Performance analysis of three-dimensional differential geometric guidance law against low-speed maneuvering targets
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.
Keywordsdifferential geometric guidance law low-speed maneuvering target Lyapunov-like approach capturability
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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