Trajectory Planning Method for Boost Phase Interceptor Based on Adaptive Energy Allocation

doi:10.3969/j.issn.1009-086x.2025.03.012

Abstract

Abstract:

To overcome the difficulty in intercepting large maneuvering targets， a trajectory planning method based on adaptive energy allocation is proposed for the boost phase interceptors. According to the generalized nominal effort miss guidance， the burnout parameters for each stage are optimized and the fire tables with different energies are established. Before launching， an energy-reserved fire table is used for trajectory planning， and some energy is reserved to cope with the unknown maneuvers of the target in the future. Once the target's maneuvers have been identified， a more energy-efficient fire table is selected to re-perform trajectory planning based on the remaining flight time of the interceptor in boost phase， so that the reserved energy could be gradually released. The simulation results show a significant improvement in the effectiveness of intercepting large maneuvering targets.

Key words: energy allocation, adaptive, trajectory planning, large maneuvering target interception, boost phase, generalized nominal effort miss

摘要：

针对大机动目标难以拦截的问题，提出了一种基于自适应能量分配的拦截弹主动段弹道规划方法。基于广义标控脱靶量制导律，通过对各级关机点参数进行优化，建立不同能量的射表。在射前使用能量保留射表进行规划，预留部分能量以应对目标未来的未知机动。当发现目标机动之后，根据拦截弹主动段剩余飞行时间，自适应选择能量更优的射表进行重规划，逐步释放射前规划所预留的能量。仿真结果表明，该方法在拦截大机动目标的场景中显著提升了拦截能力。

关键词: 能量分配, 自适应, 弹道规划, 大机动目标拦截, 主动段, 广义标控脱靶量

CLC Number:

TJ765.3

Wanchun CHEN, Jia ZHENG, Xuehe ZHENG, Qi YU, Peng ZENG, Chao WANG. Trajectory Planning Method for Boost Phase Interceptor Based on Adaptive Energy Allocation[J]. Modern Defense Technology, 2025, 53(3): 103-111.

陈万春, 郑佳, 郑学合, 于琦, 曾鹏, 王超. 拦截弹主动段自适应能量分配弹道规划方法[J]. 现代防御技术, 2025, 53(3): 103-111.

Figures/Tables 12

Fig. 1 Fire table construction process of interceptor with different energy

Fig. 2 Online update of PIP process

Fig. 3 KEI missile dimensions

Table1 KEI booster parameters

参数	一级	二级	三级
直径/m	1.0	1.0	1.0
长度/m	6.8	1.9	3.1
总质量/kg	6 200	1 100	200
推进剂质量/kg	5 700	900	100
平均推力/kN	460	120	50
燃烧时间/s	34	21	8

Fig. 4 Missile burnout point velocity optimization

Fig. 5 80% energy fire table

Fig. 6 90% energy fire table

Fig. 7 100% energy fire table

Table2 Example of burnout parameter for KEI fire table with different energy

射表能量	$γ c 1$ /（°）	$γ c 2$ /（°）	$γ c 3$ /（°）	$h c 1$ /km	$h c 2$ /km	$h c 3$ /km
80%	61	52	51	35	107	150
90%	58	52	51	35	107	150
100%	56	51	50	34	107	150

Table2 Example of burnout parameter for KEI fire table with different energy

射表能量	$γ c 1$ /（°）	$γ c 2$ /（°）	$γ c 3$ /（°）	$h c 1$ /km	$h c 2$ /km	$h c 3$ /km
80%	61	52	51	35	107	150
90%	58	52	51	35	107	150
100%	56	51	50	34	107	150

Fig. 8 AOA/normal overload-time curve in target boost phase

Fig. 9 Height-range graph using 80% fire table

Fig. 10 Height-range graph using 100% fire table

References 17

1	谢经纬，陈万春. 大气层外拦截弹建模与攻防效能分析［J］. 北京航空航天大学学报， 2018， 44（9）： 1826-1838.
	XIE Jingwei， CHEN Wanchun. Exo-atmospheric Interceptor Modeling and Penetration and Defense Effectiveness Analysis［J］. Journal of Beijing University of Aeronautics and Astronautics， 2018， 44（9）： 1826-1838.
2	赵蒙，端军红，王明宇，等. 大气层外弹道导弹中段拦截弹道规划［J］. 兵工学报， 2022， 43（7）： 1589-1595.
	ZHAO Meng， DUAN Junhong， WANG Mingyu， et al. Trajectory Planning for Exoatmospheric Midcourse Ballistic Missile Interception［J］. Acta Armamentarii， 2022， 43（7）： 1589-1595.
3	杜润乐，刘佳琪，王永海，等. 大气层外拦截器最优中制导律设计［J］. 航天控制， 2011， 29（4）： 27-31.
	DU Runle， LIU Jiaqi， WANG Yonghai， et al. An Optimal Midcourse Guidance Law for Exoatmospheric Interceptor［J］. Aerospace Control， 2011， 29（4）： 27-31.
4	赵蒙，端军红，王明宇，等. 基于零控脱靶量的大气层外拦截中制导方法研究［J］. 系统工程与电子技术， 2023， 45（2）： 538-545.
	ZHAO Meng， DUAN Junhong， WANG Mingyu， et al. Research on Midcourse Guidance Method of Extra-atmospheric Interception Based on Zero Effort Miss［J］. Systems Engineering and Electronics， 2023， 45（2）： 538-545.
5	ZHAO Shilei， CHEN Wanchun， YANG Liang， et al. Optimal Midcourse Guidance Law for the Exo-atmospheric Interceptor with Solid-Propellant Booster［J］. Aerospace Science and Technology， 2022， 127： 107670.
6	NEWMAN B. Strategic Intercept Midcourse Guidance Using Modified Zero Effort Miss Steering［J］. Journal of Guidance， Control， and Dynamics， 1996， 19（1）： 107-112.
7	陈峰，肖业伦，陈万春. 基于零控脱靶量的大气层外超远程拦截制导［J］. 航空学报， 2009， 30（9）： 1583-1589.
	CHEN Feng， XIAO Yelun， CHEN Wanchun. Guidance Based on Zero Effort Miss for Super-Range Exoatmospheric Intercept［J］. Acta Aeronautica et Astronautica Sinica， 2009， 30（9）： 1583-1589.
8	YANG S M. Analysis of Optimal Midcourse Guidance Law［J］. IEEE Transactions on Aerospace and Electronic Systems， 1996， 32（1）： 419-425.
9	ANN S， LEE S， KIM Y， et al. Midcourse Guidance for Exoatmospheric Interception Using Response Surface Based Trajectory Shaping［J］. IEEE Transactions on Aerospace and Electronic Systems， 2020， 56（5）： 3655-3673.
10	ZHAO Shilei， CHEN Wanchun， YANG Liang. Endoatmospheric Ascent Optimal Guidance with Analytical Nonlinear Trajectory Prediction［J］. International Journal of Aerospace Engineering， 2022， 2022（1）： 5729335.
11	ZARCHAN P， Tactical and Strategic Missile Guidance［M］. 6th ed. Reston： AIAA， 2012.
12	胡锦川. 高超声速飞行器平稳滑翔弹道特性及全程弹道规划与制导方法研究［D］. 北京：北京航空航天大学， 2015.
	HU Jinchuan. Research on Steady-glide Trajectory Characteristics and Algorithm Design of Trajectory Planning and Explicit Guidance for Hypersonic Vehicle［D］. Beijing： Beihang University， 2015.
13	VINH N X， BUSEMANN A， CULP R D. Hypersonic and Planetary Entry Flight Mechanics［M］. Ann Arbor： University of Michigan Press， 1980.
14	李伟刚，葛幸，王瑞臣. 美国海基中段导弹防御系统发展现状及趋势［J］. 飞航导弹， 2012（11）： 72-76.
	LI Weigang， GE Xing， WANG Ruichen. Development Status and Trends of US Sea-Based Midcourse Defense System［J］. Aerodynamic Missile Journal， 2012（11）： 72-76.
15	齐艳丽. 美国导弹防御系统动能拦截弹研制与部署现状［J］. 中国航天， 2009（1）： 31-36.
	QI Yanli. Development and Deployment of Kinetic Weapons for US Missile Defense System［J］. Aerospace China， 2009（1）： 31-36.
16	张旭，曾鹏，魏明英，等. 美国KEI导弹发展研究及性能分析［J］. 现代防御技术， 2024， 52（5）： 31-39.
	ZHANG Xu， ZENG Peng， WEI Mingying， et al. Research on the Development and Performance Analysis of the KEI Missile in the United States［J］. Modern Defence Technology， 2024， 52（5）： 31-39.
17	赵石磊. 双脉冲拦截弹标控脱靶量制导方法及协同拦截策略研究［D］. 北京：北京航空航天大学， 2022.
	ZHAO Shilei. Research on Nominal Effort Miss Guidance Method and Cooperative Interception Strategy for Dual-Pulse Interceptor［D］. Beijing： Beihang University， 2022.

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