Quaternion Based Three-Dimensional Impact Angle Control Guidance Law

Abstract

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.