A glass sheet processing system for processing a glass sheet includes a conveyor for conveying the glass sheet in a direction of conveyance, and a positioning apparatus for adjusting position of the glass sheet on the conveyor. The positioning apparatus includes a movable carriage having first and second carriage bodies. The first carriage body is translatable in the direction of conveyance, and the second carriage body is supported by the first carriage body such that the second carriage body is movable in a direction generally transverse to the direction of conveyance. The positioning apparatus further includes a first drive assembly for moving the first carriage body in the direction of conveyance, a second drive assembly for moving the second carriage body with respect to the first carriage body, and a positioner member connected to the second carriage body for contacting the glass sheet to adjust position of the glass sheet.