Graph grammars for self assembling robotic systems

In this paper we define a class of graph grammars that can be used to model and direct distributed robotic assembly or formation forming processes. We focus on the problem of synthesizing a grammar so that it generates a given, prespecified assembly. In particular, to generate an acyclic graph we synthesize a binary grammar (rules involve at most two parts), and for a general graph we synthesize a ternary grammar (rules involve at most three parts). We then show a general result that implies that no binary grammar can generate a unique stable assembly. We conclude the paper with a discussion of how graph grammars can be used to direct the synthesis of parts floating in a fluid or for self-motive robotic parts.