Research on a Differential Geometric Guidance Law Based on Fractional-Order Theory

Jikun Ye,Li Wanli,Tang Xiao

doi:10.1109/access.2020.3031611

Jikun Ye, Li Wanli + Show 1 more

Open Access

https://doi.org/10.1109/access.2020.3031611

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Abstract

In this paper, fractional-order calculus theory is used to investigate the geometric law for intercepting an agile target. In order to overcome the challenges presented by the divergence of line of sight rate (LOSR) of proportional navigation (PN), the fractional LOSR is used as a compensated term in the proposed fractional differential geometric guidance law (FDGGL). By adjusting the navigation gain of the FDGGL, the new proposed guidance law can be transformed into the traditional differential geometric guidance law (DGGL) and PN. The average overload and ballistic stability of the FDGGL are analyzed based on the fractional and control theory. Some analytical results about energy consumption and trajectory variation of the FDGGL were obtained. The simulation results shows that, compared with PN and DGGL, the FDGGL has better guidance performance when intercepting different maneuvering targets.

Highlights

With advances in science and technology, high speed maneuvering targets have becomes a real threat, and intercepting maneuvering targets is a challenging task [1], [2]
In this paper, a novel differential geometric guidance law is presented that aims to improveguidance performance based on the fractional order theory
The interception model of missile and target is established based on the differential geometry theory

Summary

INTRODUCTION

With advances in science and technology, high speed maneuvering targets have becomes a real threat, and intercepting maneuvering targets is a challenging task [1], [2]. In order to improve the robustness of intercepting the incoming target, Binfeng Pan designed a PID type fractional order guidance law by combining finite time convergence theory and fractional order theory, and verified the guidance performance of the designed fractional order guidance law with a six degree of freedom simulation [19] This method involves the calculation of the remaining flight time of interceptor, which will directly affect the final guidance accuracy. Reference [20] combines fractional order theory with the traditional PN shape, derives a fractional order extended proportional guidance law in three-dimensional space, and analyzes the average overload, trajectory straightness, and robustness of the guidance law. Based on differential geometry theory, this paper analyzes the geometric relationship between the interceptor and target engagement with the help of Frenet It designs the velocity direction expression of the interceptor when directly against the maneuvering target.

THEORY OF DIFFERENTIAL GEOMETRY

DESIGN OF THE DIFFERENTIAL GEOMETRY GUIDANCE LAW

NUMERICAL SIMULATION

Findings

CONCLUSION