Parallel Self-Assembly and Sorting of Polyominoes under Uniform Control Inputs

Automated assembly at micro and nano-scale is essential for manufacturing smaller and inexpensive products at faster rates. Traditional micro-assembly and manipulation techniques involve micro-grippers and manipulators that have limited degrees of freedom when compared to their macro-scale counterparts. A major disadvantage of these techniques is that only one part can be manufactured at a time. Thus, it would be a significant progress if control algorithms are devised that can automatically assemble a huge quantity of small scale components. We present a novel approach towards micro-assembly which employs a large swarm of micro-particles, controlled by a global signal to assemble arbitrary 2D structures. The algorithm automatically generates a micro-factory layout for a given structure, and when this layout is actuated, it manufactures the required number of copies of the shape. We have analyzed the size and time complexity of the micro-factories and present several simulation and hardware results for the assembly task. Since the assembly process is performed in open-loop, the assembled parts could have errors, and in order to detect these errors, we sort them based on their shape.Electrical and Computer Engineering, Department o

Efficient Parallel Self- Assembly Under Uniform Control Inputs

We prove that by successively combining subassemblies, we can achieve sublinear construction times for “staged” assembly of microscale objects from a large number of tiny particles, for vast classes of shapes; this is a significant advance in the context of programmable matter and self-assembly for building high-yield microfactories. The underlying model has particles moving under the influence of uniform external forces until they hit an obstacle; particles bond when forced together with a compatible particle. Previous work considered sequential composition of objects, resulting in construction time that is linear in the number N of particles, which is inefficient for large N. Our progress implies critical speedup for constructible shapes; for convex polyominoes, even a constant construction time is possible. We also show that our construction process can be used for pipelining, resulting in an amortized constant production time

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