多无人机投放下沉烟幕云团的时空覆盖最大化
Maximising the Spatiotemporal Coverage of a Descending Smoke Cloud Deployed by Multiple Drones

针对传统烟幕在精确打击防御中遮蔽时间短、协同效率低的问题，本文提出多无人机协同投放下沉烟幕云团优化方法，旨在最大化地面固定目标时空遮蔽收益。研究建立了包含导弹、无人机、烟幕弹及下沉云团的统一运动学模型，并综合均匀风场漂移、无人机最小转弯半径及导弹末段比例导引等约束，基于可见立体角设计了三维几何遮蔽准则。基于此，构建了“连续动作生成–鲁棒组合选择”分层优化框架，结合CMA-ES、增量式贪心算法与局部修复机制，实现了多机多弹协同投放优化。实验结果表明，优化方案在单机一弹、单机三弹、三机协同及五机多弹场景下，有效遮蔽时长分别达4.2 s、7.2 s、10.44 s和19.2 s，显著优于传统策略。蒙特卡洛评估揭示：小规模场景中引入鲁棒性可有效改善方案稳定性；然而，大规模时序拼接场景中，名义最优方案表现出明显脆弱性(外样本均值3.247 s，门槛可靠度0)，即使鲁棒设计，可靠度也仅提升至0.017。因此，多机协同烟幕遮蔽任务的优化必须在设计阶段充分考虑外界扰动，以兼顾遮蔽性能最大化与系统执行稳定性。
This paper studies a coordinated optimisation method for deploying sinking smoke clouds with multiple UAVs to maximise the spatiotemporal concealment of a fixed ground target against precision-guided threats. A unified kinematic model is established for missiles, UAVs, smoke grenades and sinking smoke clouds, with additional consideration of uniform wind drift, UAV minimum-turn-radius constraints and a terminal proportional-guidance extension for missiles. A three-dimensional geometric screening criterion is then developed based on the visible solid angle of the target from the missile perspective. To solve the resulting continuous-discrete coupled optimisation problem, a hierarchical framework of continuous action generation and robust combinational selection is proposed. The continuous layer uses CMA-ES to generate candidate actions, while the combinational layer employs incremental greedy selection with local repair. Numerical results show that the nominal effective screening durations in the single-UAV single-smoke, single-UAV three-smoke, three-UAV cooperative and five-UAV multi-smoke scenarios reach 4.2 s, 7.2 s, 10.44 s and 19.2 s, respectively, significantly outperforming fixed and random strategies. Monte Carlo evaluation reveals that introducing robustness can effectively improve plan stability in small-scale scenarios; however, in large-scale temporal stitching scenarios, the nominally optimal plan exhibits significant fragility (out-of-sample mean 3.247 s, threshold reliability 0), and even with robust design, reliability only increases to 0.017. Therefore, the optimisation of multi-drone collaborative smoke-screening tasks must fully consider external disturbances during the design stage to balance maximal screening performance with system execution stability.