Aug 2026· Applied Sciences· Vol 16, pp. 8211· 0 citations· 24 references
TL;DR
A formal, symmetry-based framework for behavioral reuse in arbitrary cyber–physical manufacturing systems, implemented within the Siemens NX Mechatronic Concept Designer, version NX 2506, environment is introduced, establishing symmetry-based modular simulation as a principled and scalable methodology for industrial digital-twin development in multi-robot manufacturing environments.
Abstract
The increasing complexity of cyber–physical manufacturing systems demands simulation architectures that scale with the physical plant without a proportional growth in engineering effort. This paper introduces a formal, symmetry-based framework for behavioral reuse in arbitrary cyber–physical manufacturing systems, implemented within the Siemens NX Mechatronic Concept Designer (MCD), version NX 2506, environment. Symmetry is treated rigorously, as an equivalence relation induced by a symmetry-group action over the set of plant components, and three exploitable classes are defined on this basis: structural symmetry, arising from replicated kinematic configurations; functional symmetry, arising from shared behavioral specifications across instances of a common component class; and temporal symmetry, arising from synchronized cyclic behavior across concurrent actors. From these definitions, a four-condition behavioral inheritance protocol is derived, specifying the prerequisites under which a single behavioral library template is correctly instantiated across an arbitrary number of interchangeable components. The framework is demonstrated on a production cell comprising ten conveyor sections, nine CNC machining centers (5-axis, X/Y/Z/A/B/SP), and two COMAU NJ420-3.0 manipulators—each a 6-axis articulated arm extended by an external linear rail to seven controlled axes—governed through Siemens Sinumerik RunMyRobot/Direct Control and exercised in a co-simulation environment that integrates a Create MyVirtual Machine (CMVM) Software-in-the-Loop (SiL) controller, a Simit Model-in-the-Loop (MiL) communication layer, and MCD for kinematic and behavioral emulation. Using the number of independent behavioral configuration operations as the effort metric, the symmetry-driven approach reduces machining-center configuration effort by 88.9% (from nine independent configurations to one template instantiated nine times) and robot behavioral configuration effort by 100% (both manipulators inherit from a single seven-axis library entry), while preserving full kinematic and signal-level fidelity. The inheritance mechanism is shown to tolerate heterogeneous kinematic substitution: a COMAU NJ420-3.0 may be replaced by any kinematically equivalent 6-axis manipulator in the RunMyRobot database without behavioral reconfiguration. The component and capability mapping matrix (CCMM) introduced in prior work is extended with a symmetry-annotation layer that explicitly encodes instance relationships and inheritance chains, providing a structured input to automated behavioral-deployment workflows. The results establish symmetry-based modular simulation as a principled and scalable methodology for industrial digital-twin development in multi-robot manufacturing environments.
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