Parallel Self-Assembly of Polyominoes under Uniform Control Inputs

We present fundamental progress on parallel self-assembly using large swarms of microscale particles in complex environments, controlled not by individual navigation, but by a uniform, global, external force with the same effect on each particle. Consider a 2-D grid world, in which all obstacles and particles are unit squares, and for each actuation, particles move maximally until they collide with an obstacle or another particle. We present algorithms that, given an arbitrary 2-D structure, design an obstacle layout. When actuated, this layout generates copies of the input 2-D structure. We analyze the movement and spatial complexity of the factory layouts. We present hardware results on both a macroscale, gravity-based system, and a microscale, magnetically actuated system.