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HR\,8799 is a young planetary system composed of 4 planets and a doubledebris belt. Being the first multi-planetary system discovered with the directimaging technique, it has been observed extensively since 1998. This widebaseline of astrometric measurements, counting over 50 observations in 20years, permits a detailed orbital and dynamical analysis of the system. Toexplore the orbital parameters of the planets, their dynamical history, and theplanet-to-disk interaction, we made follow-up observations of the system duringthe VLT/SPHERE GTO program. We obtained 21 observations, most of them infavorable conditions. In addition, we observed HR\,8799 with the instrumentLBT/LUCI. All the observations were reduced with state-of-the-art algorithmsimplemented to apply the spectral and angular differential imaging method. Were-reduced the SPHERE data obtained during the commissioning of the instrumentand in 3 open-time programs to have homogeneous astrometry. The preciseposition of the 4 planets with respect to the host star was calculated byexploiting the fake negative companions method. To improve the orbital fitting,we also took into account all of the astrometric data available in theliterature. From the photometric measurements obtained in differentwavelengths, we estimated the planets' masses following the evolutionarymodels. We obtained updated parameters for the orbits with the assumption ofcoplanarity, relatively small eccentricities, and periods very close to the 2:1resonance. We also refined the dynamical mass of each planet and the parallaxof the system (24.49 $\pm$ 0.07 mas). We also conducted detailed $N$-bodysimulations indicating possible positions of a~putative fifth innermost planetwith a mass below the present detection limits of $\simeq 3$~\MJup.

Orbital and dynamical analysis of the system around HR 8799. New astrometric epochs from VLT/SPHERE and LBT/LUCI