Fast Reconfiguration for Programmable Matter

The concept of programmable matter envisions a very large number of tiny and simple robot particles forming a smart material that can change its physical properties and shape based on the outcome of computation and movement performed by the individual particles in a concurrent manner. Shape reconfiguration of particle systems is the fundamental task in the algorithmic research of programmable matter. In this paper we describe a new approach for shape reconfiguration in the amoebot model. The amoebot model is a distributed model which significantly restricts memory, computing, and communication capacity of the individual particles. Thus the challenge lies in coordinating local actions of particles to produce the desired behavior of the global system. We use geometric insight to develop new primitives for programmable matter systems, which facilitate reconfiguration tasks. Among others, we introduce a new primitive, feather trees, whose geometry allows particles to traverse a tree in the presence of other overlapping trees. Using the graph structure of overlapping feather trees as an underlying network, we show how to reconfigure a particle system in a linear number of activation rounds. Our method is sensitive to the symmetric difference between input and output shape; it minimizes unnecessary disassembly and reassembly of the particle system when the symmetric difference between the initial and the target shapes is small.