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Game Theory-based Joint Optimization Algorithm for UAV Swarm Task Allocation and Trajectory Planning in Phantom Track Deception
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摘要: 针对无人机集群对组网雷达实施航迹欺骗过程中因平台故障、损毁等原因导致生成虚假航迹中断的问题，提出面向航迹欺骗的无人机集群任务分配与飞行路径联合博弈优化算法。首先，基于去中心化的集群协作机制，构建针对组网雷达的无人机集群航迹欺骗合作博弈模型。在此基础上，根据组网雷达同源检验准则，以最大化无人机集群航迹欺骗博弈效用函数为优化目标，以满足集群动力学性能与任务分配限制为约束条件，建立无人机集群航迹欺骗博弈优化模型，并通过严格势博弈理论证明纳什均衡解的存在性与收敛性。针对上述非凸、非线性混合整数优化问题，采用基于分布式联盟博弈和遗传算法的迭代算法进行求解。仿真结果表明，与现有算法相比，所提算法能够在平台故障、损毁等情况下，对无人机集群欺骗干扰任务和飞行路径进行联合重规划，提升针对组网雷达生成虚假航迹的连续性和航迹欺骗效果。Abstract: To address interruptions in phantom tracks caused by platform failures or damage during unmanned aerial vehicle (UAV) swarm deception operations against radar networks, this study proposes a game theory-based joint optimization algorithm for UAV swarm task allocation and trajectory planning. A decentralized swarm cooperation mechanism is designed to create a cooperative game model for UAV phantom track deception against radar networks. Based on the radar network homology test criterion, an optimization model is developed to maximize the utility function of the phantom track deception game, subject to constraints on UAV swarm kinematic performance and task allocation requirements. The existence and convergence of a Nash equilibrium are rigorously proven using exact potential game theory. To address the resulting non-convex, non-linear, mixed-integer optimization problem, an iterative algorithm is developed that combines distributed coalition game theory with a genetic algorithm. The simulation results demonstrate that, compared with existing approaches, the proposed algorithm effectively replans deception tasks and trajectories in response to platform failures or damage, thereby enhancing the continuity and effectiveness of phantom track generation against radar networks.
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Key words:
- Phantom track deception /
- UAV swarm /
- Radar network /
- Coalition game /
- Homology test
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图 1 针对组网雷达的无人机集群航迹欺骗示意图
Figure 1. Schematic diagram of phantom track deception by UAV swarm against radar network
图 2 雷达、无人机、虚假目标空间关系示意图
Figure 2. Schematic diagram of spatial relationship between radar, UAV, and phantom target
图 3 无人机集群航迹欺骗合作博弈原理图
Figure 3. Schematic diagram of cooperative game for phantom track deception by UAV swarm
图 6 仿真场景1多部雷达观测的虚假航迹
Figure 6. Phantom tracks with different radar perspective in scenario 1
图 11 仿真场景2多部雷达观测的虚假航迹
Figure 11. Phantom tracks with different radar perspective in scenario 2
图 17 仿真场景3多部雷达观测的虚假航迹
Figure 17. Phantom tracks with different radar perspective in scenario 3
1 基于联盟博弈的无人机集群任务分配与飞行路径联合优化算法
1. Coalitional game-based joint optimization algorithm of task allocation and trajectory planning in UAV swarm
输入：$\left( {k - 1} \right)$时刻无人机集群任务分配方案及空间坐标，k时刻
正常工作的无人机集合$ {\mathcal{W}_k} $，预设虚假航迹空间坐标${\hat p_{m,k}}$，组
网雷达站址坐标、SRC及射频参数，最大迭代次数${I_{\max }}$.输出：k时刻的无人机集群任务分配和飞行路径 优化结果. 1 将$\left( {k - 1} \right)$时刻的无人机集群任务分配方案${\mu _{k - 1}}$作为k时刻的
无人机集群初始任务分配方案;2 正常工作的各架无人机根据初始任务分配和飞行路径计算自身
效用$ {u_{n,k}}\left( {{a_{n,k}},{A_{ - n,k}}} \right) $;3 for $i = 1:{I_{\max }}$ do: 4 随机选择无人机$ n \in {\mathcal{W}_k} $，利用遗传算法 (Genetic Algorithm,
GA)求解式，在固定其它无人机策略选择情况下得到 任务分配和
飞行路径优化结果;5 计算无人机n调整策略后的自身效用 $ {u_{n,k}}\left( {{{\tilde a}_{n,k}},{A_{ - n,k}}} \right) $; 6 if $ {u_{n,k}}\left( {{{\tilde a}_{n,k}},{A_{ - n,k}}} \right) \ge $ $ {u_{n,k}}\left( {{a_{n,k}},{A_{ - n,k}}} \right) $ then: 7 无人机n更新其任务分配与飞行路径，无人机集群更新其
联盟划分;8 更新无人机n的自身效用: $ {u_{n,k}}\left( {{a_{n,k}},{A_{ - n,k}}} \right) = {u_{n,k}}\left( {{{\tilde a}_{n,k}},{A_{ - n,k}}} \right) $; 9 else: 10 无人机n保持其原有任务分配与飞 行路径; 11 end if 12 end for 13 剔除未通过同源检验的虚假航迹任务. 
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表 1 无人机集群初始任务分配
Table 1. The initial task allocation of UAV swarm
虚假航迹 雷达1 雷达2 雷达3 虚假航迹1 无人机1 无人机2 无人机3 虚假航迹2 无人机1 无人机4 无人机5 虚假航迹3 无人机6 无人机2 无人机7 虚假航迹4 无人机8 无人机9 无人机3 虚假航迹5 无人机10 无人机11 无人机12
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