Enumerating the nonisomorphic assembly configurations of modular robotic systems

A \modular" robotic system consists of joint and link modules that can be assembled in a variety of conngurations to meet diierent or changing task requirements. However, due to typical symmetries in module design, diierent assembly conngurations may lead to robotic structures which are kinematically identical, or isomorphic. This paper considers how to enumerate the non-isomorphic assembly conngurations of a modular robotic system. We introduce an Assembly Incidence Matrix (AIM) to represent a modular robot assembly con-guration. Then we use symmetries of the module geometry and graph isomorphisms to deene an equivalence relation on the AIMs. Equivalent AIMs represent isomorphic robot assembly conngurations. Based on this equivalence relation, we propose an algorithm to generate non-isomorphic assembly conngurations of an n-link tree-like robot with diierent joint and link module types. Examples demonstrate that this method is a signiicant improvement over a brute force enumeration process.