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Context. The precise determinations of stellar mass at $\sim$1% provideimportant constraints on stellar evolution models. Accurate parallaxmeasurements can also serve as independent benchmarks for the next Gaia datarelease. Aims. We aim at measuring the masses and distance of binary systemswith a precision level better than 1% using a fully geometrical and empiricalmethod. Methods. We obtained the first interferometric observations for theeclipsing systems AI Phe, AL Dor, KW Hya, NN Del, $\psi$ Cen and V4090 Sgr withthe VLTI/PIONIER combiner, which we combined with radial velocity measurementsto derive their three-dimensional orbit, masses, and distance. Results. Wedetermined very precise stellar masses for all systems, ranging from 0.04% to3.3 % precision level. We combined these measurements with stellar effectivetemperature and linear radius to fit stellar isochrones models and determinedthe age of the systems. We also derived the distance to the systems with aprecision level as high as 0.4%. Conclusions. The comparison of theoreticalmodels with stellar parameters shows that stellar models are still deficient insimultaneously fitting the stellar parameters (Teff , R and M) with such levelof precision on individual masses. This stresses the importance of preciselymeasuring the stellar parameters to better calibrate stellar evolution models.The precision of our model-independent orbital parallaxes varies from 24$\mu$asas to 70$\mu$as and they provide a unique opportunity to check on the futureGaia measurements for possible systematic errors.

The Araucaria Project: High-precision orbital parallax and masses of eclipsing binaries from infrared interferometry