3D printing presents a new and exceptionally versatile class of construction tasks for robots to undertake using granular materials found in planetary terrains. For space applications, a printing head on a mobile robotic platform could free 3D printing from the constraints of a printer’s workspace, enabling arbitrarily large structures and objects to be built with small robots. Mobile 3D printing consists of building compound parts by looping over 3 high-level steps: (1) printing directly onto the ground surface (and directly onto pre-existing segments as well); (2) relocating from one static build location to the next; (3) accurately and precisely establishing the location of the relevant interface on a pre-existing segment of the printed object, relative to the current position of the robot after relocation. This work presents an approach to mobile 3D printing that addresses these required steps in significantly greater detail than the current literature. A Rostock Delta 3D printer configuration with fused filament extrusion printing is selected to enable direct printing onto the ground surface. Printing directly onto pre-existing segments is demonstrated with a series of thermoplastic parts. Preliminary experimental stress analysis does not reveal any obvious weaknesses at the seam of a compound part, when compared to a monolithic part. Localization techniques are proposed that utilize structured light surface sensing combined with laser range-finder triangulation to precisely measure the robot’s relative translations and rotations, respectively, between build locations.