Correction: Formation Control of Wheeled Mobile Robots with Fault-Tolerance Capabilities (Robotics, (2025), 14, 5, (59), 10.3390/robotics14050059)

In the original publication [1], the artificial intelligence (AI) transparency statement was missing from the manuscript. A correction has been made to the manuscript by adding a complete AI disclosure statement in Section 2 and the Acknowledgments of the manuscript: During the preparation of this manuscript, artificial intelligence-based tools were used only for language refinement and editorial assistance. No artificial intelligence tools were used to generate research ideas, models, simulations, datasets, or analytical results. All algorithms, simulations, and analyses presented in this work were developed and executed by the authors using MATLAB-R23 based implementations. Acknowledgments: During the preparation of this manuscript, the authors used ChatGPT-4o for the purposes of language refinement and editorial assistance. The authors confirm that artificial intelligence tools were not used to generate research data, models, simulations, or experimental results in this study. The authors take full responsibility for the content of this article. The authors confirm that these changes do not affect the scientific content, results, or conclusions of the paper. This correction was approved by the Academic Editor. The original publication has been updated accordingly. A complete re-evaluation of the reference list has been performed. The following corrections have been implemented: 1. The following references were corrected for bibliographic accuracy, e.g., publication year, author names, titles, editions, page ranges, or publisher details (incorrect references are as follows): Reference [1] Location corrected. Reference [3] Publication year corrected. Reference [4] Authors’ name corrected. Reference [5] Title, edition, and publisher corrected. Reference [7] Title, edition, and publisher corrected. Reference [11] Title, edition, and publisher corrected. Reference [12] Title, edition, and publisher corrected. Reference [14] Edition corrected. Reference [15] Title, edition, and publisher corrected. Reference [16] Title, edition, and publisher corrected. Reference [17] Title, edition, and publisher corrected. Reference [19] Title, edition, and publisher corrected. Reference [20] Title, edition, and publisher corrected. Reference [21] Title, edition, and publisher corrected. Reference [22] Title, edition, and publisher corrected. Reference [23] Title, edition, and publisher corrected. Reference [24] Title, edition, and publisher corrected. Reference [29] Title, edition, and publisher corrected. Reference [31] Title, edition, and publisher corrected. Reference [35] Title, edition, and publisher corrected. Reference [40] Title, edition, and publisher corrected. Reference [48] Title, edition, and publisher corrected. Reference [49] Publication year corrected. The corrected references (with revised numbers) are provided here for convenience. [1] Ren, W.; Beard, R.W. Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications; Communications and Control Engineering Series; Springer: London, UK, 2008; Volume 27. [3] Li, Z.; Duan, Z. Cooperative Control of Multi-Agent Systems: A Consensus Region Approach; CRC Press: Boca Raton, FL, USA, 2015. [4] Olfati-Saber, R.; Murray, R.M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 2004, 49, 1520–1533. [5] Chen, J.; Sun, D.; Yang, J.; Chen, H. Leader-follower formation control of multiple non-holonomic mobile robots incorporating a receding-horizon scheme. Int. J. Robot. Res. 2010, 29, 727–747. [7] Freeman, R.A.; Yang, P.; Lynch, K.M. Stability and convergence properties of dynamic average consensus estimators. In Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, USA, 13–15 December 2006; pp. 398–403. [11] Heijmans, S.H.; Postoyan, R.; Noroozi, N.; Nešić, D.; Heemels, W.M.H. Stability analysis of networked control systems with direct-feedthrough terms: Part II–the linear case. In Proceedings of the 55th IEEE Conference on Decision and Control (CDC), Las Vegas, NV, USA, 12–14 December 2016; pp. 5974–5979. [12] Queralta, J.P.; Taipalmaa, J.; Pullinen, B.C.; Sarker, V.K.; Gia, T.N.; Tenhunen, H.; Gabbouj, M.; Raitoharju, J.; Westerlund, T. Collaborative Multi-Robot Search and Rescue: Planning, Coordination, Perception, and Active Vision. IEEE Access 2020, 8, 191617–191643. [14] Blanke, M.; Kinnaert, M.; Lunze, J.; Staroswiecki, M. Distributed Fault Diagnosis and Fault-Tolerant Control. In Diagnosis and Fault-Tolerant Control, 3rd ed.; Springer: Berlin/Heidelberg, Germany, 2016; pp. 467–518. [15] Zhai, D.; An, L.; Li, X.; Zhang, Q. Adaptive Fault-Tolerant Control for Nonlinear Systems with Multiple Sensor Faults and Unknown Control Directions. IEEE Trans. Neural Netw. Learn. Syst. 2018, 29, 4436–4446. [16] Argha, A.; Su, S.W.; Celler, B.G. Control allocation-based fault tolerant control. Automatica 2019, 103, 408–417. [17] Arıcı, M.; Kara, T. Robust adaptive fault tolerant control for a process with actuator faults. J. Process Control 2020, 92, 169–184. [19] Sun, K.; Ma, Z.; Dong, G.; Gong, P. Adaptive Fuzzy Fault-Tolerant Control of Uncertain Fractional-Order Nonlinear Systems with Sensor and Actuator Faults. Fractal Fract. 2023, 7, 862. [20] Pereira, D.A.; Al-Dujaili, A.; El Najjar, M.E.B.; Cocquempot, V.; Ma, Y. Actuator fault estimation and fault tolerant control in three physically-linked 2WD mobile robots. IFAC-PapersOnLine 2018, 51, 709–716. [21] Yang, Y.; Ding, S.X.; Li, L. On Observer-Based Fault Detection for Nonlinear Systems. Syst. Control. Lett. 2015, 82, 18–25. [22] Shi, J.; Chen, X.; Xing, S.; Liu, A.; Chen, C. Robust Cooperative Fault-Tolerant Control for Uncertain Multi-Agent Systems Subject to Actuator Faults. Sensors 2024, 24, 2651. [23] Kharrat, M.; Krichen, M.; Alkhalifa, L.; Gasmi, K. Neural-networks-based adaptive fault-tolerant control of nonlinear systems with actuator faults and input quantization. IEEE Access 2023, 11, 137680–137687. [24] Shang, Y. Resilient consensus in multi-agent systems with state constraints. Automatica 2020, 122, 109288. [29] Siegwart, R.; Nourbakhsh, I.R.; Scaramuzza, D. Introduction to Autonomous Mobile Robots, 2nd ed.; The MIT Press: Cambridge, MA, USA, 2011. [31] Hoy, M.; Matveev, A.S.; Savkin, A.V. Algorithms for collision-free navigation of mobile robots in complex cluttered environments: a survey. Robotica 2015, 33, 463–497. [35] Twu, P.; Egerstedt, M. Optimal Decentralization of Multi-Agent Motions. In Proceedings of the 2010 American Control Conference, Baltimore, MD, USA, 30 June–2 July 2010; pp. 2326–2331. [38] Pierson, A.; Schwager, M. Bio-Inspired Non-Cooperative Multi-Robot Herding. In Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, 26–30 May 2015; pp. 1843–1849. [46] Shi, Y.; Yu, B. Robust mixed H₂/H_∞ control of networked control systems with random time delays in both forward and backward communication links. Automatica 2011, 47, 754–760. [1] Ren, W.; Beard, R.W. Distributed Consensus in Multi-Vehicle Cooperative Control: Theory and Applications; Communications and Control Engineering Series; Springer: London, UK, 2008; Volume 27. [3] Li, Z.; Duan, Z. Cooperative Control of Multi-Agent Systems: A Consensus Region Approach; CRC Press: Boca Raton, FL, USA, 2015. [4] Olfati-Saber, R.; Murray, R.M. Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 2004, 49, 1520–1533. [5] Chen, J.; Sun, D.; Yang, J.; Chen, H. Leader-follower formation control of multiple non-holonomic mobile robots incorporating a receding-horizon scheme. Int. J. Robot. Res. 2010, 29, 727–747. [7] Freeman, R.A.; Yang, P.; Lynch, K.M. Stability and convergence properties of dynamic average consensus estimators. In Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, USA, 13–15 December 2006; pp. 398–403. [11] Heijmans, S.H.; Postoyan, R.; Noroozi, N.; Nešić, D.; Heemels, W.M.H. Stability analysis of networked control systems with direct-feedthrough terms: Part II–the linear case. In Proceedings of the 55th IEEE Conference on Decision and Control (CDC), Las Vegas, NV, USA, 12–14 December 2016; pp. 5974–5979. [12] Queralta, J.P.; Taipalmaa, J.; Pullinen, B.C.; Sarker, V.K.; Gia, T.N.; Tenhunen, H.; Gabbouj, M.; Raitoharju, J.; Westerlund, T. Collaborative Multi-Robot Search and Rescue: Planning, Coordination, Perception, and Active Vision. IEEE Access 2020, 8, 191617–191643. [14] Blanke, M.; Kinnaert, M.; Lunze, J.; Staroswiecki, M. Distributed Fault Diagnosis and Fault-Tolerant Control. In Diagnosis and Fault-Tolerant Control, 3rd ed.; Springer: Berlin/Heidelberg, Germany, 2016; pp. 467–518. [15] Zhai, D.; An, L.; Li, X.; Zhang, Q. Adaptive Fault-Tolerant Control for Nonlinear Systems with Multiple Sensor Faults and Unknown Control Directions. IEEE Trans. Neural Netw. Learn. Syst. 2018, 29, 4436–4446. [16] Argha, A.; Su, S.W.; Celler, B.G. Control allocation-based fault tolerant control. Automatica 2019, 103, 408–417. [17] Arıcı, M.; Kara, T. Robust adaptive fault tolerant control for a process with actuator faults. J. Process Control 2020, 92, 169–184. [19] Sun, K.; Ma, Z.; Dong, G.; Gong, P. Adaptive Fuzzy Fault-Tolerant Control of Uncertain Fractional-Order Nonlinear Systems with Sensor and Actuator Faults. Fractal Fract. 2023, 7, 862. [20] Pereira, D.A.; Al-Dujaili, A.; El Najjar, M.E.B.; Cocquempot, V.; Ma, Y. Actuator fault estimation and fault tolerant control in three physically-linked 2WD mobile robots. IFAC-PapersOnLine 2018, 51, 709–716. [21] Yang, Y.; Ding, S.X.; Li, L. On Observer-Based Fault Detection for Nonlinear Systems. Syst. Control. Lett. 2015, 82, 18–25. [22] Shi, J.; Chen, X.; Xing, S.; Liu, A.; Chen, C. Robust Cooperative Fault-Tolerant Control for Uncertain Multi-Agent Systems Subject to Actuator Faults. Sensors 2024, 24, 2651. [23] Kharrat, M.; Krichen, M.; Alkhalifa, L.; Gasmi, K. Neural-networks-based adaptive fault-tolerant control of nonlinear systems with actuator faults and input quantization. IEEE Access 2023, 11, 137680–137687. [24] Shang, Y. Resilient consensus in multi-agent systems with state constraints. Automatica 2020, 122, 109288. [29] Siegwart, R.; Nourbakhsh, I.R.; Scaramuzza, D. Introduction to Autonomous Mobile Robots, 2nd ed.; The MIT Press: Cambridge, MA, USA, 2011. [31] Hoy, M.; Matveev, A.S.; Savkin, A.V. Algorithms for collision-free navigation of mobile robots in complex cluttered environments: a survey. Robotica 2015, 33, 463–497. [35] Twu, P.; Egerstedt, M. Optimal Decentralization of Multi-Agent Motions. In Proceedings of the 2010 American Control Conference, Baltimore, MD, USA, 30 June–2 July 2010; pp. 2326–2331. [38] Pierson, A.; Schwager, M. Bio-Inspired Non-Cooperative Multi-Robot Herding. In Proceedings of the 2015 IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, USA, 26–30 May 2015; pp. 1843–1849. [46] Shi, Y.; Yu, B. Robust mixed H₂/H_∞ control of networked control systems with random time delays in both forward and backward communication links. Automatica 2011, 47, 754–760. 2. Original references [36] and [37] present in the original publication have been removed as they were not directly relevant to the topic of the paper. 3. The original reference [47], which initiated the correction process, has been fully revised to correct its bibliographic details. The bibliographic information of this reference has been corrected. Furthermore, the original reference [47] has been renumbered to [45] and all of the references and corresponding in-text citations have been globally renumbered. The revised reference is provided as follows: [45] Whidborne, J.; Istepanian, R. Genetic algorithm approach to designing finite-precision controller structures. IEE Proc.—Control. Theory Appl. 2001, 148, 377–382. [45] Whidborne, J.; Istepanian, R. Genetic algorithm approach to designing finite-precision controller structures. IEE Proc.—Control. Theory Appl. 2001, 148, 377–382. The authors apologize for any inconvenience caused and confirm that these corrections do not affect the scientific validity of the work. This correction was approved by the Academic Editor. The original publication has been updated accordingly. All changes made to the manuscript have been explicitly listed in this correction.