Enumerating the nonisomorphic assembly configurations of modular robotic systems

The authors consider how to enumerate the nonisomorphic assembly configurations of a modular robotic system. They introduce an assembly incidence matrix (AIM) to represent a modular robot assembly configuration. Then they use symmetries of the module geometry and graph isomorphisms to define an equivalence relation on the AIMs. Equivalent AIMs represent isomorphic robot assembly configurations. Based on this equivalence relation, the authors propose an algorithm for generating nonisomorphic assembly configurations of an n-link tree-like robot with different joint and link module types. Examples demonstrate that this method offers significant improvement over a brute force enumeration process.