A Bird-Flocking-Inspired Phase Transition Control Method for UAV Swarms Driven by Phase Transition Rate

doi:10.3969/j.issn.1009-086x.2026.03.004

Abstract

Abstract:

To address insufficient stability in the bird-flocking-inspired phase transition control model for UAV swarms， an improved method based on phase transition rate is proposed. By comparing the behavior of natural bird flocks with that of the bird-flocking-inspired phase transition control model， the regulatory mechanism of the temporal effect of phase transition on group stability is revealed. Based on the leader-follower architecture， a control protocol including attraction， repulsion， alignment， and circling terms is constructed. The temporal characteristics are quantified by the dynamic adjustment rate of the coefficients of behavioral control terms， which is defined as the “phase transition rate”. Simulation experiments show that under the condition of a low phase transition rate， UAV swarms can achieve stable transitions from an ordered state to three behaviors： dispersion， aggregation， and circling. Comparative experiments indicate that the order parameter of low-rate phase transition is higher than 0.9， and the span of the stable interval is 3.67 times that of high-rate phase transition， which confirms that reducing the phase transition rate can improve the stability of behavioral transitions. Furthermore， a low phase transition rate inhibits the formation of vortex phases， indicating qualitative differences in behavioral patterns across different phase transition rates. This study demonstrates significant advantages in increasing the number of phase states in UAV swarms and improving phase transition stability. It not only verifies the key regulatory mechanism of phase transition rate on the phase transition process， but also provides new theoretical and methodological support for enhancing the engineering practicability of the bird-flocking-inspired model for UAV swarms.

Key words: UAV swarm, bird-flocking-inspired model, phase transition control, phase transition rate, group behavior control

摘要：

针对无人机集群仿鸟群相变控制模型稳定性不足的问题，提出一种基于相变速率的改进方法。通过对照自然鸟群行为与仿鸟群相变控制模型，揭示了相变时间效应对群体稳定性的调控机制；基于领导者 - 跟随者架构构建包含吸引、排斥、对齐及盘旋项的控制协议，以行为控制项系数的动态调整速率量化时间特性，定义为“相变速率”。仿真实验表明，无人机集群在低相变速率条件下，可实现从有序到分散、聚集及盘旋3种行为的稳定转换。对比实验表明，低速相变的序参量高于0.9且稳定区间跨度为高速相变的3.67倍，证实降低相变速率能提升行为转换稳定性；低速相变抑制涡旋相的产生，表明不同相变速率的行为模式存在质的差异。本研究在拓展无人机集群相态数量与提升相变稳定性方面展现出显著优势，不仅验证了相变速率对相变过程的关键调控机制，更为提升无人机集群仿鸟群模型的工程实用性提供了新的理论与方法支撑。

关键词: 无人机集群, 仿鸟群模型, 相变控制, 相变速率, 群体行为控制

CLC Number:

TP273.5

Jingjing WU, Ming HE, Wei HAN, Chengzhuo LIU, Tao YUE, Haotian CHEN. A Bird-Flocking-Inspired Phase Transition Control Method for UAV Swarms Driven by Phase Transition Rate[J]. Modern Defense Technology, 2026, 54(3): 38-49.

吴晶晶, 何明, 韩伟, 刘承卓, 岳涛, 陈浩天. 一种相变速率驱动的无人机集群仿鸟群相变控制方法[J]. 现代防御技术, 2026, 54(3): 38-49.

Figures/Tables 23

Fig. 1 Macroscopic phase transition model （phase diagram）

Fig. 2 Phase transition design and control process

Fig. 3 Comparison of three group behaviors between bird flocks and UAV swarms

Fig. 4 Schematic diagram of UAV swarm control protocol and various behavior items

Fig. 5 Disordered state of UAV swarm

Fig. 6 Ordered state of UAV swarm

Fig. 7 Final morphology of UAV swarm

Fig. 8 Flight trajectory of UAV swarm

Fig. 9 Variation of order parameter

Fig. 10 Flight path of UAV swarm

Fig. 11 Variation of order parameter

Fig. 12 Phase diagram of low-speed phase transition for dispersion behavior of UAV swarm

Fig. 13 Final state of UAV swarm

Fig. 14 Flight path of UAV swarm

Fig. 15 Variation of order parameter

Fig. 16 Phase diagram of low-rate phase transition for aggregation behavior of UAV swarm

Fig.17 Final state of UAV swarm

Fig. 18 Flight path of UAV swarm

Fig. 19 Variation of order parameter

Fig. 20 Phase diagram of low-rate phase transition for circling behavior of UAV swarm

Fig. 21 Comparison of order parameter variation with control parameters under different phase transition rates

Fig. 22 Comparison of critical points and stable phase transition ranges under different phase transition rates

Fig. 23 Comparison of phase diagrams of circling behavior under different phase transition rates

References 20

[1]	何明，陈浩天，韩伟，等. 无人机仿鸟群协同控制发展现状及关键技术［J］. 航空学报， 2024， 45（20）： 184-206.
	HE Ming， CHEN Haotian， HAN Wei， et al. Development Status and Key Technologies of Cooperative Control of Bird-Inspired UAV Swarms［J］. Acta Aeronautica et Astronautica Sinica， 2024， 45（20）： 184-206.
[2]	邱华鑫，段海滨. 从鸟群群集飞行到无人机自主集群编队［J］. 工程科学学报， 2017， 39（3）： 317-322.
	QIU Huaxin， DUAN Haibin. From Collective Flight in Bird Flocks to Unmanned Aerial Vehicle Autonomous Swarm Formation［J］. Journal of University of Science and Technology Beijing， 2017， 39（3）： 317-322.
[3]	CAVAGNA A， GIARDINA I. Bird Flocks as Condensed Matter［J］. Annual Review of Condensed Matter Physics， 2014， 5： 183-207.
[4]	BASTIEN R， ROMANCZUK P. A Model of Collective Behavior Based Purely on Vision［J］. Science Advances， 2020， 6（6）： eaay0792.
[5]	ATTANASI A， CAVAGNA A， DEL CASTELLO L， et al. Emergence of Collective Changes in Travel Direction of Starling Flocks from Individual Birds' Fluctuations［J］. Journal of the Royal Society Interface， 2015， 12（108）： 20150319.
[6]	段海滨，尤灵辰，范彦铭，等. 仿鸟群自推进机制的无人机集群相变控制［J］. 自动化学报， 2025， 51（5）： 960-971.
	DUAN Haibin， YOU Lingchen， FAN Yanming， et al. Phase Transition Control of UAV Swarm Based on Bird-Inspired Self-Propelled Mechanism［J］. Acta Automatica Sinica， 2025， 51（5）： 960-971.
[7]	XUE Tingting， LI Xu， GRASSBERGER P， et al. Swarming Transitions in Hierarchical Societies［J］. Physical Review Research， 2020， 2（4）： 042017.
[8]	STORMS R F， CARERE C， ZORATTO F， et al. Complex Patterns of Collective Escape in Starling Flocks Under Predation［J］. Behavioral Ecology and Sociobiology， 2019， 73（1）： 10.
[9]	JUNG N， WEON B M， KIM P. Effects of Adaptive Acceleration Response of Birds on Collective Behaviors［J］. Journal of Physics： Complexity， 2022， 3（1）： 015014.
[10]	DUWEZ P. A Typical Example of Metastability： Metallic Glasses［J］. Journal of Vacuum Science & Technology B： Microelectronics Processing and Phenomena， 1983， 1（2）： 218-221.
[11]	CHRISTODOULIDI H， VAN DER WEELE K， ANTONOPOULOS C G， et al. Phase Transitions in Models of Bird Flocking［M］∥NICOLIS G. Chaos， Information Processing and Paradoxical Games. Singapore： World Scientific Publishing Co Pte Ltd， 2014： 383-398.
[12]	马梓瑞，司书宾，陈志伟. 鸟群行为启发的无人机集群协同控制算法［C］∥第六届体系工程学术会议论文集—体系工程与高质量发展会议论文集. 长沙：国防科技大学系统工程学院， 2024： 483-494.
	MA Zirui， SI Shubin， CHEN Zhiwei. Consensus and Cooperative Control Algorithm for UAV Swarm Inspired by Bird Flock Behavior［C］∥Proceedings of the 6th Conference on Systems Engineering-Systems Engineering and High-Quality Development. Changsha： College of Systems Engineering， National University of Defense Technology， 2024： 483-494.
[13]	邱浩楠，何明，韩伟，等. 一种仿鸟群行为的无人机集群相变控制方法［J］. 现代防御技术， 2025， 53（1）： 11-22.
	QIU Haonan， HE Ming， HAN Wei， et al. A Phase Transition Control Method for UAV Swarm Based on Birds' Behaviors［J］. Modern Defence Technology， 2025， 53（1）： 11-22.
[14]	林德平，王亚祺，钱荣荣，等. 领导-跟随协同飞行无人网络的通信容量分析［J］. 北京邮电大学学报， 2023， 46（3）： 97-102.
	LIN Deping， WANG Yaqi， QIAN Rongrong， et al. Communication Capacity Analysis for a Class of Leader-Follower Cooperative Flying Unmanned Aerial Vehicle Networks［J］. Journal of Beijing University of Posts and Telecommunications， 2023， 46（3）： 97-102.
[15]	XU Xiaoping， YAN Xiaoting， YANG Wenyuan， et al. Algorithms and Applications of Intelligent Swarm Cooperative Control： A Comprehensive Survey［J］. Progress in Aerospace Sciences， 2022， 135： 100869.
[16]	LIAO Jian， CHENG Jun， XIN Bin， et al. UAV Swarm Formation Reconfiguration Control Based on Variable-Stepsize MPC-APCMPIO Algorithm［J］. Science China Information Sciences， 2023， 66（11）： 212207.
[17]	LIU Weiheng， ZHENG Xin， DENG Zhihong. Dynamic Collision Avoidance for Cooperative Fixed-Wing UAV Swarm Based on Normalized Artificial Potential Field Optimization［J］. Journal of Central South University， 2021， 28（10）： 3159-3172.
[18]	CHEN Hao， WANG Xiangke， SHEN Lincheng， et al. Formation Flight of Fixed-Wing UAV Swarms： A Group-Based Hierarchical Approach［J］. Chinese Journal of Aeronautics， 2021， 34（2）： 504-515.
[19]	WU Jia， LUO Chunbo， LUO Yang， et al. Distributed UAV Swarm Formation and Collision Avoidance Strategies over Fixed and Switching Topologies［J］. IEEE Transactions on Cybernetics， 2022， 52（10）： 10969-10979.
[20]	XIONG Hui， DING Yaozu， LIU Jinzhen. Compact and Ordered Swarms of Unmanned Aerial Vehicles in Cluttered Environments［J］. Bioinspiration & Biomimetics， 2023， 18（5）： 056006.