A Geometrical Approach to the Incompatible Substructure Problem in Parallel Self-Assembly

The inherent massive parallelism of self-assembly is one of its most appealing attributes for autonomous construction. One challenge in parallel self-assembly is to reduce the number of incompatible substructures that can occur in order to increase the yield in target structures. Early studies demonstrated how a simple approach to component design led components to self-assemble into incompatible substructures. Approaches have been proposed to reduce the number of incompatible substructures by increasing component complexity (e.g. using mechanical switches to determine substructure conformation). In this work, we show how a geometrical approach to self-assembling target structures from the inside-out eliminates incompatible substructures and increases yield. The advantages of this approach includes the simplicity of component design, and the incorporation of additional techniques to reduce component interaction errors. An experiment using millimeter-scale, 3D printed components is used to provide physical evidence to support our geometrical approach.