The presence of ghost artifacts is a recurrent problem in EPI images, which has been recently addressed using structured low-rank matrix (SLM) methods. In this work we propose a new SLM ghost correction method called Robust Autocalibrated LORAKS (RAC-LORAKS). RAC-LORAKS considers autocalibrated k-space constraints (similar to GRAPPA) to deal with the ill-posedness of existing SLM EPI ghost correction methods. RAC-LORAKS additionally adapts these constraints to enable robustness to possible imperfections in the autocalibration data. We illustrate the capabilities of RAC-LORAKS in two challenging scenarios: highly accelerated EPI of the brain, and cardiac EPI with double-oblique slice orientation.