Assembly Configuration Representation and Kinematic Modeling for Modular Reconfigurable Robots Based on Graph Theory

Abstract

A Modular Reconfigurable Robot (MRR) composed of standard joint and link modules has the advantages of rapid changeover of assembly configurations for a diversity of application requirements. To tackle the kinematics analysis issues for an MRR, it is essential to develop a generic method to mathematically represent all possible assembly configurations and automatically generate their kinematic models. In this paper, two types of robot modules, i.e., revolute joint modules and rigid link modules, are considered as the basic building blocks of an MRR. The topological structure of an MRR is represented by a graph, termed an Assembly Graph (AG), in which all robot modules, regardless of their types, are treated as vertices, while the connecting interfaces between any two robot modules are treated as edges. Based on graph theory, a modified adjacency matrix, termed an Assembly Adjacency Matrix (AAM), is proposed to represent the assembly configuration of an MRR, in which the three-dimensional assembly information is specified with connecting port vectors for the adjacent modules. A path matrix derived from the AAM of an MRR is employed to describe the connecting sequence of its constituting modules. The local frame representation of the Product-of-Exponentials (POE) formula is employed, which is configuration-independent. Therefore, for an MRR configuration represented with an AAM, its kinematic model will be automatically generated according to its path matrix. The proposed assembly configuration representation and kinematic modeling method are validated through a dual-branch MRR configuration.