This article deals with a guidance law for impact angle control (IAC) in the 3-D space. Extended from the 2-D IAC law, the proposed guidance law is derived using a quaternion. The general form of the IAC law comprises a biased proportional navigation guidance (PNG) law, wherein a component to control the impact angle is added to the PNG law. Since the biased term consists of a rotation angle and Euler axis obtained by a quaternion coordinate transformation between the missile's velocity vector and the desired impact angle, the magnitude of the guidance command depends on the rotation angle multiplied by the biased term. Therefore, from attempting to minimize the control energy, the optimal impact roll angle causing the rotation angle to be zero is mathematically derived. The Euler axis that satisfies this optimal impact roll angle is composed of two velocity vectors; the angle between the two velocity vectors is the minimum rotation angle. Numerical simulations are performed for stationary and moving targets according to the desired impact angle.

中文翻译：

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基于四元数的三维冲击角控制导引律

本文讨论 3-D 空间中碰撞角度控制 (IAC) 的导引律。从 2-D IAC 定律扩展而来，提议的指导定律是使用四元数推导出来的。IAC法则的一般形式包括偏向比例导航制导(PNG)法则，其中在PNG法则中添加了控制撞击角度的组件。由于偏置项由旋转角和欧拉轴组成，该轴是通过导弹速度矢量和所需撞击角之间的四元数坐标变换获得的，制导命令的大小取决于旋转角乘以偏置项。因此，通过尝试最小化控制能量，从数学上推导出导致旋转角为零的最佳冲击侧倾角。满足这个最优冲击侧倾角的欧拉轴由两个速度矢量组成；两个速度向量之间的角度是最小旋转角度。根据所需的撞击角度对静止和移动目标进行数值模拟。