Configuration of a reconfigurable modular system is a tough issue because the possible configurations or structures grow exponentially with the number of modules. A library of the non-isomorphic configurations should be set up as a database for configuration design and control. In this paper, we propose a matrix-based enumerating approach for the non-isomorphic configurations of a reconfigurable modular robot system with square-cubic-cell(SCC) modules. Each SCC module considered in this study includes a cubic module body and four connectors on its lateral surfaces. Since it has a square lattice like 2D projection, configuration matrices are proposed to represent the topological information of the modular robot. Thus reconfiguration and enumeration can be programmed by matrix computation in simulation. According to combinational principle, recursive algorithms are used to find out all non-isomorphic configurations. Enumerating result for a multi-module SCC system is provided as an example. Potential applications of this approach to other reconfigurable systems with lattice-form or cubic-form modules are discussed as well. As an application, enumeration of the multi-module CONRO robot also proves the validity of this method.
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