Digital Twins in Mechatronics: A Symmetry-Based Approach to System Modelling and Analysis

This paper explores the integration of symmetry principles into digital twin models for complex mechatronic systems, highlighting their potential to enhance modelling efficiency, anomaly detection, and system scalability. By leveraging structural and functional symmetries, the proposed approach supports modular system design, reduces computational overhead, and improves predictive maintenance. A comprehensive showcase is presented, featuring a modular automated production line composed of a conveyor with 90 FIFO buffer positions, multiple CNC machining centres, and two 7-axis robots controlled via Siemens Sinumerik RunMyRobot/Direct Control. The simulation framework employs a combination of Software-in-the-Loop (SiL) and Model-in-the-Loop (MiL) methodologies using a CMVM digital twin of the CNC controller, Simit for communication simulation, and Mechatronic Concept Designer (MCD) for behaviour modelling. Hierarchical physical and functional decomposition, aligned with Weiss and Qiao's methodology, is applied to facilitate the development of a Component Mapping Matrix and ensure simulation fidelity. The presented approach demonstrates how symmetry and modularity in digital twins can accelerate deployment, enhance robustness, and improve decision-making in cyber-physical manufacturing environments.