Self-assembly of modular robots from finite number of modules using graph grammars

We wish to design decentralized algorithms for self-assembly of robotic modules that have 100% yield even if the number of available building blocks is limited, and specifically when the number of available building blocks is identical to the number of blocks required by the structure. In contrast to self-assembly at the nano and micro scales where abundant building blocks are available, modular robotic systems need to self-assemble from a limited number of modules. In particular, when self-assembly is used for reconfiguration, it is desirable that the new conformation includes all of the available modules. We propose a suite of algorithms that (1) generate a reversible graph grammar, i.e., generates rules for a desired structure that allow the structure not only to assemble, but also to disassemble, and (2) have a set of structures that are growing in parallel converge to a single structure using broadcast communication. We show that by omitting a reversal rule for the last attached module, self-assembly eventually completes, and that communication can drastically speed up this process.