{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T15:06:38Z","timestamp":1779894398186,"version":"3.53.1"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T00:00:00Z","timestamp":1779840000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Real-time cooperative control of quadrotor swarms in cluttered environments requires balancing formation maintenance, obstacle avoidance, inter-UAV safety, and per-step computational cost. This paper proposes a multilayer perceptron (MLP) surrogate for high-level objective-weight selection in a modified multi-objective pigeon-inspired optimization (modified MPIO) distributed controller. The proposed MLP surrogate learns the state-to-weight mapping of the online search and directly predicts the two-dimensional objective-weight vector, while the original flocking, gap-based obstacle-avoidance, and command generation rules are retained unchanged. The surrogate is trained from teacher-generated weight labels using randomized scenes, DAgger-based state aggregation, and risk-weighted supervision. On a fixed closed-loop benchmark, the proposed controller increases the true collision free rate from 48.00% to 86.89% and the safe success rate from 38.67% to 74.22% relative to modified MPIO, while reducing the mean per-step decision latency for the whole swarm from 8494.70 ms to 0.92 ms. The improvement is most pronounced in safety-related and runtime metrics, while the formation-related gain is comparatively modest. Ablation results show that the final benchmark performance is not explained by DAgger or risk weighting alone, and that the medium-sized surrogate provides the best safety-latency tradeoff among the tested network architectures. A qualitative AirSim case study further indicates that the same high-level surrogate controller can be executed in a higher-fidelity asynchronous multirotor simulator.<\/jats:p>","DOI":"10.3390\/s26113398","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T14:36:56Z","timestamp":1779892616000},"page":"3398","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Neural Surrogate-Enhanced Metaheuristic Optimization for Distributed Quadrotor Swarm Control"],"prefix":"10.3390","volume":"26","author":[{"given":"Jinze","family":"Li","sequence":"first","affiliation":[{"name":"School of Aeronautics and Astronautics, Sichuan University, Chengdu 610207, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-6224-249X","authenticated-orcid":false,"given":"Zeling","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sichuan University, Chengdu 610207, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8077-7984","authenticated-orcid":false,"given":"Zhaoke","family":"Ning","sequence":"additional","affiliation":[{"name":"School of Aeronautics and Astronautics, Sichuan University, Chengdu 610207, China"},{"name":"Multi-Source Information Intelligent Fusion Key Laboratory of Sichuan Province, Chengdu 610207, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.vrih.2019.12.004","article-title":"Survey on Path and View Planning for UAVs","volume":"2","author":"Zhou","year":"2020","journal-title":"Virtual Real. Intell. Hardw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1109\/TRO.2018.2857475","article-title":"A Survey on Aerial Swarm Robotics","volume":"34","author":"Chung","year":"2018","journal-title":"IEEE Trans. Robot."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rahman, M., Sarkar, N.I., and Lutui, R. (2025). A Survey on Multi-UAV Path Planning: Classification, Algorithms, Open Research Problems, and Future Directions. Drones, 9.","DOI":"10.3390\/drones9040263"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1186\/s44147-025-00582-3","article-title":"UAV Swarms: Research, Challenges, and Future Directions","volume":"72","author":"Alqudsi","year":"2025","journal-title":"J. Eng. Appl. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Arshid, K., Krayani, A., Marcenaro, L., Gomez, D.M., and Regazzoni, C. (2025). Toward Autonomous UAV Swarm Navigation: A Review of Trajectory Design Paradigms. Sensors, 25.","DOI":"10.3390\/s25185877"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1145\/37402.37406","article-title":"Flocks, Herds, and Schools: A Distributed Behavioral Model","volume":"21","author":"Reynolds","year":"1987","journal-title":"Comput. Graph."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1109\/TAC.2005.864190","article-title":"Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory","volume":"51","year":"2006","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"852","DOI":"10.1109\/TAC.2007.895842","article-title":"Emergent Behavior in Flocks","volume":"52","author":"Cucker","year":"2007","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1177\/027836499801700706","article-title":"Motion Planning in Dynamic Environments Using Velocity Obstacles","volume":"17","author":"Fiorini","year":"1998","journal-title":"Int. J. Robot. Res."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Pradalier, C., Siegwart, R., and Hirzinger, G. (2011). Reciprocal n-Body Collision Avoidance. Robotics Research, Springer.","DOI":"10.1007\/978-3-642-19457-3"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1109\/TRO.2017.2659727","article-title":"Safety Barrier Certificates for Collisions-Free Multirobot Systems","volume":"33","author":"Wang","year":"2017","journal-title":"IEEE Trans. Robot."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Miettinen, K. (1998). Nonlinear Multiobjective Optimization, Kluwer Academic Publishers.","DOI":"10.1007\/978-1-4615-5563-6"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","article-title":"A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II","volume":"6","author":"Deb","year":"2002","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4295","DOI":"10.1007\/s10462-022-10281-7","article-title":"Swarm intelligence algorithms for multiple unmanned aerial vehicles collaboration: A comprehensive review","volume":"56","author":"Tang","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Poudel, S., Arafat, M.Y., and Moh, S. (2023). Bio-Inspired Optimization-Based Path Planning Algorithms in Unmanned Aerial Vehicles: A Survey. Sensors, 23.","DOI":"10.3390\/s23063051"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"515","DOI":"10.1016\/j.ins.2018.06.061","article-title":"A Multi-Objective Pigeon-Inspired Optimization Approach to UAV Distributed Flocking among Obstacles","volume":"509","author":"Qiu","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"740","DOI":"10.1631\/FITEE.2000066","article-title":"Multi-UAV Obstacle Avoidance Control via Multi-Objective Social Learning Pigeon-Inspired Optimization","volume":"21","author":"Ruan","year":"2020","journal-title":"Front. Inf. Technol. Electron. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"108583","DOI":"10.1016\/j.compchemeng.2024.108583","article-title":"Two-dimensional model-free Q-learning-based output feedback fault-tolerant control for batch processes","volume":"182","author":"Shi","year":"2024","journal-title":"Comput. Chem. Eng."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Hu, C., Bai, J., and Zou, H. (2026). Two-dimensional iterative learning control under infinite horizon optimization for batch processes with partial actuator failures. Can. J. Chem. Eng., early view.","DOI":"10.1002\/cjce.70381"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Magni, L., Raimondo, D.M., and Allg\u00f6wer, F. (2009). A Survey on Explicit Model Predictive Control. Nonlinear Model Predictive Control: Towards New Challenging Applications, Springer.","DOI":"10.1007\/978-3-642-01094-1"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1146\/annurev-control-090419-075625","article-title":"Learning-Based Model Predictive Control: Toward Safe Learning in Control","volume":"3","author":"Hewing","year":"2020","journal-title":"Annu. Rev. Control Robot. Auton. Syst."},{"key":"ref_22","unstructured":"Gonzalez, C., Asadi, H., Kooijman, L., and Lim, C.P. (2023). Neural Networks for Fast Optimisation in Model Predictive Control: A Review. arXiv."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"100262","DOI":"10.1016\/j.dche.2025.100262","article-title":"Neural Network Implementation of Model Predictive Control with Stability Guarantees","volume":"16","author":"Khodaverdian","year":"2025","journal-title":"Digit. Chem. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s00521-021-06569-4","article-title":"A Review of Artificial Intelligence Applied to Path Planning in UAV Swarms","volume":"34","author":"Rivero","year":"2022","journal-title":"Neural Comput. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/j.robot.2008.10.024","article-title":"A Survey of Robot Learning from Demonstration","volume":"57","author":"Argall","year":"2009","journal-title":"Robot. Auton. Syst."},{"key":"ref_26","first-page":"627","article-title":"A Reduction of Imitation Learning and Structured Prediction to No-Regret Online Learning","volume":"Volume 15","author":"Ross","year":"2011","journal-title":"Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Shah, S., Dey, D., Lovett, C., and Kapoor, A. (2018). AirSim: High-Fidelity Visual and Physical Simulation for Autonomous Vehicles. Field and Service Robotics, Springer International Publishing.","DOI":"10.1007\/978-3-319-67361-5_40"},{"key":"ref_28","unstructured":"Sabatino, F. (2015). Quadrotor Control: Modeling, Nonlinear Control Design, and Simulation. [Master\u2019s Thesis, KTH Royal Institute of Technology, Automatic Control]."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"320526","DOI":"10.1155\/2014\/320526","article-title":"A Survey of Modelling and Identification of Quadrotor Robot","volume":"2014","author":"Zhang","year":"2014","journal-title":"Abstr. Appl. Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1103\/PhysRevLett.75.1226","article-title":"Novel Type of Phase Transition in a System of Self-Driven Particles","volume":"75","author":"Vicsek","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1016\/j.robot.2012.05.021","article-title":"A Novel Obstacle Avoidance Algorithm: \u201cFollow the Gap Method\u201d","volume":"60","author":"Sezer","year":"2012","journal-title":"Robot. Auton. Syst."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Tobin, J., Fong, R., Ray, A., Schneider, J., Zaremba, W., and Abbeel, P. (2017). Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World. Proceedings of the 2017 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE.","DOI":"10.1109\/IROS.2017.8202133"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1915","DOI":"10.1007\/s11431-015-5860-x","article-title":"Multi-objective pigeon-inspired optimization for brushless direct current motor parameter design","volume":"58","author":"Qiu","year":"2015","journal-title":"Sci. China Technol. Sci."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/11\/3398\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T14:39:00Z","timestamp":1779892740000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/11\/3398"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,27]]},"references-count":33,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["s26113398"],"URL":"https:\/\/doi.org\/10.3390\/s26113398","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,27]]}}}