  GRAVITY is a second generation instrument for the VLT Interferometer,
designed to enhance the near-infrared astrometric and spectro-imaging
capabilities of VLTI. Combining beams from four telescopes, GRAVITY will
provide an astrometric precision of order 10 micro-arcseconds, imaging
resolution of 4 milli-arcseconds, and low and medium resolution
spectro-interferometry, pushing its performance far beyond current infrared
interfero- metric capabilities. To maximise the performance of GRAVITY,
adaptive optics correction will be implemented at each of the VLT Unit
Telescopes to correct for the effects of atmospheric turbulence. To achieve
this, the GRAVITY project includes a development programme for four new
wavefront sensors (WFS) and NIR-optimized real time control system. These
devices will enable closed-loop adaptive correction at the four Unit Telescopes
in the range 1.4-2.4 {\mu}m. This is crucially important for an efficient
adaptive optics implementation in regions where optically bright references
sources are scarce, such as the Galactic Centre. We present here the design of
the GRAVITY wavefront sensors and give an overview of the expected adaptive
optics performance under typical observing conditions. Benefiting from newly
developed SELEX/ESO SAPHIRA electron avalanche photodiode (eAPD) detectors
providing fast readout with low noise in the near-infrared, the AO systems are
expected to achieve residual wavefront errors of \leq400 nm at an operating
frequency of 500 Hz.
