【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，该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。更多还原

【Abstract】 Objective The efficient penetration and survivability of Unmanned Aerial Vehicle(UAV) swarms in complex battlefield environments depend on robust trajectory planning. With the increasing deployment of advanced air defense systems, including radar networks, anti-aircraft artillery, and dynamic no-fly zones, conventional planning methods struggle to meet simultaneous requirements for stealth, feasibility, and safety. Although prior studies provide useful progress in UAV swarm path planning, several limitations remain.(1) Most research concentrates on detection models for single radars and does not account for the relation between UAV Radar Cross Section(RCS) and stealth trajectory optimization.(2) UAV kinematic constraints are often handled separately from stealth characteristics.(3) Environmental threats are commonly modeled as static and singular,which limits real-time adaptation to dynamic threats.(4) Stealth planning is also examined mainly for individual UAVs, with limited consideration of swarm-level coordination. This study addresses these gaps by proposing a cooperative stealth trajectory planning framework that integrates real-time threat perception with swarm dynamics optimization and strengthens survivability in contested airspace.Methods This study proposes a stealth path planning algorithm for UAV swarms based on an improved Artificial Potential Field(APF) and a Rapidly-exploring Random Trees star(RRT*) framework under dynamic threat conditions. A multi-threat environment model is first constructed to represent radars, anti-aircraft artillery, and fixed obstacles. A comprehensive stealth cost function is then developed by integrating UAV RCS characteristics and considering flight distance, radar detection probability, and artillery threat probability. A stealth trajectory optimization model is formulated to minimize the overall cost function under constraints on UAV kinematics, swarm coordination, and path feasibility. To solve this model efficiently, an enhanced APFRRT* algorithm is designed. A rolling-window strategy is applied to enable continuous local replanning in response to dynamic threats. This approach supports real-time trajectory updates and improves responsiveness to sudden changes in the threat field. A target-biased sampling method is also used to reduce sampling redundancy and increase convergence speed. By combining the global search ability of RRT* with the local adaptability of APF, the method enables UAV swarms to generate stealth-optimal paths in real time while maintaining safety and coordination in adversarial environments.Results and Discussions Simulation experiments confirm the effectiveness of the proposed algorithm. During global path planning, several UAVs enter regions threatened by dynamic no-fly zones, radars, and artillery systems, although others reach their destinations through clear paths. In the local replanning phase, affected UAVs adjust their trajectories to reduce radar detection probability and overall stealth cost. When encountering mobile threats, UAVs execute lateral evasive maneuvers to prevent collisions and ensure mission completion. Under the comparison algorithms, the detection probabilities of the UAVs requiring replanning all exceed the specified threshold for networked radar detection, which shows that these methods do not generate UAV swarm trajectories that satisfy platform safety requirements and therefore fail in practical settings.Comparative simulations show that the proposed method yields lower stealth costs and improves trajectory feasibility and swarm coordination. The algorithm achieves swarm-level stealth optimization and ensures safe and efficient penetration in dynamic environments.Conclusions This study addresses stealth trajectory planning for UAV swarms in dynamic threat environments by proposing an improved APF-RRT* algorithm. The following key findings are obtained from extensive simulations conducted in different contested scenarios(Section 5):(1) The proposed algorithm reduces the voyage distance by 11.1 km in Scene 1 and 66.9 km in Scene 2 compared with the baseline RRT* method(Tab. 3, Tab. 5). This reduction is primarily due to RCS-minimizing attitude adjustments produced through heading angle change(Fig. 3, Fig. 6).(2) The networked radar detection probability remains below the 30 percent threshold for all UAVs(Fig. 4(a), Fig. 7(a)), whereas the comparison algorithms exceed the safety limit for up to 98 percent of the group members(Fig. 4(b), Fig. 7(b), Fig. 9(a), Fig. 9(b)).(3) The rolling-window replanning mechanism supports real-time avoidance of mobile threats such as dynamic no-fly zones and antiaircraft artillery(Fig. 5, Fig. 8), while reducing the comprehensive trajectory cost by 9.0 percent in Scene 1 and15.6 percent 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 optimize swarm-level stealth performance(Fig. 2, Fig. 5, Fig. 8). These findings show the superiority of the proposed method in balancing stealth optimization, dynamic threat adaptation, and swarm kinematic feasibility. Future work will extend this framework to three-dimensional complex terrain and integrate deep reinforcement learning to strengthen predictive threat response and battlefield adaptability.更多还原