Enumerating the Non-Isomorphic Assembly Configurations of Modular Robotic Systems

A modular robotic system consists of standardized joint and link units that can be assembled into a number of different kinematic configu rations to meet various task requirements. Owing to typical symme tries in module design, different assembly configurations may lead to robotic structures that are geometrically identical, or isomorphic. This paper focuses on the problem of enumerating the set ofkinemat ically distinct modular robot assembly configurations from a given set of modules. We first consider how to enumerate the nonisomor phic (or geometrically unique) assembly configurations of a modular robotic system. Our scheme is based on a novel representation of a modular robot assembly configuration as an assembly incidence matrix (AIM). Equivalence relations based on symmetries in mod ule geometry and graph isomorphisms are defined on the AIMs. An enumeration algorithm to generate nonisomorphic assembly config urations based on this equivalence relation is proposed. We then present an algorithm to identify the kinematically equivalent robots. The application of these two algorithms will result in the set of kine matically unique assembly configurations. Examples demonstrate that this method is a significant improvement over a brute-force enu meration process.