(A) new design methodology for guidance-to-collision laws using optimal error dynamics

Abstract

In this paper, a methodology for designing an optimal collision-to-guidance law is presented for an interceptor that can maneuver vertically, horizontally, or in both vertical and horizontal directions against a target with arbitrary maneuver. A collision triangle is generated by predicting the target maneuver, and non-linear heading error dynamics is derived from the geometric conditions. In the proposed method, the guidance command, which minimizes the quadratic guidance command weighted by a specific function, nullifies the heading error from the collision course, and the heading error caused by the maneuver of the target is compensated in the feed-forward form. In addition, the guidance commands are devised so that various guidance strategies can be established according to the maneuvering freedom of the interceptor. The proposed design methodology can be applied to a target when the target's maneuver can be predicted by integrating the knowledge or assumptions about the target’s maneuver. The framework is applied to various feasible maneuvers to confirm its applicability. There are four targets to which this method is applied: a non-maneuvering target, a target that decelerates due to drag, a target that decelerates due to drag with a vertical maneuver, and a target with a ballistic trajectory after accelerating for a specific time. In addition, it is proved that the guidance law designed for the non-maneuvering target operates like the conventional guidance law, TPN, at a near collision course. The guidance laws designed for each maneuver are verified by performing numerical simulations. It is confirmed that the proposed method is more robust than the conventional guidance laws derived for non-maneuver targets by analyzing various problems that occur when implementing a methodology for practical application. Also, the sufficient condition for interception failure between the target model error and the interceptor's acceleration limit is shown analytically.