New results on three-dimensional differential geometric guidance and control problem

This paper presents a novel approach to the three-dimensional (3D) differential geometric (DG) guidance and control problem. The DG guidance commands are firstly studied in the time domain using the classical DG formulations, and the guidance curvature command is modified in order to meet the requirement of practical onboard computation. Then, DG flight control system is introduced using classical PID controller. Finally, a new necessary initial condition is derived to intercept a high-speed target, as well as to guarantee both the DG guidance commands are well defined throughout the engagement. Simulations results demonstrate that the DG guidance law works well in a realistic engagement, and performs better than conventional proportional navigation guidance law in the case of intercepting a maneuvering target. Moreover, the terms of the target's information in the DG guidance curvature command could be ignored without sacrificing the performance.