Paper abstract

 Title:  Enumerating the Non-Isomorphic Assembly Configurations of
         a Modular Robotic System
 Authors:  I.M. Chen and J. Burdick
 In:   Int. J. of Robotics Research (to appear)

ABSTRACT

A ``modular'' robotic system consists of joint and link modules that can be assembled in a variety of configurations to meet different or changing task requirements. However, due to typical symmetries in module design, different assembly configurations may lead to robotic structures which are kinematically identical, or isomorphic. This paper considers how to enumerate the non-isomorphic assembly configurations of a modular robotic system. We introduce an Assembly Incidence Matrix (AIM) to represent a modular robot assembly configuration. Then we 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, we propose an algorithm to generate non-isomorphic assembly configurations of an n-link tree-like robot with different joint and link module types. Examples demonstrate that this method is a significant improvement over a brute force enumeration process.