考虑云团衰减作用的激光制导炮弹弹道规划

doi:10.12382/bgxb.2022.1068

摘要/Abstract

摘要：

针对多云天气条件下,云团对激光信号产生较大衰减作用从而影响末制导性能这一问题,提出一种考虑云团对激光衰减作用的滑翔增程激光制导炮弹弹道规划方法。经过合理假设建立云团近似模型,在此基础上设计云团规避—控制能量最优复合规避目标函数(Compound Evasion Objective Function, CEOF)。根据激光导引头工作特性和制导炮弹的飞行特性建立弹道规划模型,采用Radau伪谱法将弹道规划问题转化为非线性规划问题(Non-linear Programming,NLP)。调用NLP求解器SNOPT求解。选取多组云团算例进行仿真分析,仿真结果验证所提弹道规划方法的有效性。研究结果表明,与传统弹道规划方法进行仿真对比,新的弹道规划方法以增加较少动能损耗、控制能量消耗和攻击时长为代价,大幅减少了云团对激光的衰减作用,验证了其优越性。

关键词: 激光制导炮弹, 云团, 弹道规划, Radau伪谱法

Abstract:

Aiming at the problem that clouds have a great attenuation effect on laser signal and affect the performance of terminal guidance in cloudy weather, a trajectory programming method of gliding extended range laser-guided projectile considering the attenuation effect of clouds on laser is proposed. A cloud approximation model is established based on the reasonable assumption, and an optimal compound evasion objective function (CEOF) of cloud evasion-control energy is designed. A trajectory programming model is established according to the working characteristics of laser seeker and the flight characteristics of guided projectile,and the trajectory programming problem is transformed into a nonlinear programming problem (NLP) by using Radaupseudospectral method. Finally, the NLP solver SNOPT is used to solve the NLP. Several groups of cloud examples are selected for simulation analysis, and the simulated results are used to verify the effectiveness of the proposed trajectory programming method. Compared with the traditional trajectory programming methods, the simulated results show that the trajectory programming method proposed in this paper reduces the attenuation of clouds on laser greatly at the cost of increasing less kinetic energy loss, and controlling energy consumption and attack time, which verifies its superiority.

Key words: laser-guided projectile, cloud, trajectory programming, Radau pseudo-spectral method

中图分类号:

TJ413.⁺6

王庆海, 陈琦, 王中原, 尹秋霖. 考虑云团衰减作用的激光制导炮弹弹道规划[J]. 兵工学报, 2024, 45(2): 474-487.

WANG Qinghai, CHEN Qi, WANG Zhongyuan, YIN Qiulin. Trajectory Programming of Laser-guided Projectile Considering the Attenuation Effect of Clouds[J]. Acta Armamentarii, 2024, 45(2): 474-487.

图/表 16

图1 滑翔增程激光制导炮弹弹道示意图

Fig.1 Trajectory diagram of gliding extended range laser-guided projectile

图2 球形云团对激光衰减能力函数示意图

Fig.2 Schematic diagram of laser attenuation function of spherical cloud cluster

图3 半主动激光末制导示意图

Fig.3 Schematic diagram of semi-active laser terminal guidance

表1 制导炮弹参数

Table 1 Parameters of guided projectile

m₀/kg	m_c/(kg·s^-1)	$F p *$ /N	s/m²	t₅/s
51.73	-0.482	1219.2	0.0133	20

表1 制导炮弹参数

Table 1 Parameters of guided projectile

m₀/kg	m_c/(kg·s^-1)	$F p *$ /N	s/m²	t₅/s
51.73	-0.482	1219.2	0.0133	20

表2 弹道变量的上下边界

Table 2 The upper and lower bounds of ballistic variables

上界与下界	v/(m·s^-1)	θ/rad	ψ_v/rad	x/km	y/km
上界	800	π/2	π/2	100	50
下界	200	-π/2	-π/2	0	0
上界与下界	z/km	m/kg	α/rad	β/rad	t/s
上界	100	51.73	π/12	π/12	300
下界	-100	44.5	-π/12	-π/12	0

表3 各阶段持续时长的上下边界

Table 3 Upper and lower bounds of the duration of each phase

上界与下界	$t d (1)$ /s	$t d (2)$ /s	$t d (3)$ /s	$t d (4)$ /s	$t d (5)$ /s
上界	300	14.068	300	300	300
下界	1	14.068	5	0	0

表3 各阶段持续时长的上下边界

Table 3 Upper and lower bounds of the duration of each phase

上界与下界	$t d (1)$ /s	$t d (2)$ /s	$t d (3)$ /s	$t d (4)$ /s	$t d (5)$ /s
上界	300	14.068	300	300	300
下界	1	14.068	5	0	0

表4 静态参数变量上下边界

Table 4 Upper and lower bounds of static parameter variables

上界与下界	θ₅/rad	ψ_v5/rad
上界	-π/6	π/2
下界	-π/2	-π/2

表5 云团参数

Table 5 Parameters of clouds

算例	R_c/m	A	p_f	x_c/km	y_c/km	z_c/km
1	1000	1.0	1.0	50.0	2.0	0.0
2	1000	1.0	1.0	50.0	2.0	2.0
3	1000	1.0	1.0	50.0	2.0	-2.0

图4 不同云团位置优化结果

Fig.4 Optimized results of different cloud cluster positions

表6 时间节点最优解

Table 6 Optimal solution of time nodes

算例	$t d (1)$ /s	$t d (2)$ /s	$t d (3)$ /s	$t d (4)$ /s	$t d (5)$ /s
1	21.823	35.891	40.891	163.089	183.089
2	21.212	35.280	40.280	155.401	175.401
3	21.208	35.276	40.276	155.401	175.401

表6 时间节点最优解

Table 6 Optimal solution of time nodes

算例	$t d (1)$ /s	$t d (2)$ /s	$t d (3)$ /s	$t d (4)$ /s	$t d (5)$ /s
1	21.823	35.891	40.891	163.089	183.089
2	21.212	35.280	40.280	155.401	175.401
3	21.208	35.276	40.276	155.401	175.401

表7 落角约束

Table 7 Constraint of drop angle

算例	θ_fU/(°)
1	-30
2	-45
3	-60

表8 云团参数

Table 8 Parameters of clouds

云团	R_c/m	A	p_f	x_c/km	y_c/km	z_c/km
1	1000	1.0	0.1	50.5	2.5	0
2	1000	5.0	0.5	50.0	2.0	-1.0
3	1000	0.5	0.5	50.0	2.0	1.0

图5 不同云团半径优化结果

Fig.5 Optimized results of different radii of cloud cluster

表9 云团参数

Table 9 Parameters of clouds

云团	R_c/m	A	p_f	x_c/km	y_c/km	z_c/km
1	1200	1.0	2.0	50.0	3.0	-6.0
2	1000	1.0	0.1	50.0	3.0	6.0
3	1000	1.0	0.2	50.2	2.0	0
4	2000	1.0	1.0	50.0	2.0	-1.0
5	1200	2.0	1.0	60.0	3.0	0
6	1000	1.0	0.1	50.0	2	1.0
7	2000	1.0	1.0	50.0	3.0	0
8	2000	1.0	0.2	51.0	3.5	-5.0

图6 对比仿真优化结果

Fig.6 Comparison of simulated results

表10 评价指标

Table 10 Evaluation indexes

目标函数	J_acl	J_CPOOF	J_MATOF	$v f 5$
CEOF	1.272	8.329	185.689	284.177
CPOOF	14.206	3.877	168.309	287.295
MATOF	14.150	6.304	164.026	286.791

表10 评价指标

Table 10 Evaluation indexes

目标函数	J_acl	J_CPOOF	J_MATOF	$v f 5$
CEOF	1.272	8.329	185.689	284.177
CPOOF	14.206	3.877	168.309	287.295
MATOF	14.150	6.304	164.026	286.791

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