Optimization design method of winged aircraft formation configuration and communication topology for cooperative penetration
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摘要:
有翼飞行器编队构型和通信拓扑优化在编队协同突防应用场景下有着迫切需求。针对编队构型优化中的参考基准选择和飞行器/拦截力量/战场之间关系的建模问题，提出一种基于突防通道的编队构型优化设计方法。通过通信拓扑优化获得领导者飞行器角色，先使用各组长的几何中心、后使用领导者飞行器作为编队构型的参考基准，设计时变编队构型的显式表达式，摆脱了对事先获取领导者飞行器先验信息的依赖；建立有翼飞行器突防通道模型，保证有翼飞行器在各战场栅格处的探测、反探测、机动规避能力优势；针对通信拓扑优化需要兼顾信息共享和均衡网络负载的问题，在编队构型约束下构建通信拓扑，提出基于最小生成树和最优刚性图的通信拓扑优化设计方法，给出基于战场威胁态势的拓扑切换策略，实现了编队构型和通信拓扑的优化。以有翼飞行器编队协同突防探测拦截威胁为例，验证了所提方法的有效性。
Abstract:In the cooperative penetration application scenario, there is an immediate need to optimize the communication topology and wing aircraft formation structure. A formation configuration optimization design method based on penetration thoroughfares is proposed to address the issues of reference benchmark selection and modeling of aircraft/interception force/battlefield relationships in formation configuration optimization. The leader aircraft’s role is obtained by the optimization of the communication topology. The formation configuration is referenced by the geometric centers of the leader aircraft and each team leader in turn. Explicit expressions for the formation configuration are designed to eliminate the dependence on obtaining prior information about the leader aircraft. A penetration thoroughfares model is established for winged aircraft to ensure their advantages in detection, anti-detection, and maneuver avoidance capabilities at various battlefield grids. To address the issue of balancing information sharing and network load on communication topology optimization, a communication topology is constructed under the constraints of formation configuration. In order to optimize both formation configuration and communication topology, a topology switching strategy depending on battlefield conditions is suggested after a communication topology optimization approach based on minimal spanning tree and optimal rigid graph is presented. Finally, the effectiveness of the designed optimization method is verified by taking the cooperative penetration against military threats for winged aircraft as an example.
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图 3 栅格战场环境下有翼飞行器突破探测拦截威胁示意图
Figure 3. Schematic diagram of winged aircraft breakthrough detection and interception threat in gridded battlefield environment
图 6 基于突防通道模型的编队构型优化设计框架
Figure 6. Optimization design framework for formation configuration based on penetration channel model
图 7 基于最优刚性图和最小生成树的通信拓扑优化设计框架
Figure 7. Communication topology optimization design framework based on optimal rigid graph and minimum spanning tree
图 8 编队构型和通信拓扑的耦合求解流程
Figure 8. Joint design procedure of formation configuration and communication topology
图 12 各组长绕型别初始位置的旋转角度优化结果
Figure 12. Result of optimizing rotation angle of each group around type reference position
图 14 不同时刻通信拓扑优化过程
Figure 14. Communication topology optimization process at different times
图 16 基于最优持久图的通信拓扑优化结果
Figure 16. Optimization results of communication topology based on optimal persistence graph
图 17 基于最优刚性图的通信拓扑优化结果
Figure 17. Optimization results of communication topology based on optimal rigid graph
图 18 基于最小生成树的通信拓扑优化结果
Figure 18. Optimization results of communication topology based on minimum spanning tree
图 21 9枚有翼飞行器在0～60 s内不同时刻编队构型位置截图
Figure 21. Screenshot of formation configuration positions of 9 winged aircraft during 0 to 60 s
表 1 基本队形描述
Table 1. Basic formation description
基本队形 形状 尺寸变量 2 
2相对1顺时针
旋转角度$\theta $3 
2和3相对1顺时针
旋转角度$\theta $注：红色三角形代表组长。 
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表 2 阵位设置情况
Table 2. Formation setting
作战单元 x/km z/km 几何中心 −30 30 威胁1 40 −60 威胁2 40 −70 威胁3 30 −50 威胁4 50 −50 威胁5 60 −30 威胁6 70 −40 威胁7 80 −40 威胁8 60 −40 威胁9 60 −50 威胁10 60 −60 威胁11 70 −50 威胁12 70 −60 威胁13 70 −70 威胁14 80 −50 威胁15 80 −60
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表 3 有翼飞行器性能指标
Table 3. Performance index of winged aircraft
${R_{\rm{DE}}}$/km ${\vartheta _{\mathrm{R}}}$/(°) ${P_{\rm{DE}}}$ ${K_{\rm{DE}}}$ ${m_{\rm{DE}}}$ $W$/m 180 65 0.95 1.6 3 0.8 ${\lambda^{\text{L}}}$/m ${A_{{\mathrm{RCS}}}}$/m2 ${m_{{\mathrm{des}}}}$ ${R_{{\mathrm{bat}}}}$/km $V$/(m·s−1) ${a_{\max }}$/(m·s−2) 5 0.3 0.5 300 2000 60
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表 4 探测拦截威胁性能指标
Table 4. Performance indicators of detection and interception threat
${R_{\rm{DE}}}$/km ${\vartheta _{\mathrm{R}}}$/(°) ${P_{\rm{DE}}}$ ${K_{\rm{DE}}}$ ${m_{\rm{DE}}}$ $W$/m 150 45 0.9 2 2 1 λL/m ${A_{{\mathrm{RCS}}}}$/m2 ${m_{{\mathrm{des}}}}$ ${R_{{\mathrm{bat}}}}$/km $V$/(m·s−1) ${a_{\max }}$/(m·s−2) 7 0.9 0.3 300 1000 120
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表 5 编队构型优化参数对比
Table 5. Comparison of formation configuration optimization parameters
编组
方案最大
适应度迭代
次数组员绕组长的
旋转角度/（°）各组长绕型
别初始位置的
旋转角度/（°）方案1 0.7059 17 296.4，312.8，
299.5172.2 方案2 0.7086 19 338.3，319.6，
302.7，338322.8
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表 6 时变编队构型参数设计结果
Table 6. Design results of time-varying formation vector parameters
飞行器 相对距离${A_i}$/km 相对相位${\varphi _i}$/（°） 飞行器1 10 −21.71 飞行器2 50 −142.78 飞行器3 48.84 −131.25 飞行器4 70.71 −97.78 飞行器5 78.59 −93.05 飞行器6 50 −52.78 飞行器7 58.82 −47.8 飞行器8 67.96 −44.12
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