低空飞行器集群编队避障与轨迹协同规划

杜城龙; 曾昭阳; 吴迪; 桂瑰; 李繁飙; 阳春华

doi:10.16383/j.aas.c260283

低空飞行器集群编队避障与轨迹协同规划

doi: 10.16383/j.aas.c260283 cstr: 32138.14.j.aas.c260283

杜城龙^1,,
曾昭阳^1,,
吴迪^2,,
桂瑰^1,,
李繁飙^1,,
阳春华^1,

1.
中南大学自动化学院长沙 410083
2.
海南大学电子科学与技术学院海口 570228

基金项目: 国家自然科学基金(62533005, U2570207, 62303492, 62473381), 湖南省自然科学基金(2025JJ40056), 湖南省科技创新计划(2026RC1005)资助

详细信息

作者简介:
杜城龙：中南大学自动化学院副教授. 主要研究方向为分布式控制与优化, 多智能体强化学习, 无人系统及飞机起降控制技术. E-mail: chenglong_du@csu. edu. cn

曾昭阳：中南大学自动化学院硕士研究生. 主要研究方向为移动机器人运动规划与控制. E-mail: ZhaoyangZENG@csu. edu. cn

吴迪：海南大学电子科学与技术学院讲师. 主要研究方向为分布式无人机集群协同感知, 决策与控制. E-mail: hainuwudi@hainanu. edu. cn

桂瑰：中南大学自动化学院教授. 主要研究方向为智能交通系统, 大数据交通模型. E-mail: guigui@csu. edu. cn

李繁飙：中南大学自动化学院教授. 主要研究方向为复杂工业过程智能控制与优化, 空天飞行器智能控制. E-mail: fanbiaoli@csu. edu. cn

阳春华：中南大学自动化学院教授. 主要研究方向为复杂工业过程建模与优化控制, 智能自动化系统与装置. 本文通信作者. E-mail: ychh@csu. edu. cn

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出版历程
- 网络出版日期: 2026-10-21

Low-Altitude Aircraft Swarms Formation Obstacle Avoidance and Trajectory Cooperation Planning

1.
School of Automation, Central South University, Changsha 410083
2.
School of Electronic Science and Technology, Hainan University, Haikou 570228

Funds: Supported by National Natural Science Foundation of China (62533005, U2570207, 62303492, 62473381), Hunan Provincial Natural Science Foundation of China (2025JJ40056), and Science and Technology Innovation Program of Hunan Province (2026RC1005)

More Information

Author Bio:
DU Cheng-Long　Associate Professor at the School of Automation, Central South University. His research interests include distributed control and optimization, multi-agent reinforcement learning, unmanned systems, and aircraft takeoff and landing control technology

ZENG Zhao-Yang　Master's student at the School of Automation, Central South University. His research interests include motion planning and control of mobile robots

WU Di　Lecturer at the School of Electronic Science and Technology, Hainan University. His research interests include distributed cooperative perception, decision-making, and control for UAV swarms

GUI Gui　Professor at the School of Automation, Central South University. Her research interests include intelligent transportation systems and big-data traffic models

LI Fan-Biao　Professor at the School of Automation, Central South University. His research interests include intelligent control and optimization of complex industrial processes and intelligent control of aerospace vehicles

YANG Chun-Hua　Professor at the School of Automation, Central South University. Her research interests include process modeling and optimal control, and intelligent optimization and manufacturing in process industries. Corresponding author of this paper

摘要

摘要: 低空飞行器集群轨迹协同规划的核心挑战在于协调编队保持与避障灵活性. 同时, 现有方法因采用高维状态建模, 普遍存在计算复杂度高, 规划效率低的问题, 制约了其实际应用. 为此, 本文提出一种基于仿射A-RRT$^{\ast}$ (Accelerated-RRT$^{\ast}$)的低空飞行器集群轨迹协同规划方法. 基于三维编队仿射变换的降维方法, 将路径搜索空间从$3N$维压缩至7 维, 并提出融合双向探索与节点复用优化的A-RRT$^{\ast}$路径规划算法, 在快速生成集群全局路径的同时降低模型维数和计算负担. 在此基础上, 基于欧几里得符号距离场的梯度信息对全局路径进行安全修正, 并对修正路径进行时空参数重优化, 进而快速构建具有优化裕度的序列凸安全区域. 进一步地, 将编队保持约束以软约束惩罚项的形式引入兼顾平滑性与能耗的二次规划模型, 实现编队保持约束下的低空飞行器集群平滑轨迹生成. 仿真结果表明, 所提框架在复杂低空环境中能够兼顾编队保持, 安全避障和轨迹质量, 并降低模型复杂度与计算开销.
- 低空飞行器 /
- 集群编队 /
- 轨迹规划 /
- 快速搜索随机树 /
- 仿射变换
Abstract: A core challenge in cooperative trajectory planning for low-altitude aircraft swarms lies in coordinating formation keeping with obstacle-avoidance flexibility. Meanwhile, existing methods typically rely on high-dimensional state representations, resulting in high computational complexity and low planning efficiency, which hinder practical deployment. To address this issue, an affine A-RRT$^{\ast}$ (Accelerated-RRT$^{\ast}$)-based method is proposed for formation obstacle avoidance and cooperative trajectory planning of low-altitude aircraft swarms. By introducing a three-dimensional formation affine transformation, the path-search space is reduced from $3N$ dimensions to a 7-dimensional configuration space. An A-RRT$^{\ast}$ path planner integrating bidirectional exploration and node-reuse optimization is then developed to rapidly generate global paths while reducing model dimensionality and computational burden. Furthermore, the global paths are safely refined using gradient information from the Euclidean signed distance field, followed by spatiotemporal parameter re-optimization of the corrected paths to efficiently construct sequential convex safe regions with sufficient optimization margins. Formation-keeping constraints are also incorporated into a quadratic programming formulation as soft penalty terms, together with smoothness and energy objectives, to generate smooth swarm trajectories under formation-keeping requirements. Simulation results demonstrate that the proposed framework balances formation keeping, safe obstacle avoidance, and trajectory quality in complex low-altitude environments while reducing model complexity and computational cost.
- low-altitude aircraft /
- swarm formation /
- trajectory planning /
- rapidly-exploring random tree /
- affine transformation

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图 1 基于刚性规划和仿射规划的方法对比

Fig. 1 Comparison of rigid planning and affine transformation-based approaches

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图 2 低空飞行器集群编队规划系统架构

Fig. 2 Low-altitude aircraft swarm formation planning system architecture

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图 3 基于ESDF的路径安全修正

Fig. 3 ESDF-based path safety correction

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图 4 路径时空参数重优化

Fig. 4 Path spatiotemporal parameter re-optimization

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图 5 一组随机低空飞行仿真场景

Fig. 5 A set of random low-altitude flight simulation scenarios

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图 6 一组低空飞行仿真规划结果

Fig. 6 A set of low-altitude flight simulation planning results

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表 1 基准实验统计结果

Table 1 Statistics of baseline experiments

规划情景	前端搜索算法	后端优化算法	规划时间均值/标准差 /$\mathrm{s}$	轨迹长度均值/标准差 /$\mathrm{m}$	轨迹代价均值/标准差
楼宇(1)	RRT-connect	QP	0. 15/0. 06	314. 49/37. 92	241. 55/32. 93
	RRT$^{\ast}$	QP	1. 15/0. 85	274. 74/19. 74	151. 54/69. 43
	A-RRT$^{\ast}$	QP	0. 12/0. 07	284. 78/26. 22	159. 44/58. 10
	A-RRT$^{\ast}$	B-spline	0. 12/0. 06	293. 37/31. 65	233. 26/78. 81
楼宇(2)	RRT-connect	QP	0. 43/0. 37	469. 88/31. 86	249. 85/28. 68
	RRT$^{\ast}$	QP	2. 42/1. 93	426. 96/31. 77	190. 37/75. 21
	A-RRT$^{\ast}$	QP	0. 37/0. 25	457. 85/48. 74	200. 80/44. 06
	A-RRT$^{\ast}$	B-spline	0. 40/0. 34	480. 84/60. 23	398. 27/140. 97
密林(1)	RRT-connect	QP	6. 14/3. 61	783. 24/67. 28	594. 38/92. 02
	RRT$^{\ast}$	QP	8. 99/3. 63	666. 52/51. 91	303. 54/34. 45
	A-RRT$^{\ast}$	QP	6. 64/3. 32	660. 97/38. 13	335. 36/42. 93
	A-RRT$^{\ast}$	B-spline	6. 51/3. 37	679. 02/62. 33	398. 30/108. 08
密林(2)	RRT-connect	QP	11. 04/7. 67	1209. 33/69. 03	610. 94/83. 71
	RRT$^{\ast}$	QP	22. 68/19. 77	1036. 03/43. 59	320. 84/32. 16
	A-RRT$^{\ast}$	QP	9. 88/6. 72	1058. 86/40. 83	341. 37/46. 58
	A-RRT$^{\ast}$	B-spline	9. 41/7. 32	1083. 95/51. 60	516. 89/154. 76

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