动态威胁下基于改进APF-RRT*算法的无人机集群隐身航迹规划算法

张欣睿; 时晨光; 吴志锋; 闻雯; 周建江

doi:10.11999/JEIT250554

动态威胁下基于改进APF-RRT*算法的无人机集群隐身航迹规划算法

doi: 10.11999/JEIT250554 cstr: 32379.14.JEIT250554

张欣睿^{1, 2},
时晨光^{1, 2, ,},
吴志锋²,
闻雯^{1, 2},
周建江¹

1.
南京航空航天大学雷达成像与微波光子技术教育部重点实验室，江苏南京 211106
2.
江淮前沿技术协同创新中心合肥 230000

基金项目: 国家自然科学基金面上项目(62271247)，江苏省自然科学基金优秀青年基金项目(BK20240181)，航空科学基金(20220055052001)，江苏高校“青蓝工程”、江淮前沿技术协同创新中心追梦基金课题(2023-ZM01D001)

详细信息

作者简介:
张欣睿：男，硕士研究生，主要研究方向为无人机集群隐身航迹规划

时晨光：男，教授、博士生导师，主要研究方向包括飞行器集群射频隐身技术、网络化雷达协同探测与资源管理等

吴志锋：男，工程师，主要研究方向为电磁空间一体化

闻雯：男，硕士研究生，主要研究方向为无人机集群隐身航迹规划

周建江：男，教授，主要研究方向包括飞行器射频隐身技术、雷达目标特性分析、航空电子信息技术等

通讯作者:
时晨光　scg_space@163.com

中图分类号: TN957
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出版历程
- 收稿日期: 2025-06-16
- 修回日期: 2025-11-03
- 录用日期: 2025-11-03
- 网络出版日期: 2025-11-12

Stealthy Path Planning Algorithm for UAV Swarm Based on Improved APF-RRT* Under Dynamic Threat

ZHANG Xinrui^{1, 2},
SHI Chenguang^{1, 2
, ,},
WU Zhifeng²,
WEN Wen^{1, 2},
ZHOU Jianjiang¹

1.
Key Laboratory of Radar Imaging and Microwave Photonics, Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
2.
Jianghuai Advance Technology Center, Hefei, 230000, China

Funds: This work is supported in part by the National Natural Science Foundation of China under Grant 62271247, in part by the Natural Science Foundation of Jiangsu Province under Grant BK20240181, in part by the National Aerospace Science Foundation of China under Grant 20220055052001, in part by Qing Lan Project of Jiangsu Province, and in part by Dreams Foundation of Jianghuai Advance Technology Center under Grant 2023-ZM01D001

摘要

摘要: 当前无人机集群在复杂战场环境中的高效突防与生存能力着重依赖于精确的航迹规划，然而动态威胁环境下多种探测与拦截手段的存在，使得传统航迹规划难以同时满足隐身性、可行性和安全性要求。为此，本文提出一种动态威胁下基于改进人工势场(Artificial Potential Field, APF)与快速随机扩展树星(Rapidly-Exploring Random Trees Star, RRT*)算法的无人机集群隐身航迹规划算法。首先，构建包含雷达、高射炮及固定障碍物的多元威胁环境模型，并结合无人机雷达散射截面(Radar Cross Section, RCS)，推导包含航程、组网雷达检测概率及高射炮威胁概率的无人机集群隐身航迹规划综合代价函数。其次，以最小化无人机集群隐身航迹规划的综合代价函数为优化目标，结合航迹可行性判定和无人机集群动力学等限制为约束条件，构建动态威胁下无人机集群隐身航迹规划模型。最后，提出了一种改进APF-RRT*算法，并对上述优化模型进行求解。仿真结果表明，所提算法在保证航迹可行性及动力学约束的前提下，相较于现有方法能够有效降低无人机集群的综合代价，提高了无人机集群航迹的隐身性能，实现更优的协同突防效果。
- 隐身航迹规划 /
- 无人机集群 /
- 动态威胁 /
- 人工势场 /
- 快速随机扩展树星
Abstract: Objective The efficient penetration and survivability of unmanned aerial vehicle (UAV) swarms in complex battlefield environments critically depend on robust trajectory planning. With the increasing deployment of advanced air defense systems—featuring radar network, anti-aircraft artillery and dynamic no-fly zones—conventional planning methods struggle to meet simultaneous requirements for stealth, feasibility, and safety. Although prior studies have contributed valuable insights into UAV swarm path planning, they present several limitations: (1) Most research focuses on detection models for single radars and does not sufficiently incorporate the coupling between UAV radar cross section (RCS) and stealth trajectory optimization; (2) UAV kinematic constraints are often treated independently of stealth characteristics; (3) Environmental threats are typically modeled as static and singular, overlooking real-time dynamic threats; (4) Stealth planning is predominantly studied for individual UAVs, with limited attention to swarm-level coordination. This work addresses these gaps by proposing a cooperative stealth trajectory planning framework that integrates real-time threat perception with swarm dynamics optimization, significantly enhancing survivability in contested airspace. Methods To overcome the aforementioned challenges, this paper proposes a stealth path planning algorithm for UAV swarm based on improved artificial potential field (APF) and rapidly-exploring random trees star (RRT*) framework under dynamic threat. First, a multi-threat environment model is constructed, incorporating radars, anti-aircraft artillery, and fixed obstacles. A comprehensive stealth cost function is developed by integrating UAV RCS characteristics, accounting for flight distance, radar detection probability, and artillery threat probability. Second, a stealth trajectory optimization model is formulated with the objective of minimizing the overall cost function, subject to strict constraints on UAV kinematics, swarm coordination, and path feasibility. To solve this model efficiently, an enhanced APF-RRT* algorithm is designed. A rolling-window strategy is introduced to facilitate continuous local replanning in response to dynamic threats, enabling real-time trajectory updates and improving responsiveness to sudden changes in the threat landscape. Furthermore, a target-biased sampling technique is applied to reduce sampling redundancy, thereby enhancing algorithmic convergence speed. By combining the global search capability of RRT* with the local adaptability of APF, the proposed approach enables UAV swarms to generate stealth-optimal paths in real time while maintaining high levels of safety and coordination in adversarial environments. Results and Discussions Simulation experiments validate the effectiveness of the proposed algorithm. During global path planning, some UAVs enter regions threatened by dynamic no-fly zones, radars, and artillery systems, while others successfully reach their destinations through unobstructed paths. In the local replanning phase, affected UAVs adaptively adjust their trajectories to minimize radar detection probability and overall stealth cost. When encountering mobile threats, UAVs perform lateral evasive maneuvers to avoid collisions and ensure mission completion. In contrast, the detection probabilities of the UAVs requiring replanning all exceed the specified threshold for networked radar detection under the comparison algorithms. This indicates that, in practical scenarios, the comparison algorithms fail to generate UAV swarm trajectories that meet platform safety requirements, rendering them ineffective. Comparative simulations demonstrate that the proposed method significantly outperforms existing approaches by reducing stealth costs and improving trajectory feasibility and swarm coordination. The algorithm achieves optimal swarm-level stealth and ensures safe and efficient penetration in dynamic environments. Conclusions This study addresses the problem of stealth trajectory planning for UAV swarms in dynamic threat environments by proposing an improved APF-RRT* algorithm. The following key findings are derived from extensive simulations conducted across different contested scenarios (Section 5): (1) The proposed algorithm reduces the voyage distance by 11.1km in scene 1 and 66.9km in scene 2 compared with the baseline RRT* method (Tab. 3, Tab. 5), primarily due to RCS-minimizing attitude adjustments by heading angle chang (Fig. 3, Fig. 6); (2) The networked radar detection probability remains below the 30% threshold for all UAVs (Fig. 4(a), Fig. 7(a)), whereas comparison algorithm exceed the safety limit of 98% of the group members at most (Fig. 4(b), Fig. 7(b), Fig. 9(a), Fig. 9(b)); (3) The rolling-window replanning mechanism enables real-time avoidance of mobile threats such as dynamic no-fly zones and anti-aircraft artillery (Fig. 5, Fig. 8), while simultaneously reducing the comprehensive trajectory cost by 9.0% in Scene 1 and 15.6% in Scene 2 compared with the baseline RRT method (Tab. 3, Tab. 5). (4) Cooperative constraints embedded in the planning algorithm maintain safe inter-UAV separation and jointly optimize swarm-level stealth performance (Fig. 2, Fig. 5, Fig. 8). These results collectively demonstrate the superiority of the proposed method in balancing stealth optimization, dynamic threat adaptation, and swarm kinematic feasibility. Future research will extend this framework to 3D complex terrain environments and integrate deep reinforcement learning to further enhance predictive threat response and battlefield adaptability.
- Stealthy path planning /
- UAV swarm /
- Dynamic threat /
- Artificial potential field /
- Rapidly-exploring random trees star

HTML全文

图 1 RRT*算法示意图

Figure 1. Schematic diagram of RRT* algorithm

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图 2 场景一中无人机集群航迹规划结果

Figure 2. Path planning results of UAV swarm in scene 1

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图 3 场景一中无人机集群航向角变化

Figure 3. Change of heading angle of UAV swarm in scene 1

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图 4 场景一中组网雷达对无人机集群检测概率变化

Figure 4. Change of detection probability of UAV swarm by radar network in scene 1

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图 5 场景二中无人机集群航迹规划结果

Figure 5. Path planning results of UAV swarm in scene 2

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图 6 场景二中人机集群航向角变化

Figure 6. Change of heading angle of UAV swarm in scene 2

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图 7 场景二中组网雷达对无人机集群检测概率变化

Figure 7. Change of detection probability of UAV swarm by radar network in scene 2

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图 8 场景三中无人机集群航迹规划结果

Figure 8. Path planning results of UAV swarm in scene 3

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图 9 场景三中对比算法下组网雷达检测概率变化

Figure 9. Change of detection probability by radar network under comparison algorithm in scene 3

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1 改进APF-RRT*算法求解步骤

1. Procedure of improved APF-RRT* algorithm

输入：创建初始节点集合$ X $，初始化路径集合$Z$，构建初始搜索　树$ Tre{e_{{\text{start}}}} $。
输出：无人机集群最终路径集合$ P $。
步骤1：计算势场参数：结合式(12)至式(14)分别计算势场引力　${F_{{\text{att}}}}$、势场斥力${F_{{\text{rep}}}}$以及为$ X $受到的合力${F_{{\text{all}}}}$；
步骤2：目标偏置采样：结合式(9)以概率$ {P_{{\text{th}}}} $生成偏向目标的采　样点$ {{\boldsymbol X}_{{\text{rand}}}} $，否则执行随机采样$ {{\boldsymbol X}_{{\text{rand}}}} \leftarrow rand $；
步骤3：节点扩展：在树中寻找最近邻节点$ {{\boldsymbol X}_{{\text{nearest}}}} $，结合势场引　导方向与步长，由式(11)生成新节点${{\boldsymbol X}_{{\text{new}}}}$；
步骤4：滚动窗口检测：在局部窗口内动态检测新节点${{\boldsymbol X}_{{\text{new}}}}$与最　近邻节点$ {{\boldsymbol X}_{{\text{nearest}}}} $之间的连线是否满足无人机平台安全要求以及　约束条件，若不满足，则返回步骤2。若满足，则在${{\boldsymbol X}_{{\text{new}}}}$的扩展　范围内根据式(10)计算综合代价${F_{{\text{rrt*}}}}$，选择最优父节点；
步骤5：更新数据结构：更新搜索树$ Tre{e_{{\text{start}}}} $，添加${{\boldsymbol X}_{{\text{new}}}}$并优化　父节点连接；
步骤6：检验终止条件：若${{\boldsymbol X}_{{\text{new}}}}$到当前子目标的距离小于阈值　$\delta $，则路径回溯至起点，更新路径集合$ P $，否则返回步骤2；若　当前子目标非最终目标，以${{\boldsymbol X}_{{\text{new}}}}$为新起点，生成下一滚动窗口　子目标，返回步骤1。

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表 1 无人机的起点终点设置

Table 1. Starting and ending points of the UAV

无人机序号	起点/km	终点/km
UAV1	(25, 90)	(550, 550)
UAV2	(50, 75)	(390, 275)
UAV3	(25, 125)	(475, 385)
UAV4	(25, 175)	(300, 500)
UAV5	(100, 50)	(550, 225)
UAV6	(25, 200)	(200, 550)

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表 2 场景一中威胁位置设置

Table 2. Threat location setting in scene 1

威胁名称	威胁坐标/km	威胁名称	威胁坐标/km
雷达1	(250, 250)	雷达6	(320, 405)
雷达2	(125, 250)	雷达7	(195,395)
雷达3	(250, 125)	雷达8	(455, 465)
雷达4	(125, 125)	禁飞区	(420, 280)
雷达5	(455, 175)

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表 3 场景一中不同算法性能对比

Table 3. Performance comparison of different algorithms in scene 1

算法	航程/km	综合代价	运行时间/s
所提算法	1314.0	15.3403	100.7304
对比算法	1325.1	16.8436	82.9551

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表 4 场景二中动态威胁位置设置

Table 4. Dynamic threat location setting in scene 2

威胁名称	威胁坐标/km
雷达5	(455, 165)
雷达6	(320, 435)
雷达7	(225,535)
雷达8	(475, 445)
高射炮	(435, 290)
禁飞区	(170, 370)

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表 5 场景二中不同算法性能对比

Table 5. Performance comparison of different algorithms in scene 2

算法	航程/km	综合代价	运行时间/s
所提算法	1327.0	15.1000	111.0575
对比算法	1393.9	17.8896	80.3487

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