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.

Network-Induced Soft Sets and Stock Market Applications

“…Graph theory is an area of discrete mathematics whose popularity has increased in recent years, not only regarding theoretical developments, but also regarding its applications for numerous aspects [39][40][41][42][43][44][45]. Graph theory can be easily used in solving daily life problems, and it has been employed quite frequently in more theoretical studies, data analyses, and artificial intelligence applications.…”

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“…Studies such as: (Gunji et al, 2022), (Watson and Hermans, 2019) and (Kosec et al, 2020) have utilised graphs to model assembly sequences and their assemblability, with the latter integrating tolerance analysis via error propagation. Innovative applications such as using knowledge graphs for process planning (Zhou et al, 2022), kinematic modelling of a configurable assembly cell (Zhang et al, 2022) and the generation of graphs from boundary representation models that incorporate error transfer and tolerances (Li and Hou, 2021), exemplify the evolving role of graph theory in this field. Furthermore, the concept of knowledge graphs (see Akroyd et al, 2021) has also been used to build a semantic understanding of systems, aiming to develop comprehensive Digital Twins.…”

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