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HR8799 is orbited by at least four giant planets, making it a prime targetfor the recently commissioned Spectro-Polarimetric High-contrast ExoplanetREsearch (VLT/SPHERE). As such, it was observed on five consecutive nightsduring the SPHERE science verification in December 2014. We aim to take fulladvantage of the SPHERE capabilities to derive accurate astrometricmeasurements based on H-band images acquired with the Infra-Red Dual-bandImaging and Spectroscopy (IRDIS) subsystem, and to explore the ultimateastrometric performance of SPHERE in this observing mode. We also aim topresent a detailed analysis of the orbital parameters for the four planets. Wereport the astrometric positions for epoch 2014.93 with an accuracy down to 2.0mas, mainly limited by the astrometric calibration of IRDIS. For each planet,we derive the posterior probability density functions for the six Keplerianelements and identify sets of highly probable orbits. For planet d, there isclear evidence for nonzero eccentricity ($e \simeq 0.35$), without completelyexcluding solutions with smaller eccentricities. The three other planets areconsistent with circular orbits, although their probability distributionsspread beyond $e = 0.2$, and show a peak at $e \simeq 0.1$ for planet e. Thefour planets have consistent inclinations of about $30\deg$ with respect to thesky plane, but the confidence intervals for the longitude of ascending node aredisjoint for planets b and c, and we find tentative evidence fornon-coplanarity between planets b and c at the $2 \sigma$ level.

VLT/SPHERE robust astrometry of the HR8799 planets at milliarcsecond-level accuracy Orbital architecture analysis with PyAstrOFit