基于扩展边界法的导弹可达性判定方法

张运杰; 张逢哲; 周颉鑫; 周锐; 邹亭

doi:10.13700/j.bh.1001-5965.2023.0630

基于扩展边界法的导弹可达性判定方法

doi: 10.13700/j.bh.1001-5965.2023.0630

1.
北京航空航天大学自动化科学与电气工程学院，北京 100191
2.
北京宇航系统工程研究所，北京 100076
3.
军事科学院国防科技创新研究院，北京 100071

基金项目:

国家自然科学基金(61773031)

详细信息

通讯作者:
E-mail：zhr@buaa.edu.cn

中图分类号: V448.2；TP18
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- 文章访问数: 172
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- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2023-09-28
- 录用日期: 2023-12-06
- 网络出版日期: 2023-12-18
- 整期出版日期: 2025-11-25

Reachability evaluation method for ballistic missile based on extended boundary method

1.
School of Automation Science and Electrical Engineering，Beihang University，Beijing 100191，China
2.
Beijing Institute of Astronautical Systems Engineering，Beijing 100076，China
3.
Defense Innovation Institute，Chinese Academy of Military Sciences，Beijing 100071，China

Funds:

National Natural Science Foundation of China (61773031)

More Information

Corresponding author: E-mail：zhr@buaa.edu.cn

摘要

摘要:
考虑6自由度多弹头弹道导弹模型，针对诸元计算中各分导弹头目标的可达性判定问题，提出一种新型的可达性快速判定方法。建立以俯仰偏航程序角控制的导弹分导模型，以较小程序角差值顺序打靶拟合导弹的实际可达区域并分析其特点。针对可达区域与目标点的几何关系，引入射线法设计了可编程化的可达性判定方法。在此基础上，设计了基于带方向边界扩展思想的可达区域动态拟合方法，并研究不可达区域动态扩展原理，实现了多目标可达性快速判定。通过仿真实验，验证了所提方法在可达性判定问题中具有更快的速度和更高的精度。
- 导弹可达区 /
- 扩展边界法 /
- 射线法 /
- 可达性判定 /
- 分导式导弹
Abstract:
A new rapid reachability evaluation method is proposed for the multiple-warhead ballistic missile to solve the problem of rapid reachability decisions for MIRVs(Multiple Independently Targetable Re-entry Vehicle) in ballistic data calculation. Firstly, the MIRV model, controlled by the pitching and yawing angle of the missile, is established to fit the actual reachability area and analyze its characteristics. The second is a programmable method that uses the enhanced Ray method to determine the geometrical link between targets and reachable areas. Based on this, an integrated dynamical fit algorithm is shown and the method of expanding inaccessible region for reachability evaluation based on the idea of expanding boundary to targets is proposed in order to achieve the quick computation of multi-target's reachability. Finally, MATLAB simulation results verify the quickness and accuracy of the reachability evaluation in combination with the proposed decision algorithm.
- reachable domain of missile /
- extended boundary method /
- ray algorithm /
- reachability evaluation /
- multi-headed ballistic missile

HTML全文

图 1 弹头可达区域示例

Figure 1. Example of warhead reachable area

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图 2 射线法示意图

Figure 2. Illustration of ray algorithm

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图 3 交点条件示意图

Figure 3. Illustration of intersection conditions

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图 4 判断点在线上示意图

Figure 4. Illustration of the judgment point on the line

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图 5 射线法判断可达性示意图

Figure 5. Illustration of the judgment reachability by ray algorithm

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图 6 最大外接矩形

Figure 6. Largest external rectangle

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图 7 不可达区域扩展原理示意图

Figure 7. Illustration of the principle of unreachable area expansion

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图 8 扩展边选择示意图

Figure 8. Illustration of extended edge selection

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图 9 中值扩展原理示意图

Figure 9. Illustration of the principle of median expansion

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图 10 算法流程图

Figure 10. The flow chart of algorithm

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图 11 可达区域扩展仿真图

Figure 11. Simulation figure of reachable area expansion

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图 12 不可达区域扩展仿真图

Figure 12. Simulation figure of unreachable area expansion

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图 13 多弹头边界拓展仿真图

Figure 13. Simulation figure of multi-warhead boundary expansion

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表 1 民兵-III型导弹参数

Table 1. Missile parameters of Minuteman III

发动机	发动机质量/kg	推进剂质量/kg	直径/m	推力/kN	工作时间/s
一级发动机	22680	22080	1.67	912.0	61.6
二级发动机	7050	6246	1.32	270.0	65.2
三级发动机	3650	3317	1.32	157.5	59.6

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表 2 扩展边界各阶段时间

Table 2. Duration of the phases of different expansion boundary stages

计算阶段	扩展弹道计算/s	不可达判定/s	可达区扩展操作/s	射线法可达性判定/s
初始可达区域	11.996227	0.035478		0.001861
第1次扩展	4.629599	0.003335	0.000450	0.001147
第2次扩展	4.334603	0.000415	0.000094	0.000544
第3次扩展	4.279724	0.000271	0.000055	0.000463
第4次扩展	4.848804	0.001997	0.000133	0.000451

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表 3 扩展效率

Table 3. Expanded efficiency

计算阶段	$ \dfrac{拟合区}{实际可达区}\bigg/ $%	弹道计算总次数	等效边界打靶拟合计算弹道次数
初始可达区域	70.59	6	6
扩展1次	92.02	7	≈11
扩展2次	97.97	8	≈17
扩展3次	99.49	9	≈33
扩展4次	99.87	10	≈65

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