
simultaneously fitting the stellar parameters (Teff , R and M) with such level
of precision on individual masses. This stresses the importance of precisely
measuring the stellar parameters to better calibrate stellar evolution models.
The precision of our model-independent orbital parallaxes varies from 24$\mu$as
as to 70$\mu$as and they provide a unique opportunity to check on the future
Gaia measurements for possible systematic errors.

Solar and Stellar Astrophysics