Trajectory-shaping guidance based on optimality formulation for cooperative attack of multiple interceptors

In this study, we present an optimal guidance structure that achieves impact angle and time constraints for the salvo attack of multiple missiles. As the first step in deriving a guidance law, we define a desired profile of the look angle that satisfies the impact angle and time constraints using a polynomial function of the relative range. The guidance command is configured based on the optimality formulation that achieves the desired profile of the look angle while minimizing the usage of the normal acceleration. The resulting trajectory under the proposed law is expressed as a polynomial form whose exponents can be selected to satisfy the desired constraints with the impact courses of various curvatures. In addition, the proposed law can achieve a wide range of terminal constraints since the time-to-go, which is difficult to estimate for a trajectory with a small radius of curvature, is not required for implementation. The numerical simulation results show that the proposed law achieves precise interception under various terminal conditions, validating the proposed law.