Differential geometric guidance law design for varying-speed missile

Abstract

A unified differential geometric guidance law (DGGL) design framework for varying-speed missiles against stationary targets is proposed in this paper. The varying-speed missile guidance model is established in the arc-length domain with the help of the classical differential geometry curve theory. It is strictly proven that DGGL is a natural and intuitive choice for varying-speed missiles when intercepting stationary targets since the influence of missile speed is directly eliminated in the guidance model and also during the guidance law design process. Hence, the guidance performance of DGGL will remain the same, no matter how the missile speed changes. After that, the error dynamics approach, which is widely used in the guidance law design field for constant-speed missiles in the time domain, is extended to the arc-length domain for DGGL design. Besides, the nonlinearity of the guidance model is fully considered when designing DGGL, hence the guidance errors caused by linearizations and small-angle assumptions are avoided. Then, taking the representative optimal error dynamics (OED) as an example, the corresponding OED-based DGGLs for zero-effort-miss-control, impact-angle-control, and flying-range-control are respectively derived. Finally, the derived illustrative guidance laws are simulated and compared with their time-domain counterparts to verify the effectiveness and superiority of the proposed unified DGGL design framework.