Scalable Shape Sculpting via Hole Motion: Motion Planning in Lattice-Constrained Modular Robots

We describe a novel shape formation algorithm for ensembles of 2-dimensional lattice-arrayed modular robots, based on the manipulation of regularly shaped voids within the lattice (“holes”). The algorithm is massively parallel and fully distributed. Constructing a goal shape requires time proportional only to the complexity of the desired target geometry. Construction of the shape by the modules requires no global communication nor broadcast floods after distribution of the target shape. Results in simulation show 97.3% shape compliance in ensembles of approximately 60,000 modules, and we believe that the algorithm will generalize to 3D and scale to handle millions of modules.