Three-dimensional Multi-missile Cooperative Guidance Law with Time and Space Constraints

This study focuses on the problem of multiple air-to-air missiles coordinated intercepting maneuvering targets in three-dimensional (3-D) space. A fixed time cooperative interception law with attack time and line-of-sight (LOS) angle limitations is proposed. Firstly, we extended the commonly used two-dimensional (2-D) space guidance model to 3-D space, and constructs a 3-D missile-target relative motion model. Secondly, the missile guidance model is decoupled to along and perpendicular to the LOS, and in the LOS direction, a cooperative guiding law based on fixed-time consistency theory is intended to guarantee that all missiles strikes the target at the same moment. Moreover, in the LOS normal direction, an adaptive approach rule is created, and the LOS angle of each missile is regulated to reaching to a given value in a defined time. According to the proposed fixed time fast non-singular terminal sliding mode surface, and spatial coordination is accomplished. In addition, based on Lyapunov stability theory, a detailed fixed time stability analysis is given. In the end, simulation is used to verify the feasibility and efficacy of the guideline law.