A system for drilling one or more boreholes in a face of a mine passage including markers attached to the mine passage. A drilling machine includes one or more drills for drilling the one or more boreholes, and a first sensor for sensing a position of the markers. Based on the sensed position of the at least two markers, a computer determines: (i) a survey vector generally parallel to the line; and (ii) a face plane generally orthogonal to the survey vector and coincident with a location where the survey vector intersects the face. A controller may be provided for automatically controlling the feeding of the drill(s) based on the location of the face plane and the back plane to form the boreholes in the face. A back plane may also be determined to ensure that all boreholes are drilled to a corresponding depth. Related methods are also disclosed.