# 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.

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## 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

Authors

### Corresponding author

Correspondence to Kebo Li.

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