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Flight Path Optimization Method for Dynamic Area Coverage Based on Multi-aircraft Radars
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摘要: 传统面向区域覆盖的多机航迹优化方法大多针对静态环境建立优化模型，在复杂动态环境下面临着模型失配的挑战。因此，该文提出了一种多机雷达协同区域动态覆盖航迹优化方法。首先，该方法引入衰减因子来表征机载雷达对动态环境的实际覆盖效果，将动态覆盖背景下的区域覆盖率作为优化函数，并结合待优化多维航迹控制参数约束，构建了多机雷达协同区域动态覆盖航迹优化的数学模型。然后，采用随机优化法对协同区域动态覆盖航迹优化问题进行了求解。最后，仿真实验表明，相对于采用预设航迹的多机雷达搜索模式，所提航迹优化方法能够显著提高动态区域的动态覆盖性能，且相较于面向静态环境的传统航迹优化模型，动态覆盖性能平均提升约6%。Abstract: Most traditional multi-aircraft flight path optimization methods are oriented toward area coverage, use static optimization models, and face the challenge of model mismatch under complex dynamic environments. Therefore, this study proposes a flight path optimization method for dynamic area coverage based on multi-aircraft radars. First, we introduce an attenuation factor to this method to characterize the actual coverage effect of airborne radar on a dynamic environment, and we take the area coverage rate under the dynamic area coverage background as the optimization function. After integrating the constraints of multi-dimensional flight path control parameters to be optimized, we built a mathematical model for dynamic area coverage flight path optimization based on multi-aircraft radars. Then, the stochastic optimization method is used to solve the flight path optimization problem of dynamic area coverage. Finally, the simulation results show that the proposed flight path optimization method can significantly improve the dynamic coverage performance in dynamic areas compared with the search mode using preset flight paths based on multi-aircraft radars. Compared with the traditional flight path optimization method oriented to static environments, the dynamic coverage performance of our proposed method is improved by approximately 6% on average.
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图 3 衰减因子随时刻差值变化曲线图
Figure 3. Curves of attenuation factor variation with time difference
图 5 零时刻无人机航迹控制参数示意图
Figure 5. Examples of flight path control parameters at the zero time
图 9 传统静态优化方法所得大致航迹图
Figure 9. Rough flight path of traditional static optimization method
图 10 3种搜索方法有效覆盖率曲线对比图
Figure 10. Comparison between curves of effective coverage rate variation of three searching methods
表 1 优化模型运行流程示意表
Table 1. Running process of the optimization model
步骤 流程内容 ① 计算基于时刻n的各时刻${\alpha _i}\left( n \right)$，$i = 1,2, \cdots ,n$ ② 设置待优化无人机编号$m = 1$ ③ 基于待优化无人机时刻$ n - 1 $的解，生成可行解数量为${q_{\max }}$的解空间${ {\boldsymbol{C} }_n} = \left\{ {{\boldsymbol{c}}'_1,{\boldsymbol{c}}'_2, \cdots ,{\boldsymbol{c}}_{ {q_{\max } } }'} \right\}$ ④ 求解待优化无人机时刻n的解${{\boldsymbol{c}}_n} \in {{\boldsymbol{C}}_n}$，使${{\boldsymbol{c}}_n}$对应的有效覆盖率为${{\boldsymbol{C}}_n}$中最大 ⑤ 令$m = m + 1$，若$m \le M$则返回步骤③ ⑥ 令$n = n + 1$，优化程序进入下一时刻 
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表 2 仿真参数设定表
Table 2. Simulation parameter settings
参数 设定值 ${R_0}$ 90 m ${\varphi _0}$ $\dfrac{2}{3}\pi$ ${t_d}$ 1 s ${L_{\max }}$ 200 m $\Delta {\psi _{\max }}$ $\dfrac{1}{4}\pi$ ${n_\alpha }$ 60 s $\gamma $ 10 ${q_{\max }}$ 100
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