Abstract
The performance of the three-dimensional differential geometric guidance law with proportional navigation formation against a target maneuvering arbitrarily with time-varying normal acceleration is thoroughly analyzed using the Lyapunov-like approach. The validation of this guidance law is firstly proved, and then the performance issues such as capturability, heading error control efficiency, line of sight rate convergence, and commanded acceleration requirement are analyzed, under the condition that the missile is initially flying toward the target with a speed advantage. It is proved that an intercept can occur and the line of sight rate and missile commanded acceleration can be limited in certain ranges, if the initial heading error is small and the navigation gain is sufficiently large. The nonlinear relative dynamics between the missile and the target is taken into full account, and the analysis process is simple and intuitive, due to the use of a convenient line of sight rotating coordinate system. Finally, the new theoretical findings are validated by numerical simulations.
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11 February 2022
A Correction to this paper has been published: https://doi.org/10.1007/s42064-022-0136-2
References
Struik, D. J. Lectures on classical differential geometry. Dover, 1988: 10–20.
Adler, F. Missile guidance by three-dimensional proportionalnavigation. Journal of Applied Physics, 1956, 27(5): 500–507.
Chiou, Y.-C., Kuo, C.-Y. Geometric approach to three-dimensional missile guidance problems. Journal of Guidance, Control, and Dynamics, 1998, 21(2): 335–341.
Chiou, Y. C., Kuo, C.-Y. Geometric analysis of missile guidance command. IEEE Proceedings: Control Theory and Applications, 2000, 147(2): 205–211.
Kuo, C.-Y., Soetanto, D., Chiou, Y.-C. Geometric analysis of fight control command for tactical missile guidance. IEEE Transactions on Control Systems Technology, 2001, 9(2): 234–243.
Li, C., Jing, W., Wang, H., Qi, Z. Iterative solution to differential geometricguidance problem. Aircraft Engineering and Aerospace Technology, 2006, 78(5): 415–425.
Li, C. Y., Jing, W. X., Wang, H., Qi, Z. A novel approach to the 2D differential geometric guidance problem. Transactions of the Japan Society for Aeronautical and Space Sciences, 2007, 50(167): 34–40.
Li, C.-Y., and Jing, W.-X. Fuzzy PID controller for 2D differential geometricguidance and control problem. IET Control Theory Application, 2007, 1(3): 564–571.
Li, C., Jing, W., Wang, H., Qi, Z. Gain-varying guidance algorithm using differential geometric guidance command. IEEE Transactions on Aerospace and Electronic Systems, 2010, 46(2): 725–736.
Dhananjay, N., Ghose, D., Bhat, M. S. Capturability of a geometric guidance law in relative velocity space. IEEE Transactions on Control Systems Technology, 2009, 17(1): 111–122.
Ye, J., Lei, H., Xue, D., Li, J., Shao, L. Nonlinear differential geometric guidance for maneuvering target. Journal of System Engineering and Electronics, 2012, 23(5): 752–760.
Ariff, O., Zbikowski, R., Tsourdos, A., White, B. Differential geometric guidance based on the involute ofthe target's trajectory. Journal of Guidance, Control, and Dynamics, 2005, 28(5): 990–996.
White, B. A., Zbikowski, R., Tsourdos, A. Direct intercept guidance using differential geometricconcepts. IEEE Transactions on Aerospace and Electronic Systems, 2007, 43(3): 899–919.
Shneydor, N. A. Missile guidance and pursuit: kinematics, dynamics and control. Horwood Publishing Limited, 1998.
Li, K. B., Chen, L., Bai, X. Z. Differential geometric modeling of guidance problem for interceptors. Science China Technological Sciences, 2011, 54(9): 2283–2295.
Li, K. B., Chen, L., Tang, G. J. Improved differential geometric guidance commands for endoatmospheric interception of high-speed targets. Science China Technological Sciences, 2013, 56(2): 518–528.
Li, K. B., Chen, L., Tang, G. J. Algebraic solution of differential geometric guidance command and time delay control. Science China Technological Sciences, 2015, 58(3): 565–573.
Li, K. B., Shin, H.-S., Tsourdos, A., Chen, L. Performance analysis of a three-dimensional geometric guidance law using Lyapunov-like approach. 22nd Mediterranean Conference on Control and Automation, 2014.
Wang, W., Chen, L., Li, K., Lei, Y. One active debris removal system design and error analysis. Acta Astronautica, 2016, 128: 499–512.
Meng, Y., Chen, Q., Ni, Q. A new geometric guidance approach to spacecraft near-distance rendezvous problem. ActaAstronautica, 2016, 129: 374–383.
Ha, I.-J., Hur, J.-S., Ko, M.-S., Song, T.-L. Performance analysis of PNG laws for randomly maneuvering targets. IEEE Transactions on Aerospace and Electronic Systems, 1990, 26(5): 713–721.
Kim, B. S., Lee, J. G., Han, H. S. Biased PNG law for impact with angular constraint. IEEE Transactions on Aerospace and Electronic Systems, 1998, 34(1): 277–288.
Song, S.-H., Ha, I.-J. A lyapunov-like approach to performance analysis of 3-dimension pure PNG laws. IEEE Transactions on Aerospace and Electronic Systems, 1994, 30(1): 238–248.
Oh, J. H., Ha, I. J. Capturability of the three-dimensiona pure PNG Law. IEEE Transactions on Aerospace and Electronic Systems, 1999, 35(2): 491–503.
Ben-Asher, J., Levinson, S. New proportional navigation law for ground-to-airsystems. Journal of Guidance, Control, and Dynamics, 2003, 26(5): 822–825.
Acknowledgements
This work was co-supported by the National Natural Science Foundation of China (Grant Nos. 61690210 and 61690213) and the National Basic Research Program of China ("973" Program, Grant No. 2013CB733100).
Kebo Li would like to thank Prof. Bang Wie of the Asteroid De ection Research Center of Iowa State University for his careful review of this paper. The authors also appreciate the anonymous reviewers for many constructive comments and corrections that substantially improved the quality of this paper.
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Kebo Li received the B.S., M.S., and Ph.D. degrees from National University of Defense Technology, Changsha, China, in 2008, 2011, and 2016, respectively. Now, he is a lecturer in the Department of Aerospace, College of Aerospace Science and Engineering, National University of Defense Technology. His main research interests include flight vehicle dynamics, guidance and control.
Wenshan Su received his B.S. and M.S. degrees from National University of Defense Technology, China, in 2012 and 2014, respectively. Now he is a Ph.D. candidate. His main research interests are flight vehicle dynamics, guidance and control.
Lei Chen received his M.S. and Ph.D. degrees in flight vehicle design from National University of Defense Technology, in 1997 and 2000, respectively. Now he is a professor at the college of Aerospace Science and Engineering. His research interests are flight vehicle dynamics, guidance and control, as well as space collision probability.
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Li, K., Su, W. & Chen, L. Performance analysis of three-dimensional differential geometric guidance law against low-speed maneuvering targets. Astrodyn 2, 233–247 (2018). https://doi.org/10.1007/s42064-018-0023-z
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DOI: https://doi.org/10.1007/s42064-018-0023-z