Extended differential geometric guidance law for intercepting maneuvering targets

doi:10.21629/JSEE.2018.05.15

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (5): 1046-1057.doi: 10.21629/JSEE.2018.05.15

• Control Theory and Application • Previous Articles Next Articles

Extended differential geometric guidance law for intercepting maneuvering targets

Jingshuai HUANG¹(), Hongbo ZHANG^1,*(), Guojian TANG¹(), Weimin BAO²()

¹ College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
² China Aerospace Science and Technology Corporation, Beijing 100048, China

Received:2017-01-18 Online:2018-10-26 Published:2018-11-14
Contact: Hongbo ZHANG E-mail:hjs_nudt@126.com;zhanghb1304@ nudt.edu.cn;tangguojian@nudt.edu.cn;baoweimin@cashq.ac.cn
About author:HUANG Jingshuai was born in 1993. He received his B.S. degree in aircraft design and engineering from Nanjing University of Aeronautics and Astronautics in 2013 and M.S. degree in aeronautical and astronautical science and technology form National University of Defense Technology in 2015, respectively. Now, he is a Ph.D. candidate in National University of Defense Technology. His research interests are in flight vehicle dynamics, intercept guidance and control. E-mail: hjs_nudt@126.com|ZHANG Hongbo was born in 1981. He received his Ph.D. degree in aeronautics and astronautics from National University of Defense Technology in 2009. Currently, he is an associate professor and a master tutor in the College of Aerospace Science and Engineering, National University of Defense Technology. His research interests include orbit dynamics and control, flight vehicle dynamics and control, and entry guidance. E-mail: zhanghb1304@ nudt.edu.cn|TANG Guojian was born in 1964. He received his Ph.D. degree in control theory and engineering from National University of Defense Technology in 2000. At present, he is a professor and doctoral supervisor in the College of Aerospace Science and Engineering, National University of Defense Technology. His research interests are mainly in flight vehicle dynamics, guidance, and control. E-mail: tangguojian@nudt.edu.cn|BAO Weimin was born in 1960. Currently, he is an academician of Chinese Academy of Sciences and a researcher in China Aerospace Science and Technology Corporation. In addition, he is a doctoral supervisor in the College of Aerospace Science and Engineering, National University of Defense Technology. His research interests are mainly in flight vehicle overall design. E-mail: baoweimin@cashq.ac.cn

Abstract

Abstract:

Without assumptions made on motion states of missile and target, an extended differential geometric guidance law is derived. Through introducing a line of sight rotation coordinate system, the derivation is simplified and has more explicit physical significances. The extended law is theoretically applicable to any engagement scenarios. Then, on basis of the extended law, a modified one is designed without the requirement of target acceleration and an approach is proposed to determining the applied direction of commanded missile acceleration. Qualitative analysis is carried out to study the capture performance and a criterion for capture is given. Simulation results indicate the two laws are effective and make up the deficiency that pure proportional navigation suitable for endoatmospheric interceptions cannot deal with high-speed maneuvering targets. Furthermore, the correctness of the criterion is validated.

Key words: missile guidance, maneuvering target, extended differential geometric guidance law, capture performance, proportional navigation

Jingshuai HUANG, Hongbo ZHANG, Guojian TANG, Weimin BAO. Extended differential geometric guidance law for intercepting maneuvering targets[J]. Journal of Systems Engineering and Electronics, 2018, 29(5): 1046-1057.

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References 29

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Setting	Missile	Target
Initial position/km	(1, 20, 1.5)	(4, 30, 1.5)
Initial speed/(km/s)	1	0.4
Initial pointing of t	(0.6395, 0.7543, 0.1486)	(1, 0, 0)
Initial pointing of n	(0.4726, – 0.2333, – 0.8498)	—
Maneuvering manner	—	T₁: (0, 2_g0, 3_g0); T₂: (0, 2_g0, 4_g0 cos t)

Guidance law	T1		T2
Guidance law	Miss distance/m	Δv/(m/s)	Miss distance/m	Δv/(m/s)
EDGGL	0.893 7	453.609 0	0.572 2	516.655 0
MEDGGL	2.045 8	678.697 6	1.122 5	512.967 2
ATPN	0.621 4	382.178 4	0.608 8	447.278 9
TPN	1.869 7	613.499 1	3.283 5	397.705 2
PPN	1.358 4	571.554 3	0.935 0	398.742 9

Setting	Missile	Target
Initial position/km	(3.75, 30, 2.25)	(33.75, 45, 2.25)
Initial speed/(km/s)	2.1	2.7
Initial pointing of t	(0.480 0, 0.870 3, 0.110 4)	(– 1, 0, 0)
Initial pointing of n	(– 0.541 0, 0.392 7, – 0.743 7)	—
Maneuvering manner	—	K₁: (0, _g0, 2_g0); K₂: (0, _g0, 3_g0 cos t)

Guidance law	K₁		K₂
Guidance law	Miss distance/m	Δv/(m/s)	Miss distance/m	Δv/(m/s)
EDGGL	0.169 9	329.913 9	0.094 5	456.046 2
MEDGGL	0.381 7	406.016 7	0.094 5	456.046 2
ATPN	0.381 7	406.016 7	0.252 8	503.499 4
TPN	0.497 2	350.245 5	0.111 9	432.855 9
PPN	27.063 2	436.560 7	106.775 7	594.267 8

Number	Initial t_m	Initial n_m	r0ω0
A1	(0.639 5, 0.754 3, 0.148 6)	(0.472 6, – 0.233 3, – 0.849 8)	0.149 1 < 0.6
A2	(0.589 5, 0.654 3, 0.473 7)	(0.609 9, 0.024 0, – 0.792 1)	0.473 7 < 0.6
A3	(0.500 5, 0.654 3, 0.566 9)	(0.706 7, 0.069 4, – 0.704 1)	0.574 3 < 0.6
A4	(0.499 5, 0.604 3, 0.620 7)	(0.631 0, 0.237 2, – 0.738 7)	0.625 6>0.6

Extended differential geometric guidance law for intercepting maneuvering targets

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Number	Initial t_m	Initial n_m	r0ω0
B1	(0.480 0, 0.870 3, 0.110 4)	(– 0.541 0, 0.392 7, – 0.743 7)	0.111 0 < 0.285 7
B2	(0.490 0, 0.848 0, 0.202 0)	(– 0.538 8, 0.476 8, – 0.694 6)	0.205 1 < 0.285 7
B3	(0.513 0, 0.820 3, 0.252 9)	(– 0.560 9, 0.543 3, – 0.624 7)	0.262 6 < 0.285 7
B4	(0.503 0, 0.810 3, 0.300 7)	(– 0.523 2, 0.562 4, – 0.640 4)	0.310 0>0.285 7