Modified Pure Proportional Navigation Guidance Law for Impact Time Control

Abstract

The analytic solution for the time-to-go of the pure proportional navigation guidance law against a stationary target is derived considering full nonlinear engagement kinematics without near-collision course approximation. The solution is globally exact for all flying directions with respect to the target and is generally exact for all possible values of the guidance gain. The time-to-go solution is used to design an almost-globally asymptotically stable guidance law for intercepting a stationary target with the impact time constraint. The impact-time-control guidance law is designed based on the pure proportional navigation guidance law with a modified nonlinear time-varying guidance gain. The proposed impact-time-control guidance law does not have the drawbacks of the existing impact-time-control guidance laws, such as a narrow capture zone, a limited set of feasible initial conditions, restricted achievable impact time, singularity, and nonzero terminal lateral acceleration command. Numerical simulations are performed to support the theoretical findings and to demonstrate the performance of the proposed method.