A drilling rig includes a rig floor, first and second support structures, a mast, a lower drilling machine, a continuous drilling unit, an upper drilling machine, and an upper mast assembly. The rig floor includes a V-door defining a V-door axis extending perpendicularly from the side of the rig floor that includes the V-door. The first and second support structures define a traverse corridor having a traverse corridor axis, wherein the traverse corridor axis is perpendicular to the V-door axis. The drilling rig may be used for continuous drilling of a wellbore.