Abstract We present an overview of the SkyMapper optical follow-up programme for gravitational-wave event triggers from the LIGO/Virgo observatories, which aims at identifying early GW170817-like kilonovae out to
$\sim200\,\mathrm{Mpc}$
distance. We describe our robotic facility for rapid transient follow-up, which can target most of the sky at
$\delta<+10\deg $
to a depth of
$i_\mathrm{AB}\approx 20\,\mathrm{mag}$
. We have implemented a new software pipeline to receive LIGO/Virgo alerts, schedule observations and examine the incoming real-time data stream for transient candidates. We adopt a real-bogus classifier using ensemble-based machine learning techniques, attaining high completeness (
$\sim98\%$
) and purity (
$\sim91\%$
) over our whole magnitude range. Applying further filtering to remove common image artefacts and known sources of transients, such as asteroids and variable stars, reduces the number of candidates by a factor of more than 10. We demonstrate the system performance with data obtained for GW190425, a binary neutron star merger detected during the LIGO/Virgo O3 observing campaign. In time for the LIGO/Virgo O4 run, we will have deeper reference images allowing transient detection to
$i_\mathrm{AB}\approx 21\,\mathrm{mag}$
.