终端航向角与时间约束的迭代再入制导方法

doi:10.12305/j.issn.1001-506X.2026.02.24

Abstract

Abstract:

An iterative reentry guidance method based on angle of attack profile correction and bank reversals search is proposed to meet constraints on the time and heading angle of the mid-terminal shift in hypersonic vehicle. To address the time and range constraints of the gliding phase, a dual-parameter drag acceleration profile with corridor-boundary interpolation is designed in the longitudinal-plane. The heading angle constraint is transformed into a nonlinear optimization problem of the lateral-plane bank angle reversal point, and a bank angle reversal search strategy based on simulated annealing-sequential quadratic programming （SA-SQP） hybrid optimization is developed. Furthermore, in order to reduce the coupling interference error between longitudinal and lateral guidance, a predictor-corrector method with real-time correction of the angle of attack profile is proposed to improve the guidance accuracy. Numerical simulation experiments verify that the algorithm can satisfy the constraints of flight time, range, heading angle, etc., and has high guidance accuracy and strong mission adaptability. Monte Carlo simulations further validate the adaptability and robustness of the method against initial state deviations and process disturbances.

Key words: reentry guidance, multi-constraint guidance, lateral guidance, angle of attack profile correction

CLC Number:

V 448.235

Wanru HAN, Junhui LIU, Jiayuan SHAN, Jianan WANG. Iterative reentry guidance method with terminal heading angle and time constraints[J]. Systems Engineering and Electronics, 2026, 48(2): 638-651.

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References 30

1	MEASE K D, CHEN D T, TEUFEL P, et al. Reduced-order entry trajectory planning for acceleration guidance[J]. Journal of Guidance, Control, and Dynamic, 2002, 25 (2): 257- 266.
2	CHENG X H, SONG X, WANG L. A model predictive solution to cooperative guidance of hypersonic reentry vehicle with impact angle and distance coordination[J]. Aerospace Science and Technology, 2024, 145, 108855. doi: 10.1016/j.ast.2023.108855
3	YU W B, YANG J, CHEN W C. Entry guidance based on analytical trajectory solutions[J]. IEEE Trans. on Aerospace and Electronic Systems, 2022, 58 (3): 2438- 2466. doi: 10.1109/TAES.2021.3133387
4	LI Z H, HE B, WANG M H, et al. Time-coordination entry guidance for multi-hypersonic vehicles[J]. Aerospace Science and Technology, 2019, 89, 123- 135. doi: 10.1016/j.ast.2019.03.056
5	PAN L, PENG S C, XIE Y, et al. 3D guidance for hypersonic reentry gliders based on analytical prediction[J]. Acta Astronautica, 2020, 167, 42- 51. doi: 10.1016/j.actaastro.2019.07.039
6	XIE Z H, WEI C Z, CUI N G, et al. An analytical reentry solution based online time-coordinated A^* path planning method for hypersonic gliding vehicles considering no-fly-zone constraint[J]. Aerospace, 2024, 11, 499. doi: 10.3390/aerospace11060499
7	XU H, CAI G B, MU C X, et al. Analytical reentry guidance framework based on swarm intelligence optimization and altitude-energy profile[J]. Chinese Journal of Aeronautics, 2023, 36 (12): 336- 348. doi: 10.1016/j.cja.2023.07.029
8	SHI P, XU J J, CHENG L, et al. Real-time lateral predictor-corrector entry guidance with terminal heading angle constraint[J]. IEEE Trans. on Aerospace and Electronic Systems, 2025, 62(2): 2106−2119.
9	XU T, CHEN Y Z, WANG Y M, et al. EMI threat assessment of UAV data link based on multi-task CNN[J]. Electronics, 2023, 12 (7): 1631. doi: 10.3390/electronics12071631
10	PENG H, ZHANG Y F, YANG S, et al. Battlefield image situational awareness application based on deep learning[J]. IEEE Intelligent Systems, 2020, 35 (1): 36- 43. doi: 10.1109/MIS.2019.2953685
11	WANG C X, FU W X, ZHANG T, et al. An AOA optimal positioning method incorporating station error and sensor deployment[J]. Aero- space, 2022, 9 (12): 766.
12	DING X H, DONG S. Improving positioning algorithm based on RSSI[J]. Wireless Personal Communications, 2020, 110, 1921- 1923.
13	LI Z T, ZHANG H B. Terminal guidance with attack time and impact angle constraints for hypersonic vehicle in dive phase[J]. International Journal of Aerospace Engineering, 2018, 9237109.
14	WANG R G, TANG S, ZHANG D. Short-range reentry guidance with impact angle and impact velocity constraints for hypersonic gliding reentry vehicle[J]. IEEE Access, 2019, 7, 47437- 47450. doi: 10.1109/ACCESS.2019.2909589
15	LIU Z Z, ZHENG G D, ZHANG B, et al. Predictor-corrector reentry guidance for hypersonic glide vehicles based on high-precision analytical solutions[J]. Aerospace Science and Technology, 2024, 155, 109545. doi: 10.1016/j.ast.2024.109545
16	CHENG X H, SONG X, CHEN S, et al. Geometric approach to lateral guidance for reentry vehicle[J]. IEEE Trans. on Aerospace and Electronic Systems, 2025, 61 (1): 1208- 1214. doi: 10.1109/TAES.2024.3449247
17	QIAO H, SUN P, LI X G. General reentry trajectory planning method based on improved maneuver coefficient[J]. IEEE Access, 2019, 7, 5447- 5456. doi: 10.1109/ACCESS.2018.2889926
18	XIE W J, WANG P C, YAN X L, et al. Rapid and near-analytical planning method for entry trajectory under time and full-state constraints[J]. Aerospace, 2024, 11, 580. doi: 10.3390/aerospace11070580
19	LIU X, LI X, ZHANG H J, et al. Entry guidance with terminal time constraint based on reduced-order dynamics[J]. IEEE Trans. on Aerospace and Electronic Systems, 2025, 61(3): 5949−5961.
20	LIANG Z X, LONG J T, ZHU S Y, et al. Entry guidance with terminal approach angle constraint[J]. Aerospace Science and Technology, 2020, 102: 105876.
21	YU W B, YAO Y Z, CHEN W C. Analytical cooperative entry guidance for rendezvous and formation flight[J]. Acta Astronautica, 2020, 171, 118- 138. doi: 10.1016/j.actaastro.2020.02.044
22	王新宇, 梁学智, 施锐, 等. 高超声速滑翔飞行器协同轨迹规划方法[J]. 航空兵器, 2022, 29 (5): 1- 10.
	WANG X Y, LIANG X Z, SHI R, et al. Collaborative trajectory planning method for hypersonic glide vehicle[J]. Aero Weaponry, 2022, 29 (5): 1- 10.
23	李青羊, 刘俊辉, 单家元, 等. 一种攻角剖面可实时修正的再入制导算法[J]. 战术导弹技术, 2024 (3): 99- 107.
	LI Q Y, LIU J H, SHAN J Y, et al. A reentry guidance algorithm with real-time correction of attack angle profile[J]. Tactical Missile Tech- nology, 2024 (3): 99- 107.
24	陈克俊, 刘鲁华, 孟云鹤. 远程火箭飞行动力学与制导[M]. 长沙: 国防工业出版社, 2014.
	CHEN K J, LIU L H, MENG Y H. Launch vehicle flight dynamics and guidance[M]. Changsha: National Defense Industry Press, 2014.
25	NOAA, NASA, USAF. U. S. Standard atmosphere[M]. Washington, D.C: Government Printing Office, 1976.
26	HARPOLD J C, GRAVES C A. Shuttle entry guidance[J]. Journal of the Astronautical Sciences, 1978, 27 (3): 239- 268.
27	乔浩. 高超声速滑翔导弹协同制导技术研究[D]. 西安: 西北工业大学, 2019.
	QIAO H. Cooperative guidance for hypersonic glide missile[D]. Xi’an: Northwestern Polytechnical University, 2019.
28	MORALES J L, NOCEDAL J. WU Y C. A sequential quadratic programming algorithm with an additional equality constrained phase[J]. IMA Journal of Numerical Analysis, 2012 (2): 553- 579.
29	AMOURA K, MANSOURI R, BETTAYEB M, et al. Closed-loop step response for tuning PID-fractional-order-filter controllers[J]. ISA Transactions, 2016, 64, 247- 257. doi: 10.1016/j.isatra.2016.04.017
30	PHILLIPS T H. A common aero vehicle (CAV) model, description, and employment guide[R]. Arlington: Schafer Corporation for AFRL and AFSPC, 2003: 1−12.

状态	参数	取值
初始状态	${h_0}$/km	45
	${v_0}$/（m/s）	5 200
	$ {\lambda _0} $/（°）	4
	${\phi _0}$/（°）	−4
	${\psi _0}$/（°）	30
终端状态	${h_{\text{f}}}$/km	26
	${v_{\text{f}}}$/（m/s）	2 000
	${\lambda _{\text{f}}}$/（°）	15
	${\phi _{\text{f}}}$/（°）	15

任务	${\lambda _0}$/（°）	${\phi _0}$/（°）	${\psi _0}$/（°）	${\psi _{\text{f}}}$/（°）	$s_{\text{f}}^*$/km	$t_{\text{f}}^*$/s
1	5	−3.2	30	25	2 326.1	622
2	−5	3	60	45	2 584.2	725
3	-8	25	−250	−255	2 667.1	765
4	8	38	−205	−220	2 673.2	751
5	−10	10	75	40	2 793.9	780
6	5	30	−210	−250	1 976.3	550

任务	$\Delta {h_{\text{f}}}$ /m	$ \Delta {v_{\text{f}}} $ /（m/s）	$\Delta {\psi _{\text{f}}}$ /（°）	$\Delta {s_{\text{f}}}$ /km	$\Delta {t_{\text{f}}}$ /s
1	590	−0.71	−0.11	1.74	1.8
2	355	−0.10	−0.93	2.43	2.1
3	−48	1.47	0.04	0.93	2.3
4	137	2.00	−1.04	0.91	2.8
5	−32	1.07	2.00	0.85	2.0
6	155	1.01	−1.80	0.84	0.9

调节系数	任务
调节系数	1	2	3	4	5	6
$ {k_1} $	0.636	0.057	0.000	0.107	0.142	0.663
$ {k_2} $	0.492	0.786	0.800	0.639	0.511	0.837

方法	$\Delta {h_{\text{f}}}$/m	$ \Delta {v_{\text{f}}} $/ （m/s）	$\Delta {\psi _{\text{f}}}$/ （°）	$\Delta {s_{\text{f}}}$/km	$\Delta {t_{\text{f}}}$/s
本文方法	590	−0.71	−0.11	1.74	1.8
对比方法	−75	−0.14	1.18	6.93	−1.3

Iterative reentry guidance method with terminal heading angle and time constraints

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偏差参数	$h$/m	$v$/（m/s）	$\lambda $/（°）	$\phi $/（°）	$\gamma $/（°）	$\psi $/（°）
$3\sigma $	500	40	1	1	1	1

状态参数	$\Delta {h_{\text{f}}}$ /m	$ \Delta {v_{\text{f}}} $ /（m/s）	$\Delta {\psi _{\text{f}}}$/（°）	$\Delta {s_{\text{f}}}$ /km	$\Delta {t_{\text{f}}}$ /s
平均误差	502	0.13	1.04	2.65	2.08

[1]	Shenming QUAN, Songyan WANG, Tao CHAO, Ming YANG. Reentry guidance method based on improved artificial potential field method [J]. Systems Engineering and Electronics, 2023, 45(7): 2158-2169.
[2]	ZENG Xian-fa， WANG Jie-yao， WANG Xiao-hu. Gliding guidance based on energy and analytical predictor-corrector [J]. Systems Engineering and Electronics, 2013, 35(12): 2582-2588.
[3]	ZHENG Zong-zhun,WANG Yong-ji,XIE Fu-qiang,LI Chuan-feng. Trajectory tracking law for hypersonic vehicles based on H_∞ robust dynamic inversion [J]. Journal of Systems Engineering and Electronics, 2010, 32(6): 1309-1313.

偏差参数	${C_D}$	${C_L}$	$\rho $
$3\sigma $	10	10	10