{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T04:47:00Z","timestamp":1792039620466,"version":"4.4.0"},"reference-count":57,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T00:00:00Z","timestamp":1790899200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Education of Shanxi Province","award":["TK244903110"],"award-info":[{"award-number":["TK244903110"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This study presents a synergetic control approach for coordinating the motion of a UAV swarm based on self-organization principles and energy potential interactions. The proposed method effectively addresses the known limitations of traditional potential field techniques by introducing a procedure for synthesizing the synergetic control of swarm motion using a virtual force field with symmetric attraction and repulsion functions. A Lyapunov\/LaSalle stability analysis and a geometric safety radius argument show that this keeps the swarm\u2019s motion conflict-free, subject to the platform\u2019s kinematic constraints, and supports stable formation maintenance. Damping terms are incorporated into the equations of motion to eliminate self-oscillations and, via an energy (Lyapunov) argument, we show that the resulting system converges to the critical point set of the total interaction potential. A synergetic controller based on virtual pendulum meters is introduced to prevent stagnation. A specialized mathematical framework is developed to mitigate the curse of dimensionality, as confirmed through simulations, although the per-step computational cost scales approximately quadratically with swarm size. The swarm formation time increases sublinearly with the number of UAVs, highlighting the approach\u2019s scalability. A swarm self-organization modeling study reveals three characteristic phases: namely, chaotic motions, transitional reconfiguration, and ordered swarm behavior. The formation process corresponds to a gradual minimization of inter-UAV interaction energy, while stable collective motion is achieved by maintaining a constant polarization of vehicle heading angles. Through simulations, parameter ranges that provide optimal synergetic properties during swarm formation and coordinated movement are identified. The findings are further illustrated, as a proof of concept, through real-world experimental tests of swarm control.<\/jats:p>","DOI":"10.3390\/s26196269","type":"journal-article","created":{"date-parts":[[2026,10,2]],"date-time":"2026-10-02T16:50:38Z","timestamp":1790959838000},"page":"6269","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Synergetic Control Framework for Autonomous UAV Swarm Coordination"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8797-4868","authenticated-orcid":false,"given":"Valerii","family":"Chepizhenko","sequence":"first","affiliation":[{"name":"Institute of Information Technologies and Systems of the National Academy of Sciences of Ukraine, 03187 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4012-9821","authenticated-orcid":false,"given":"Svitlana","family":"Pavlova","sequence":"additional","affiliation":[{"name":"School of Software, Shanxi Agricultural University, Taiyuan 030031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fuzhong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Software, Shanxi Agricultural University, Taiyuan 030031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,10,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bu, Y., Yan, Y., and Yang, Y. 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