Fixed-Time Circular Impact-Time Guidance with Look Angle Constraint

Abstract

A fixed-time nonlinear circular guidance law that satisfies the impact time constraint is proposed. By utilizing the geometric principle that the length of a circular arc connecting the missile and the target can be analytically calculated, the exact expression of time-to-go is obtained. Thus, the impact time error can be shaped to zero, and the missile can intercept the target at the desired time, which is crucial in a salvo attack. The settling time of the impact time error is proved to be bounded by a fixed time, which does not depend on initial conditions, but is only determined by two guidance parameters. Moreover, the criteria for choosing the guidance parameters values are established analytically, rather than by trial-and-error or empirically, which can provide valuable guidelines for guidance law designers. To address the look angle constraint, deviated pure pursuit (DPP) is employed, and switching logic between guidance laws is provided. Unlike many existing impact time control guidance laws, the formulation of the one proposed is based on nonlinear engagement kinematics, and the implementation does not execute numerical calculations, which can improve the guidance accuracy and reduce computation burdens on the guidance system. A series of nonlinear simulations are implemented to verify the effectiveness of the proposed guidance law.