Rapid Trajectory Planning for Glide-guided Projectiles in Single-gun Multi-shot Scenarios Considering Time-spatial Coordination

doi:10.12382/bgxb.2023.0614

Abstract

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

CLC Number:

TJ413.⁺6

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.

Figures/Tables 12

Table 1 Projectile parameters

m/kg	S/m²	k_c
40.4	0.0133	35

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

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

Fig.1 Trajectory curves of a single projectile

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

Fig.2 Comparison of different discrete points

Fig.3 Comparison of convex error results

Fig.4 Centralized cooperatively simulated results

Fig.5 Distributed cooperatively simulated results

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

Fig.6 Cooperative results under multi-constraints

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]

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]

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

References 25

[1]	陈琦. 滑翔增程制导炮弹弹道优化及制导控制方法研究[D]. 南京: 南京理工大学, 2017.
	CHEN Q. Investigation on trajectory optimization and guidance & control scheme for a type of gliding guided projectiles[D]. Nanjing: Nanjing University of Science and Technology, 2017. (in Chinese)
[2]	赵建博, 杨树兴. 多导弹协同制导研究综述[J]. 航空学报, 2017, 38(1): 22-34.
	ZHAO J B, YANG S X. Review of multi-missile cooperative guidance[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(1): 22-34. (in Chinese)
[3]	张达, 刘克新, 李国飞. 多约束条件下的协同制导研究进展[J]. 南京信息工程大学学报(自然科学版), 2020, 12(5): 530-539.
	ZHANG D, LIU K X, LI G F. Recent advances of cooperative guidance under multiple constraints[J]. Journal of Nanjing University of Information Science and Technology(Natural Science Edition), 2020, 12(5):530-539. (in Chinese)
[4]	CHEN Q, WANG Z Y. Optimal trajectory for time-on-target of a guided projectile using direct collocation method[C]// Proceedings of 2013 International Conference on Mechatronic Sciences, Electric Engineering and Computer.Shenyang,China:IEEE, 2013.
[5]	许强强, 葛健全, 杨涛, 等. 面向突防的多导弹协同弹道规划方法[J]. 中国惯性技术学报, 2018, 26(4): 524-530.
	XU Q Q, GE J Q, YANG T, et al. Cooperative trajectory planning for penetration of multiple missiles[J]. Journal of Chinese Inertial Technology, 2018, 26(4):524-530. (in Chinese)
[6]	刘超越, 张成. 基于分布式并行伪谱-神经网络脉冲导弹多阶段协同轨迹优化[J]. 兵工学报, 2020, 41(10):1988-2000. doi: 10.3969/j.issn.1000-1093.2020.10.008
	LIU C Y, ZHANG C. Multi-stage cooperative trajectory optimization of dual-pulse missile based on decentralized parallel pseudo-spectral-neural network algorithm[J]. Acta Armamentarii, 2020, 41(10):1988-2000. (in Chinese)
[7]	BONALLI R, LEW T, PAVONE M. Analysis of theoretical and numerical properties of sequential convex programming for continuous-time optimal control[J]. IEEE Transactions on Automatic Control, 2022, 68(8): 4570-4585. doi: 10.1109/TAC.2022.3207865 URL
[8]	TSIOTRAS P, BAKOLAS E, ZHAO Y. Initial guess generation for aircraft landing trajectory optimization[C]// Proceedings of AIAA Guidance, Navigation, and Control Conference.Portland, OR,US:AIAA, 2011:6689.
[9]	DONG W, WEN Q Q, XIA Q L, et al. Multiple-constraint cooperative guidance based on two-stage sequential convex programming[J]. Chinese Journal of Aeronautics, 2020, 33(1): 296-307. doi: 10.1016/j.cja.2019.07.026 URL
[10]	MA Y Y, PAN B F, YAN R. Feasible sequential convex programming with inexact restoration for multistage ascent trajectory optimization[J]. IEEE Transactions on Aerospace and Electronic Systems, 2022, 59(2): 1217-1230.
[11]	张远龙, 谢愈. 滑翔飞行器弹道规划与制导方法综述[J]. 航空学报, 2020, 41(1): 45-57.
	ZHANG Y L, XIE Y. Review of trajectory planning and guidance methods for gliding vehicles[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(1): 45-57. (in Chinese)
[12]	XU G T, LONG T, WANG Z, et al. Trust-region filtered sequential convex programming for multi-UAV trajectory planning and collision avoidance[J]. ISA Transactions, 2022, 128: 664-676. doi: 10.1016/j.isatra.2021.11.043 URL
[13]	ZHANG D X, ZHANG Y L. PySCP:a multiple-phase optimal control software using sequential convex programming[J]. International Journal of Aerospace Engineering, 2022. DOI:10.1155/2022/2969809.
[14]	王庆海, 陈琦, 王中原, 等. 基于伪谱凸优化和L1罚函数的弹道规划方法研究[J]. 弹道学报, 2022, 34(1): 22-30. doi: 10.12115/j.issn.1004-499X(2022)01-004
	WANG Q H, CHEN Q, WANG Z Y, et al. Research on trajectory programming method based on pseudo-spectral convex optimization and l1 penalty function[J]. Journal of Ballistics, 2022, 34(1): 22-30. (in Chinese)
[15]	LIU S Y, LI S, LIU Y J, et al. Research on anti-ship missile cooperative trajectory planning based on gauss pseudo-spectral method[C]//Proceedings of the 2021 5th Chinese Conference on Swarm Intelligence and Cooperative Control. Singapore: Springer, 2022:1163-1176.
[16]	JIANG H, AN Z, YU Y N, et al. Cooperative guidance with multiple constraints using convex optimization[J]. Aerospace Science and Technology, 2018, 79: 426-440. doi: 10.1016/j.ast.2018.06.001 URL
[17]	李征, 彭博, 陈海东, 等. 可重复使用航天器时间协同飞行轨迹优化[J]. 计算机仿真, 2020, 37(1): 40-45.
	LI Z, PENG B, CHEN H D, et al. Time-coordination reentry trajectory design for reusable launch vehicle[J]. Computer Simulation, 2020, 37(1): 40-45. (in Chinese)
[18]	杨盛雷, 王海川, 刘剑威. 远程滑翔增程弹单炮多发同时弹着控制方法[J]. 指挥控制与仿真, 2010, 32(3): 99-103.
	YANG S L, WANG H C, LIU J W. Multiple round simultaneous impact control method of long-rang gliding extended range projectile[J]. Command Control & Simulation, 2010, 32(3): 99-103. (in Chinese)
[19]	韩子鹏. 弹箭外弹道学[M]. 北京: 北京理工大学出版社, 2014.
	HAN Z P. External ballistics of projectiles[M]. Beijing: Beijing Institute of Technology Press, 2014. (in Chinese)
[20]	LIU X F, LU P, PAN B F. Survey of convex optimization for aerospace applications[J]. Astrodynamics, 2017, 1(1): 23-40. doi: 10.1007/s42064-017-0003-8
[21]	钱杏芳, 林瑞雄, 赵亚男. 导弹飞行力学[M]. 北京: 北京理工大学出版社, 2013.
	QIAN X F, LIN R X, ZHAO Y N. Missile flight mechanics[M]. Beijing: Beijing Institute of Technology Press, 2013. (in Chinese)
[22]	RYOO C K. Optimal guidance laws with terminal impact angle constraint[J]. Journal of Guidance Control and Dynamics, 2005, 4(28):724-732.
[23]	MATTINGLEY J, BOYD S. CVXGEN: a code generator for embedded convex optimization[J]. Optimization and Engineering, 2012, 13(1):1-27. doi: 10.1007/s11081-011-9176-9 URL
[24]	CHO S, CHOI H. A convex programming-based approach to trajectory optimization for survivability enhancement of homing missiles[J]. International Journal of Aeronautical and Space Sciences, 2022, 23(5):992-1008. doi: 10.1007/s42405-022-00491-2
[25]	PEI P, FAN S P, WANG W, et al. Online reentry trajectory optimization using modified sequential convex programming for hypersonic vehicle[J]. IEEE Access, 2021, 9: 23511-23525. doi: 10.1109/Access.6287639 URL