New Scale Technologies makes miniature piezoelectric motors:
Piezoelectric actuators in the SQUIGGLE motor ultrasonically vibrate a threaded nut, producing an orbital motion. The nut vibration directly rotates a mating threaded screw to create precise linear motion — with no parasitic drag, no backlash, and very high stiffness. The motor holds its position with the power off.
This simple, robust piezo motor generates no magnetic fields, is vacuum compatible, and can be made from non-ferrous metals for use in MRI, scanning electron microscopy and focused ion microscopy applications.
Combine some of these with a miniature low-power DSP, and you have the makings of one tiny robot. What on earth you’d want a miniature robot for is beyond me, but it comforts me to know its possible.