Guidance Law Design for Varying-Speed Missile Based on Classic Differential Geometric Principle

Abstract

For the guidance law design problem of the varying-speed missile against the stationary target, a differential geometric guidance law (DGGL) design approach is proposed in this paper. The missile kinematic model and guidance model in the arc-length domain are first derived through the differential geometric curve theory (DGCT). The concept of guidance curvature is introduced. Then, considering the nonlinearity of the guidance model, the error dynamic approach is extended to the arc-length domain, and several typical desired error dynamic equations are introduced. On this basis, taking the optimal error dynamics approach as an example, the corresponding DGGLs are derived. The optimality of the designed guidance law is extended to the scenarios of nonlinearity and varying speed. Finally, the corresponding DGGLs are simulated and compared in varying-speed missile scenarios to demonstrate the effectiveness of the proposed approach.