{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T18:17:42Z","timestamp":1760552262237,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,31]],"date-time":"2025-05-31T00:00:00Z","timestamp":1748649600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research and Application of Small UAV Collaborative Inspection Technology in Substation","award":["5218A024000J"],"award-info":[{"award-number":["5218A024000J"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study investigates the cooperative substation inspection problem for multi-unmanned aerial vehicle systems (MUAVs) subjected to uncertain disturbances. To enhance inspection reliability and efficiency, a novel distributed fixed-time group consensus control scheme is proposed. In this framework, radial basis function neural networks (RBF NNs) are employed to approximate both intrinsic nonlinear uncertainties and uncertain disturbances affecting UAV dynamics. Subsequently, a distributed fixed-time controller is developed via backstepping techniques, where fixed-time command filters are integrated to circumvent the complexity explosion inherent to conventional backstepping. Furthermore, an approximation error compensation system is established. It mitigates estimation inaccuracies arising from RBF NN approximations and command filtering processes. The mathematical analysis demonstrates that the proposed controller ensures the fixed-time convergence of group consensus errors into an adjustable residual set. Finally, numerical simulations and MUAV group formation simulations validate the robustness against aerodynamic uncertainties.<\/jats:p>","DOI":"10.3390\/sym17060857","type":"journal-article","created":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T03:57:18Z","timestamp":1748923038000},"page":"857","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multiple UAV Cooperative Substation Inspection: A Robust Fixed-Time Group Formation Control Scheme"],"prefix":"10.3390","volume":"17","author":[{"given":"Lirong","family":"Xiao","sequence":"first","affiliation":[{"name":"State Grid Jiangxi Electric Power Limited Liability Company Nanchang Power Supply Branch, Nanchang 330103, China"}]},{"given":"Zhongwei","family":"Xiao","sequence":"additional","affiliation":[{"name":"State Grid Jiangxi Electric Power Limited Liability Company Nanchang Power Supply Branch, Nanchang 330103, China"}]},{"given":"Zheng","family":"Fu","sequence":"additional","affiliation":[{"name":"State Grid Jiangxi Electric Power Limited Liability Company Nanchang Power Supply Branch, Nanchang 330103, China"}]},{"given":"Cheng","family":"Cheng","sequence":"additional","affiliation":[{"name":"State Grid Jiangxi Electric Power Limited Liability Company Nanchang Power Supply Branch, Nanchang 330103, China"}]},{"given":"Fan","family":"Li","sequence":"additional","affiliation":[{"name":"Jiangxi Electric Power Research Institute of State Grid, Nanchang 330096, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1364-8653","authenticated-orcid":false,"given":"Yang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1016\/j.asej.2020.05.004","article-title":"Recent advancement in smart grid technology: Future prospects in the electrical power network","volume":"12","author":"Zulqarnain","year":"2021","journal-title":"Ain Shams Eng. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1002\/asjc.2806","article-title":"Formation control of unmanned aerial vehicle swarms: A comprehensive review","volume":"25","author":"Quan","year":"2023","journal-title":"Asian J. Control"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Phadke, A., and Medrano, F.A. (2022). Towards Resilient UAV Swarms\u2014A Breakdown of Resiliency Requirements in UAV Swarms. Drones, 6.","DOI":"10.3390\/drones6110340"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3032","DOI":"10.1109\/TII.2020.3004816","article-title":"Placement and Routing Optimization for Automated Inspection With Unmanned Aerial Vehicles: A Study in Offshore Wind Farm","volume":"17","author":"Hwei","year":"2021","journal-title":"IEEE Trans. Ind. Inf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1007\/s42452-023-05299-7","article-title":"Development of power transmission line detection technology based on unmanned aerial vehicle image vision","volume":"5","author":"Xu","year":"2023","journal-title":"SN Appl. Sci."},{"key":"ref_6","first-page":"065208","article-title":"Research on collaborative inspection key technologies for multi-UAVs and multi-nests","volume":"6","author":"Hongwei","year":"2024","journal-title":"AIP Adv."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Jacobsen, R.H., Matlekovic, L., Shi, L., Malle, N., Ayoub, N., Hageman, K., Hansen, S., Nyboe, F.F., and Ebeid, E. (2023). Design of an Autonomous Cooperative Drone Swarm for Inspections of Safety Critical Infrastructure. Appl. Sci., 13.","DOI":"10.3390\/app13031256"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Nordin, M.H., Sharma, S., Khan, A., Gianni, M., Rajendran, S., and Sutton, R. (2022). Collaborative Unmanned Vehicles for Inspection, Maintenance, and Repairs of Offshore Wind Turbines. Drones, 6.","DOI":"10.3390\/drones6060137"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2121","DOI":"10.1109\/TCSI.2021.3061386","article-title":"Fixed-Time Fault-Tolerant Formation Control for Heterogeneous Multi-Agent Systems With Parameter Uncertainties and Disturbances","volume":"68","author":"Cheng","year":"2021","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"109608","DOI":"10.1016\/j.ast.2024.109608","article-title":"Adaptive Neural Network Based Quadrotor UAV Formation Control Under External Disturbances","volume":"155","author":"Singha","year":"2024","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Liu, Z., Li, J., and Shen, J. (2024). Leader\u2013Follower UAVs Formation Control Based on a Deep Q-Network Collaborative Framework. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-54531-w"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"21227","DOI":"10.1007\/s11071-024-10094-z","article-title":"Distributed Consensus of Nonlinear Stochastic Multi-Agent Systems with Input and Output Delays via Predictive Control","volume":"112","author":"Deng","year":"2024","journal-title":"Nonlinear Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wu, P., Li, Y., and Xue, D. (2024). Multi-Target Tracking with Multiple Unmanned Aerial Vehicles Based on Information Fusion. Drones, 8.","DOI":"10.3390\/drones8120704"},{"key":"ref_14","first-page":"200","article-title":"Fixed-Time Group Consensus of Nonlinear Multi-Agent Systems via Pinning Control","volume":"19","author":"Hao","year":"2021","journal-title":"Automatica"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1929","DOI":"10.1109\/TAC.2021.3069398","article-title":"Cluster Consensus Control of Linear Multiagent Systems Under Directed Topology With General Partition","volume":"67","author":"Luo","year":"2022","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1696","DOI":"10.1002\/rnc.7051","article-title":"Adaptive control for a class of high-order nonlinear parameterized systems with multiple unknown control directions by switching linear controllers","volume":"34","author":"Hu","year":"2024","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1936","DOI":"10.1109\/TRO.2021.3071615","article-title":"A Decentralized Cluster Formation Containment Framework for Multirobot Systems","volume":"37","author":"Hu","year":"2021","journal-title":"IEEE Trans. Robot"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1109\/TMECH.2021.3068259","article-title":"Multimobile Robot Cluster System for Robot Machining of Large-Scale Workpieces","volume":"27","author":"Zhao","year":"2022","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"163654","DOI":"10.1109\/ACCESS.2024.3489422","article-title":"Forced Multi-Agent Bipartite Consensus Control: Application to Quadrotor Formation Flying","volume":"12","author":"Guerrero","year":"2024","journal-title":"IEEE Access"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"9984","DOI":"10.1002\/rnc.7502","article-title":"Distributed Fast F-T Control for UAV Formation in the Presence of Unknown Input Disturbances","volume":"34","author":"Liao","year":"2024","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Huang, W., Guo, Y., and Ran, G. (IEEE Trans. Intell. Veh., 2024). Fast Finite-Time Formation Control of UAVs with Multiple Loops and External Disturbances, IEEE Trans. Intell. Veh., early access.","DOI":"10.1109\/TIV.2024.3420939"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Guo, X., Li, Q., and Yao, Q. (Int. J. Robust Nonlinear Control, 2025). Fixed-Time Dynamic Event-Triggered Formation Control for Unmanned Aerial-Ground Vehicle (UAV-UGV) Heterogeneous System, Int. J. Robust Nonlinear Control, Early Access.","DOI":"10.1002\/rnc.7937"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1016\/j.automatica.2014.02.019","article-title":"Finite-Time Coordination in Multiagent Systems Using Sliding Mode Control Approach","volume":"50","author":"Ghasemi","year":"2014","journal-title":"Automatica"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.isatra.2023.03.001","article-title":"Fixed-Time Connectivity-Preserving Consensus of Periodically Disturbed Nonlinear Multi-Agent Systems with Limited Communication Ranges","volume":"138","author":"Yi","year":"2023","journal-title":"ISA Trans."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1109\/TNNLS.2022.3176625","article-title":"Adaptive Neural Fixed-Time Tracking Control for High-Order Nonlinear Systems","volume":"35","author":"Ma","year":"2024","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"24","DOI":"10.54254\/2755-2721\/96\/20241327","article-title":"Application of PID Control Technology in Unmanned Aerial Vehicles","volume":"96","author":"Shi","year":"2024","journal-title":"Appl. Comput. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhang, P., Wang, Z., and Zhu, Z. (2024). Enhanced Multi-UAV Formation Control and Obstacle Avoidance Using IAAPF-SMC. Drones, 8.","DOI":"10.3390\/drones8090514"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Yu, Y., Chen, J., Zheng, Z., and Yuan, J. (2024). Distributed Finite-Time ESO-Based Consensus Control for Multiple Fixed-Wing UAVs Subjected to External Disturbances. Drones, 8.","DOI":"10.3390\/drones8060260"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Liu, W., Lyu, S.-K., Liu, T., Wu, Y.-T., and Qin, Z. (2024). Multi-Target Optimization Strategy for Unmanned Aerial Vehicle Formation in Forest Fire Monitoring Based on Deep Q-Network Algorithm. Drones, 8.","DOI":"10.3390\/drones8050201"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1842","DOI":"10.1017\/S0263574724000559","article-title":"Radial Basis Function Neural Networks for Formation Control of Unmanned Aerial Vehicles","volume":"42","author":"Bui","year":"2024","journal-title":"Robotica"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.isatra.2018.12.013","article-title":"Fixed-time disturbance observer based fixedtime backstepping control for an air-breathing hypersonic vehicle","volume":"88","author":"Wang","year":"2019","journal-title":"ISA Trans."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.automatica.2015.10.049","article-title":"Fault-tolerant finite time consensus for multiple uncertain nonlinear mechanical systems under single-way directed communication interactions and actuation failures","volume":"63","author":"Wang","year":"2016","journal-title":"Automatica"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1109\/TCYB.2019.2963681","article-title":"Fuzzy adaptive practical fixed-time consensus for second-order nonlinear multi-agent systems under actuator faults","volume":"51","author":"Wu","year":"2021","journal-title":"IEEE Trans. Cybern."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/857\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:44:43Z","timestamp":1760031883000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/857"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,31]]},"references-count":33,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["sym17060857"],"URL":"https:\/\/doi.org\/10.3390\/sym17060857","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,5,31]]}}}