A manufacturing method employing a robotic assembly system includes first and second fastener system components that are positioned by a robotic assembly on opposite sides of at least two structural pieces that are to be fastened together. The first system component includes a particular tool of a plurality of different types of tools, where the particular tool installs a particular fastener of a plurality of different types of fasteners. Each tool includes a block or base of magnetic material with a passageway opening for the fastener associated with the tool passing through the base. The robotic assembly positions the tool against one side of the structural pieces to be fastened, and positions an electromagnet assembly on the opposite side of the structural pieces. Activating the electromagnet assembly clamps the structural pieces together. With the fastener positioned in a hole through the structural pieces, the tool is activated to install the fastener between the structural pieces.