考虑时空协同的滑翔制导炮弹单炮多发快速弹道规划

doi:10.12382/bgxb.2023.0614

摘要/Abstract

摘要：

针对单炮多发应用场景,研究在时间、空间协同等多约束条件下的滑翔制导炮弹快速协同弹道规划问题。为平衡序列凸优化(Sequential Convex Programming,SCP)算法在快速性与最优性之间的冲突,提出一种改进的SCP算法;考虑到多约束条件下可行域较小、初值敏感性较高的特点,设计两种迅速且有效的迭代初值生成方案;为充分发挥弹群整体控制能力,采取集中式的协同规划策略,同步求解所有方程组,以达成全局规划目标。仿真实验结果表明,新算法能够较好地解决多约束条件下的协同规划问题,与现有文献中的常见算法进行对比,具备良好的收敛性能和较高的计算效率。

关键词: 滑翔制导炮弹, 协同弹道规划, 单炮多发, 多约束, 快速规划

Abstract:

The rapid cooperative trajectory planning problem of glide-guided projectiles under multiple constraint conditions, such as time-spatial coordination, in single-gun multi-shot application scenarios is investigated An improved SCP strategy is proposed to balance the conflict between rapidity and optimality in sequential convex programming (SCP) method. Considering the small feasible region and high sensitivity to initial values under multiple constraints, two fast and effective iterative initial value generation schemes are designed. Aiming to fully exploit the overall control capability of projectile group, a centralized cooperative planning strategy is employed to solve all equation sets simultaneously. Simulated results demonstrate that the proposed method can effectively address the cooperative planning problem under multiple constraints, exhibiting good convergence performance and high computational efficiency.

Key words: glide-guided projectiles, cooperative trajectory planning, single-gun multi-shot, multiple constraints, rapid planning

中图分类号:

TJ413.⁺6

尹秋霖, 陈琦, 王中原, 王庆海. 考虑时空协同的滑翔制导炮弹单炮多发快速弹道规划[J]. 兵工学报, 2024, 45(3): 798-809.

YIN Qiulin, CHEN Qi, WANG Zhongyuan, WANG Qinghai. Rapid Trajectory Planning for Glide-guided Projectiles in Single-gun Multi-shot Scenarios Considering Time-spatial Coordination[J]. Acta Armamentarii, 2024, 45(3): 798-809.

图/表 12

表1 制导炮弹参数

Table 1 Projectile parameters

m/kg	S/m²	k_c
40.4	0.0133	35

表2 仿真参数

Table 2 Simulation parameters

参数	数值	参数	数值
(x₀,y₀,z₀)/km	(0,15,0)	(x_T,y_T,z_T)/km	(45,0,1)
v₀/(m·s^-1)	300	v_fmin/(m·s^-1)	200
θ₀/(°)	0	ψ_v0/(°)	0
$α m a x *$ /(°)	10	$β m a x *$ /(°)	5

表2 仿真参数

Table 2 Simulation parameters

参数	数值	参数	数值
(x₀,y₀,z₀)/km	(0,15,0)	(x_T,y_T,z_T)/km	(45,0,1)
v₀/(m·s^-1)	300	v_fmin/(m·s^-1)	200
θ₀/(°)	0	ψ_v0/(°)	0
$α m a x *$ /(°)	10	$β m a x *$ /(°)	5

图1 单发弹丸轨迹曲线

Fig.1 Trajectory curves of a single projectile

表3 不同规划算法对比

Table 3 Comparison of different algorithms

算法	目标函数值	迭代次数	规划时间/s
APM	1.1811	8	5.9917
SCP	1.1735	21	3.1317
ISCP	1.1757	14	2.3757

图2 不同离散点个数对比

Fig.2 Comparison of different discrete points

图3 凸化误差结果对比

Fig.3 Comparison of convex error results

图4 集中式协同仿真结果

Fig.4 Centralized cooperatively simulated results

图5 分布式协同仿真结果

Fig.5 Distributed cooperatively simulated results

表4 不同协同策略对比

Table 4 Comparison of different cooperative strategies

协同策略	目标函数值	规划时间/s
集中式	4.4887	8.1033
分布式	4.9884	12.2533

图6 多约束协同弹丸运动曲线

Fig.6 Cooperative results under multi-constraints

表5 多约束仿真参数

Table 5 Simulation parameters under multi-constraints

参数	数值	参数	数值
(x₀,y₀,z₀)/km	(0,15,0)	(x_T,y_T,z_T)/km	(45,0,0)
v₀/(m·s^-1)	300	v_fmin/(m·s^-1)	200
θ₀/(°)	0	ψ_v0/(°)	0
$α m a x *$ /(°)	15	$β m a x *$ /(°)	10
θ_f1/(°)	[-90,-75]	ψ_vf1/(°)	[-5,5]
θ_f2/(°)	[-75,-60]	ψ_vf2/(°)	[5,15]
θ_f3/(°)	[-60,-45]	ψ_vf3/(°)	[-15,-5]
θ_f4/(°)	[-45,-30]	ψ_vf4/(°)	[15,25]
θ_f5/(°)	[-30,-15]	ψ_vf5/(°)	[-25,-15]

表5 多约束仿真参数

Table 5 Simulation parameters under multi-constraints

参数	数值	参数	数值
(x₀,y₀,z₀)/km	(0,15,0)	(x_T,y_T,z_T)/km	(45,0,0)
v₀/(m·s^-1)	300	v_fmin/(m·s^-1)	200
θ₀/(°)	0	ψ_v0/(°)	0
$α m a x *$ /(°)	15	$β m a x *$ /(°)	10
θ_f1/(°)	[-90,-75]	ψ_vf1/(°)	[-5,5]
θ_f2/(°)	[-75,-60]	ψ_vf2/(°)	[5,15]
θ_f3/(°)	[-60,-45]	ψ_vf3/(°)	[-15,-5]
θ_f4/(°)	[-45,-30]	ψ_vf4/(°)	[15,25]
θ_f5/(°)	[-30,-15]	ψ_vf5/(°)	[-25,-15]

表6 不同迭代初值对比

Table 6 Comparison of different initial guesses

迭代初值	目标函数值	生成耗时/s	规划时间/s
积分解	10.9118	0.6046	17.5424
TSG	10.7501	1.3525	12.3906
CVXGEN	10.6211	0.6603	11.1888

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