A computational-geometry-based 3-dimensional guidance law to control impact time and angle

Abstract

In this paper, a new guidance law is proposed based on computational geometry with impact time and angle constraints against a stationary target in three dimensions. The law is based on the principle of following a specified trajectory toward the target, and this trajectory is composed of a log-aesthetic space curve segment and a collision line segment. The collision line formulates a direction identical to the desired impact angle, which leads to the satisfaction of the impact angle constraint. The log-aesthetic space curve is used to drive the missile from the initial velocity vector to the collision line. The impact time is controlled by adjusting the trajectory length, which is realized by tuning the end point position of the curve segment along the collision line. Moreover, the position range of the end point and the maximum curvature of the trajectory are considered to ensure that the trajectory is achievable and flyable. A numerical iterative method is used to determine the end point position and curve parameters of the required trajectory. Numerical simulations are demonstrated to illustrate the performance of the proposed method in simultaneous attack scenarios.