Three-dimensional construction with mobile robots and modular blocks

We present a decentralized algorithmic approach to automatically building user-specified three-dimensional structures from modular units. Our bipartite system comprises passive units (blocks), responsible for embodying the structure and determining where further units can legally be attached, and active units (robots), responsible for transporting passive units. The algorithmic issues are correspondingly decomposed into two parts: (1) deciding where passive units may be attached; and (2) getting them to those locations. For the first part, we give simple, scalable rules for attachment and prove that they will reliably lead to the construction of any desired structure from a large class of three-dimensional shapes. For the second part, we compare three approaches: random movement, systematic search and gradient-following; each approach is successively faster but requires more communication overhead and/or unit capabilities. The system we describe enables guaranteed construction of desired structures using very simple agent algorithms, taking a high-level specification as the only required input. The topic of collective construction is related to the problems of programmed self-assembly and self-reconfiguration in modular robots, and the rules governing block attachment presented here may be usefully applied to such systems.