{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:44:35Z","timestamp":1760031875986,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T00:00:00Z","timestamp":1743724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Laboratory project of Spatial Intelligent Control Technology","award":["HTKJ2023KL502020","NJ2023-19","51875293"],"award-info":[{"award-number":["HTKJ2023KL502020","NJ2023-19","51875293"]}]},{"name":"Jiangsu Province Demonstration and Promotion Project of Modern Agricultural Machinery Equipment and Technology","award":["HTKJ2023KL502020","NJ2023-19","51875293"],"award-info":[{"award-number":["HTKJ2023KL502020","NJ2023-19","51875293"]}]},{"name":"National Natural Science Foundation of China","award":["HTKJ2023KL502020","NJ2023-19","51875293"],"award-info":[{"award-number":["HTKJ2023KL502020","NJ2023-19","51875293"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Drone swarms often need to fly cooperatively in complex spaces filled with multiple obstacles. In such scenarios, they must meet the requirements of both external obstacle avoidance and internal collision avoidance while maintaining a certain topological configuration among individuals. This easily leads to problems such as congestion, oscillation, and poor stability, including being out of control. Thus, it is essential to measure system-wide stability, regulate the autonomous cooperative evolution of swarms, and enhance their adaptation to environmental changes. To solve this problem, using the symmetric unmanned aerial vehicle (UAV) swarm as the research object, a group entropy measurement theory for the stability of drone swarms is proposed. We introduce an entropy-based metric for group motion consistency. This metric serves as a fitness index for individual collaboration, enabling adaptive adjustment of drone swarm coherence under multi-obstacle conditions. Finally, simulation experiments are conducted to verify the effectiveness of the established theory and algorithm.<\/jats:p>","DOI":"10.3390\/sym17040552","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T11:31:00Z","timestamp":1743766260000},"page":"552","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Target Enclosing Control of Symmetric Unmanned Aerial Vehicle Swarms Based on Crowd Entropy"],"prefix":"10.3390","volume":"17","author":[{"given":"Juan","family":"Dong","sequence":"first","affiliation":[{"name":"School of Electronics & Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China"},{"name":"Department of Mechanical and Electrical Engineering, Heilongjiang Institute of Construction Technology, Harbin 150025, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5477-1810","authenticated-orcid":false,"given":"Yunping","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044, China"}]},{"given":"Liang","family":"Xu","sequence":"additional","affiliation":[{"name":"Department of Warship Command, Dalian Naval Academy\u2019 PLA, Dalian 116018, China"}]},{"given":"Tianyu","family":"Niu","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Information Science and Technology, Nanjing 210044, China"}]},{"given":"Zhiliang","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Electronics & Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China"}]},{"given":"Hui","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Engineering Science, Shandong Xiehe University, Jinan 250109, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"147","DOI":"10.3390\/drones6060147","article-title":"Towards the unmanned aerial vehicles (UAVs): A comprehensive review","volume":"66","author":"Mohsan","year":"2022","journal-title":"Drones"},{"key":"ref_2","first-page":"109","article-title":"Unmanned aerial vehicles (UAVs): Practical aspects, applications, open challenges, security issues, and future trends","volume":"16","author":"Mohsan","year":"2023","journal-title":"Intell. Serv. Robot."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1017\/aer.2022.75","article-title":"Applications and classifications of unmanned aerial vehicles: A literature review with focus on multi-rotors","volume":"127","author":"Sabour","year":"2023","journal-title":"Aeronaut. J."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1617","DOI":"10.1002\/rob.22325","article-title":"UAV-based simultaneous localization and mapping in outdoor environments: A systematic scoping review","volume":"41","author":"Wang","year":"2024","journal-title":"J. Field Robot."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1109\/MWC.131.2200442","article-title":"UAV-enabled integrated sensing and communication: Opportunities and challenges","volume":"31","author":"Meng","year":"2023","journal-title":"IEEE Wirel. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"19346","DOI":"10.1109\/JIOT.2022.3165278","article-title":"Autonomous cooperative search model for multi-UAV with limited communication network","volume":"9","author":"Fei","year":"2022","journal-title":"IEEE Internet Things J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"100869","DOI":"10.1016\/j.paerosci.2022.100869","article-title":"Algorithms and applications of intelligent swarm cooperative control: A comprehensive survey","volume":"135","author":"Xu","year":"2022","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2451","DOI":"10.1109\/TPAMI.2015.2414427","article-title":"Greta-a novel global and recursive tracking algorithm in three dimensions","volume":"37","author":"Attanasi","year":"2015","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"doi-asserted-by":"crossref","unstructured":"Ouellette, N.T. (2022). A physics perspective on collective animal behavior. Phys. Biol., 19.","key":"ref_9","DOI":"10.1088\/1478-3975\/ac4bef"},{"key":"ref_10","first-page":"177","article-title":"UAV swarm target encirclement control based on group entropy measurement","volume":"53","author":"Lin","year":"2023","journal-title":"Sci. China Technol. Sci."},{"doi-asserted-by":"crossref","unstructured":"Vir\u00e1gh, C., V\u00e1s\u00e1rhelyi, G., Tarcai, N., Sz\u00f6r\u00e9nyi, T., Somorjai, G., Nepusz, T., and Vicsek, T. (2014). Flocking algorithm for autonomous flying robots. Bioinspiration Biomim., 9.","key":"ref_11","DOI":"10.1088\/1748-3182\/9\/2\/025012"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"eaat3536","DOI":"10.1126\/scirobotics.aat3536","article-title":"Optimized flocking of autonomous drones in confined environments","volume":"3","author":"Somorjai","year":"2018","journal-title":"Sci. Robot."},{"doi-asserted-by":"crossref","unstructured":"Braga, R.G., da Silva, R.C., Ramos, A.C.B., and Mora-Camino, F. (2018). Collision Avoidance Based on Reynolds Rules: A Case Study Using Quadrotors. Information Technology-New Generations, Springer.","key":"ref_13","DOI":"10.1007\/978-3-319-54978-1_96"},{"unstructured":"Zhang, T., Li, Y., Wang, C., Xie, G., and Lu, Z. (2021, January 18\u201324). Fop: Factorizing optimal joint policy of maximum-entropy multi-agent reinforcement learning. Proceedings of the International Conference on Machine Learning, Virtual.","key":"ref_14"},{"doi-asserted-by":"crossref","unstructured":"Park, J., Kim, J., Jang, I., and Kim, H.J. (August, January 31). Efficient multi-agent trajectory planning with feasibility guarantee using relative bernstein polynomial. Proceedings of the 2020 IEEE International Conference on Robotics and Automation (ICRA), Paris, France.","key":"ref_15","DOI":"10.1109\/ICRA40945.2020.9197162"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"eabd8668","DOI":"10.1126\/scirobotics.abd8668","article-title":"Implicit coordination for 3D underwater collective behaviors in a fish-inspired robot swarm","volume":"6","author":"Berlinger","year":"2021","journal-title":"Sci. Robot."},{"key":"ref_17","first-page":"99","article-title":"Dynamics Models and Group Entropy Measurement of Swarm Intelligence Systems","volume":"65","author":"Luo","year":"2022","journal-title":"Sci. China Inf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"105139","DOI":"10.1109\/ACCESS.2020.3000064","article-title":"Unmanned aerial vehicles (uavs): Collision avoidance systems and approaches","volume":"8","author":"Yasin","year":"2020","journal-title":"IEEE Access"},{"key":"ref_19","first-page":"89","article-title":"Unmanned Aerial Vehicle (UAV) Swarm Cooperation: Key Technologies and Development Trends","volume":"37","author":"Li","year":"2024","journal-title":"J. Aerosp. Eng."},{"doi-asserted-by":"crossref","unstructured":"Fina, L., Smith, D.S., Carnahan, J., and Sevil, H.E. (2022). Entropy-based distributed behavior modeling for multi-agent UAVs. Drones, 6.","key":"ref_20","DOI":"10.3390\/drones6070164"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"108478","DOI":"10.1016\/j.ress.2022.108478","article-title":"Importance measure-based phased mission reliability and UAV number optimization for swarm","volume":"223","author":"Feng","year":"2022","journal-title":"Reliab. Eng. Syst. 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