I imagine having two little microbots working like tweezers. Theoretically, it's possible to manipulate the field to make one of the robots rotate. Two magnets rotating in tandem could make something like a tiny pair of tweezers.
The problem: there is solderpaste on the board before placement. Therefore, you have to bring the components to the board from above and push them into the solder paste. The suction based pick and place machines are well suited for this task. Tiny robots walking over the board (with lots of obstructions such as solder-paste and through holes) are not such a good match.
Actually, I bet this would be possible if the bots had a tiny magnetically actuated suction piston. You’d have to figure out how to create electromagnetic force in the z-direction independently from the x-y force though. Not sure if that’s possible.
Put the whole thing in the dark, small solar cells on top and then short circuit them through a coil, that could power a tiny gripper whenever they are lit up.
