Coverage-based Cluster Cooperative Encirclement of High-speed and Highly Maneuverable Targets
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摘要: 集群协同围捕技术在空天防御领域逐渐扮演愈加关键的角色, 本文基于碰撞平面等效覆盖方法, 在三维空间内基于非线性动态模型提出一种新的高速强机动目标的覆盖策略. 首先基于三维圆锥体可达域提出新的碰撞平面覆盖等效方法, 阐释加速度覆盖和位置覆盖的区别与联系, 并从几何角度分析交会角对完全覆盖的影响; 其次, 考虑实际环境下飞行器过载弱于目标的情况, 基于偏置比例导引设计协同制导律, 能够实现对目标加速度的覆盖, 并基于覆盖率和零控脱靶量提出分段覆盖动态调节与快速收敛策略, 使得多飞行器在前期能够保持高覆盖率, 后期能够降低整体的脱靶量, 实现围捕覆盖的优势; 最后, 结合数值仿真进行了可行性验证.Abstract: The cooperative encirclement technology is playing an increasingly critical role in the air and space defense domain. In this paper, a new coverage strategy for high-speed, highly maneuvering targets in three-dimensional space is proposed based on the collision plane equivalent coverage method using nonlinear dynamic models. First, a new collision plane coverage equivalent method based on the three-dimensional cone of approach is proposed, explaining the differences and connections between velocity coverage and position coverage, and analyzing the influence of the intercept angle on complete coverage from a geometric perspective. Second, considering the case where the flight vehicle's overload is less than that of the target in real-world conditions, a cooperative guidance law based on the biased proportional guidance is designed to achieve velocity coverage of the target, and a dynamic adjustment and fast convergence strategy based on coverage rate and zero-control miss distance is proposed to enable the multi-vehicle to maintain a high coverage rate in the early stage and reduce the overall miss distance in the later stage, thereby achieving the advantage of encirclement coverage. Finally, the feasibility is verified through numerical simulation.
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图 1 三维空间内飞行器可达域
Fig. 1 The reachable domain of an interceptor in three-dimensional space
图 10 对最大正向机动的目标的围捕覆盖
Fig. 10 The encirclement coverage of the target with the maximum positive maneuverability
图 11 对负向最大机动的目标的围捕覆盖
Fig. 11 The encirclement coverage of the target with the maximum negative maneuverability
图 12 脱靶量关于目标机动的分布
Fig. 12 Distribution of miss distance with respect to target maneuvering
图 13 目标以随机时间切换的方波机动过载
Fig. 13 Overload of target maneuvering with random time-switched square wave pattern
图 14 对目标随机时间方波机动的围捕覆盖
Fig. 14 The encirclement for the random square wave maneuvering target
表 1 不同过载比下的飞行器数量
Table 1 The number of interceptors under different overload ratios
$\mu$ $[\sqrt{3}/2,\; 1)$ $[\sqrt{2}/2,\; \sqrt{3}/2)$ $[0. 609,\; \sqrt{2}/2)$ [0. 555, 0. 609) [0. 5, 0. 555) $n$ 3 4 5 6 7 
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表 2 初始的制导参数
Table 2 Initial guidance parameters
制导参数 ${{{M}}_{{{1}}}}$ ${{{M}}_{{{2}}}}$ ${{{M}}_{{{3}}}}$ ${{{M}}_{{{4}}}}$ ${{{M}}_{{{5}}}}$ ${{{M}}_{{{6}}}}$ $B_{y}$ 44.49338 0 − 44.4938 − 28.1938 28.1938 0 $B_{z}$ − 14.7910 − 46.5865 − 14.7910 38.0842 38.0842 0 $\eta_{My,\; 0}\; ({}^\circ)$ 9.4049 0 − 9.4049 − 5.8450 5.8450 0 $\eta_{Mz,\; 0}\; ({}^\circ)$ − 3.0309 − 9.8796 − 3.0309 7.9790 7.9790 0
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表 3 目标以最大加速度机动的情况下的脱靶量
Table 3 Miss distance under target maximum acceleration maneuver
机动形式 调节策略 有效拦截目标的飞行器 对应脱靶量 最大正向机动 预设调节 $M_3$ 1.18 m 动态调节 $M_2,\; M_3$ 0. 95 m, 1.12 m 最大负向机动 预设调节 $M_5$ 1.35 m 动态调节 $M_5$ 1.22 m
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表 4 目标以随机方波机动的情况下的脱靶量
Table 4 Miss distance under target maneuvering with random square wave pattern
机动形式 调节策略 有效拦截目标的飞行器 对应脱靶量 随机方
波机动预设调节 $M_6$ 0.85 m 动态调节 $M_2,\; M_3,\; M_6$ 0.62 m, 0.73 m, 0.80 m
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