Trajectory Programming of Laser-guided Projectile Considering the Attenuation Effect of Clouds

doi:10.12382/bgxb.2022.1068

Abstract

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

CLC Number:

TJ413.⁺6

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.

Figures/Tables 16

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

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

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

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

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

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

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

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

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

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

Fig.4 Optimized results of different cloud cluster positions

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

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

Table 7 Constraint of drop angle

算例	θ_fU/(°)
1	-30
2	-45
3	-60

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

Fig.5 Optimized results of different radii of cloud cluster

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

Fig.6 Comparison of simulated results

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

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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