{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T23:12:45Z","timestamp":1768259565663,"version":"3.49.0"},"reference-count":55,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,13]],"date-time":"2025-04-13T00:00:00Z","timestamp":1744502400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study presents a framework for designing symmetry-aware cooperative controllers to synchronize two SCARA LS3-B401S robots, ensuring precision, adaptability, and fault tolerance in flexible manufacturing environments. Four control strategies\u2014Proportional\u2013Integral\u2013Derivative (PID), Adaptive Sliding Mode Control (ASMC), Adaptation-Enabled Neural Network (ANN), and Inverse-Dynamics with Disturbance Observer (ID-DO)\u2014were evaluated through high-fidelity MATLAB\/Simulink simulations (fixed 1 ms step size, ode4 solver), using dynamic SolidWorks 2022 models validated under realistic perturbations, including \u00b10.0005 rad sensor noise and \u00b15% mass variation. Among the strategies, the ANN controller\u2014implemented as an 8-10-4 multi-layer perceptron\u2014achieved the highest performance, consistently reducing trajectory errors by over 99%, maintaining symmetry deviations below 0.001 rad, and recovering from \u00b10.08 rad disturbances in 0.12 s. Its stabilization time averaged 0.247 s across joints, and energy consumption dropped to 0.01 J\/s, representing a 98% improvement over PID. Despite a higher computational load (12.5 MFLOPS, 2.80 ms per iteration), GPU acceleration brought execution times below 1.4 ms, ensuring compliance with industrial 5 ms control cycles. These results establish a scalable foundation for next-generation multi-robot systems, with planned physical validation on SCARA LS3-B401S robots equipped with high-resolution encoders and advanced processors. By leveraging symmetry-driven coordination (S=I), the proposed framework supports resilient, sustainable, and high-precision manufacturing, aligned with the goals of Industry 5.0.<\/jats:p>","DOI":"10.3390\/sym17040591","type":"journal-article","created":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T09:06:51Z","timestamp":1744621611000},"page":"591","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Symmetry-Driven Fault-Tolerant Synchronization in Multi-Robot Systems: Comparative Simulation of Adaptive Neural and Classical Controllers"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7197-8928","authenticated-orcid":false,"given":"Claudio","family":"Urrea","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, Faculty of Engineering, University of Santiago of Chile, Las Sophoras 165, Estaci\u00f3n Central, Santiago 9170124, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-7528-4390","authenticated-orcid":false,"given":"Pablo","family":"Sari","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Faculty of Engineering, University of Santiago of Chile, Las Sophoras 165, Estaci\u00f3n Central, Santiago 9170124, Chile"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Solanes, J.E., Gracia, L., and Valls Miro, J. 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