面向突防的滑翔制导炮弹弹道规划方法

尹秋霖; 陈琦; 王中原; 王庆海

doi:10.13700/j.bh.1001-5965.2023.0049

面向突防的滑翔制导炮弹弹道规划方法

doi: 10.13700/j.bh.1001-5965.2023.0049

南京理工大学能源与动力工程学院，南京 210094

基金项目: 国家自然科学基金(52202475)；江苏省自然科学基金(BK20200498)

详细信息

通讯作者:
E-mail：qichen@njust.edu.cn

中图分类号: TJ413⁺.6
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- 被引次数: 0
出版历程
- 收稿日期: 2023-02-14
- 录用日期: 2023-06-02
- 网络出版日期: 2023-06-26
- 整期出版日期: 2024-10-31

Trajectory programming method of gliding-guided projectiles for penetration

School of Energy and Power Engineering，Nanjing University of Science and Technology，Nanjing 210094，China

Funds: National Natural Science Foundation of China (52202475); Natural Science Foundation of Jiangsu Province (BK20200498)

More Information

Corresponding author: E-mail：qichen@njust.edu.cn

摘要

摘要:
针对滑翔制导炮弹在不可避免的威胁区域内选择突防方案的问题，从量化威胁值的角度建立了敌方防御手段的数学模型，基于模型设计了全程综合威胁值最低的规划指标，提出考虑目标防御威胁的弹道规划方法。为实现滑翔制导炮弹全程飞行过程中初始弹道倾角、偏角、火箭点火时刻、滑翔启控时刻等各参数的最佳匹配，建立了多阶段全弹道规划模型，并采用hp自适应伪谱法将最优控制问题转换为非线性规划问题求解。通过仿真验证了在该指标下滑翔制导炮弹对目标防御的规避效果，分析了影响有效性的因素。与传统弹道规划方法进行对比，证明了所提方法的优越性。
- 滑翔制导炮弹 /
- 突防 /
- 威胁建模 /
- 全弹道规划 /
- hp自适应伪谱法
Abstract:
Aiming at the problem of gliding-guided projectile penetration schemes in inevitable threat areas, mathematical models of the enemy’s defense are established from the perspective of quantifying the threat value. Based on the model, a cost function with the lowest comprehensive threat value in the whole process is designed. To accomplish the best possible matching of the initial trajectory inclination, deflection angle, rocket ignition time, gliding start time, and other parameters over the course of the flight, a multi-stage full trajectory planning model is created. Then, the hp adaptive pseudo-spectral method is used to transform the optimal control problem into a nonlinear programming problem. The evading effect of the projectile on target defense is verified by simulation, and the factors affecting the effectiveness are analyzed. The proposed method’s advantages over conventional trajectory programming techniques are also examined.
- gliding-guided projectile /
- penetration /
- threat modeling /
- full trajectory programming /
- hp adaptive pseudo-spectral method

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图 1 全弹道规划流程

Figure 1. Flow of full trajectory planning

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图 2 场景1仿真结果

Figure 2. Simulation results of Scene 1

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图 3 场景2仿真结果

Figure 3. Simulation results of Scene 2

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图 4 场景3仿真结果

Figure 4. Simulation results of Scene 3

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图 5 与传统方法对比结果（算例3）

Figure 5. Results compared with traditional methods (Example 3)

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表 1 滑翔弹参数

Table 1. Gliding-guided projectile parameter

参数	数值
$m/{\text{kg}}$	44.5
${m_{\rm{p}}}/{\text{kg}}$	7.23
$S/{{\text{m}}^2}$	0.013 3
${T_{\rm{p}}}/{\text{N}}$	1 219.2
${t_{\mathrm{b}}}/{\text{s}}$	14.068
${k_{\rm{c}}}$	35

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表 2 目标防御参数

Table 2. Target defense parameter

参数	数值
${R_{{\mathrm{r}}\max }}/{\text{km}}$	50
${R_{{\mathrm{g}}\min }}/{\text{km}}$	2
${R_{{\mathrm{g}}\max }}/{\text{km}}$	7
${R_{{\mathrm{p}}\min }}/{\text{km}}$	1
${R_{{\mathrm{p}}\max }}/{\text{km}}$	3

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表 3 仿真参数

Table 3. Simulation parameter

参数	数值	参数	数值
${x_0}/{\text{km}}$	0	${\psi _{{\mathrm{v}}0\max }}/({\text{°}})$	90
${y_0}/{\text{km}}$	0	${T_{\max }}/{\text{s}}$	300
${{\textit{z}}_0}/{\text{km}}$	0	$ {V}_{{\mathrm{f}}\mathrm{min}}/(\text{m}\cdot {\text{s}}^{-1})$	250
${x_{\mathrm{T}}}/{\text{km}}$	60	$\alpha _{\max }^*/({\text{°}})$	15
${y_{\mathrm{T}}}/{\text{km}}$	0	$\beta _{\max }^*/({\text{°}})$	10
${{\textit{z}}_{\mathrm{T}}}/{\text{km}}$	1	$\alpha $	0.1
$ {V}_{0}/(\text{m}\cdot {\text{s}}^{-1}) $	800	$\beta $	0.5
${\theta _{0\min }}/({\text{°}}) $	0	$\gamma $	0.2
${\theta _{0\max }}/({\text{°}})$	90	$\eta $	0.3
${\psi _{{\mathrm{v}}0\min }}/({\text{°}})$	−90

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表 4 场景1雷达位置

Table 4. Radar position of Scene 1

算例	雷达位置坐标/km
1	(10,0,2)
2	(10,0,−5)
3	(10,0,10)

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表 5 场景1全弹道规划结果

Table 5. Full trajectory programming results of Scene 1

算例	$ {\theta _0}/({\text{°}}) $	$ {\psi _{{\mathrm{v}}0}}/({\text{°}}) $	$ {t_{\mathrm{i}}}/{\mathrm{s}} $	$ {t_{\rm{o}}}/{\mathrm{s}} $	$ {t_{\mathrm{f}}}/{\mathrm{s}} $	威胁值
1	56.72	4.38	9.55	69.31	185.29	19.61
2	56.26	−14.53	9.80	67.10	191.34	16.13
3	56.02	20.09	10.51	65.09	201.38	12.25

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表 6 场景2雷达位置

Table 6. Radar position of Scene 2

算例	雷达位置坐标/km
1	(40,0,−1)
2	(40,0,2/3)
3	(40,0,−15)

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表 7 场景2全弹道规划结果

Table 7. Full trajectory programming results of Scene 2

算例	$ {\theta _0}/({\text{°}}) $	$ {\psi _{{\mathrm{v}}0}}/({\text{°}}) $	$ {t_{\mathrm{i}}}/{\mathrm{s}} $	$ {t_{\rm{o}}}/{\mathrm{s}} $	$ {t_{\mathrm{f}}}/{\mathrm{s}} $	威胁值
1	64.12	−9.44	16.34	66.42	196.29	29.40
2	64.13	−0.96	16.08	69.54	193.20	30.25
3	65.11	−27.99	22.71	69.60	221.87	8.85

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表 8 场景3雷达位置

Table 8. Radar position of Scene 3

算例	雷达位置坐标/km
1	(10,0,2)，(40,0,−1)
2	(10,0,−1)，(40,0,2)
3	(15,0,20)，(50,0,−5)
4	(10,0,−20)，(50,0,10)

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表 9 场景3全弹道规划结果

Table 9. Full trajectory programming results of Scene 3

算例	$ {\theta _0}/({\text{°}}) $	$ {\psi _{{\mathrm{v}}0}}/({\text{°}}) $	$ {t_{\mathrm{i}}}/{\mathrm{s}} $	$ {t_{\rm{o}}}/{\mathrm{s}} $	$ {t_{\mathrm{f}}}/{\mathrm{s}} $	威胁值
1	60.18	−3.51	10.80	66.33	188.56	45.93
2	60.21	1.59	10.87	61.53	188.83	45.87
3	61.99	1.99	13.65	61.42	191.05	35.39
4	61.69	−1.61	13.48	67.89	190.33	32.25

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表 10 雷达位置

Table 10. Radar positions

算例	雷达位置坐标/km
1	(10,0,2)
2	(40,0,−1)
3	(60,0,1)
4	(15,0,20)，(50,0,−5)

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表 11 传统方法全弹道规划结果

Table 11. Full trajectory programming results of traditional methods

方法	$ {\theta _0}/({\text{°}}) $	$ {\psi _{{\mathrm{v}}0}}/({\text{°}}) $	$ {t_{\mathrm{i}}}/{\mathrm{s}} $	$ {t_{\rm{o}}}/{\mathrm{s}} $	$ {t_{\mathrm{f}}}/{\mathrm{s}} $	能量消耗/（rad²·s）
2	63.07	−0.86	17.48	43.42	200.32	17.02
3	58.57	−0.95	10.77	50.83	196.32	22.24

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表 12 不同算例中与传统方法对比结果

Table 12. Results compared with traditional methods in different examples

算例	威胁值			方法1的能量消耗/（rad²·s）	方法1的飞行时间/s
算例	方法1	方法2	方法3	方法1的能量消耗/（rad²·s）	方法1的飞行时间/s
1	19.51	29.65	28.69	22.51	197.76
2	28.35	41.95	42.25	24.31	202.86
3	21.79	34.46	34.51	24.93	203.07
4	34.58	53.33	53.05	24.29	200.78

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