Performance analysis of three-dimensional differential geometric guidance law against low-speed maneuvering targets

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.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    Struik, D. J. Lectures on classical differential geometry. Dover, 1988: 10–20.

    Google Scholar 

  2. [2]

    Adler, F. Missile guidance by three-dimensional proportionalnavigation. Journal of Applied Physics, 1956, 27(5): 500–507.

    Article  MATH  Google Scholar 

  3. [3]

    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.

    Article  Google Scholar 

  4. [4]

    Chiou, Y. C., Kuo, C.-Y. Geometric analysis of missile guidance command. IEEE Proceedings: Control Theory and Applications, 2000, 147(2): 205–211.

    MathSciNet  Google Scholar 

  5. [5]

    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.

    Article  Google Scholar 

  6. [6]

    Li, C., Jing, W., Wang, H., Qi, Z. Iterative solution to differential geometricguidance problem. Aircraft Engineering and Aerospace Technology, 2006, 78(5): 415–425.

    Article  Google Scholar 

  7. [7]

    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.

    Article  Google Scholar 

  8. [8]

    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.

    Article  Google Scholar 

  9. [9]

    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.

    Article  Google Scholar 

  10. [10]

    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.

    Article  Google Scholar 

  11. [11]

    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.

    Article  Google Scholar 

  12. [12]

    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.

    Article  Google Scholar 

  13. [13]

    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.

    Article  Google Scholar 

  14. [14]

    Shneydor, N. A. Missile guidance and pursuit: kinematics, dynamics and control. Horwood Publishing Limited, 1998.

    Google Scholar 

  15. [15]

    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.

    Article  MATH  Google Scholar 

  16. [16]

    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.

    Article  Google Scholar 

  17. [17]

    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.

    Article  Google Scholar 

  18. [18]

    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.

    Google Scholar 

  19. [19]

    Wang, W., Chen, L., Li, K., Lei, Y. One active debris removal system design and error analysis. Acta Astronautica, 2016, 128: 499–512.

    Article  Google Scholar 

  20. [20]

    Meng, Y., Chen, Q., Ni, Q. A new geometric guidance approach to spacecraft near-distance rendezvous problem. ActaAstronautica, 2016, 129: 374–383.

    Article  Google Scholar 

  21. [21]

    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.

    Article  Google Scholar 

  22. [22]

    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.

    Article  Google Scholar 

  23. [23]

    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.

    Article  Google Scholar 

  24. [24]

    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.

    Article  Google Scholar 

  25. [25]

    Ben-Asher, J., Levinson, S. New proportional navigation law for ground-to-airsystems. Journal of Guidance, Control, and Dynamics, 2003, 26(5): 822–825.

    Article  Google Scholar 

Download references

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Kebo Li.

Additional information

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.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

Keywords

  • differential geometric guidance law
  • low-speed maneuvering target
  • Lyapunov-like approach capturability