期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 51, 期 6, 页码 949-962出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2006.876950
关键词
cooperative control; self assembly; symbolic methods
In this paper, we define a class of graph grammars that can be used to model and direct concurrent robotic self-assembly and similar self-organizing processes. We give several detailed examples of the formalism and then 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). In both cases, we characterize the number of concurrent steps required to achieve the assembly. We also 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 self-assembly of robotic parts.
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