An Optimal Geometrical Guidance Law for Impact Time and Angle Control

This article proposes an impact time and angle control guidance law based on geometry without estimating the time-to-go. A moving virtual target is artificially placed on the desired collision line, and the missile pursues the virtual target to satisfy the desired impact angle. The moving speed of the virtual target is also dynamically adjusted to cater for the impact time constraint. We prove that the proposed geometrical rule ensures target capturability and zero terminal guidance command. Then, the standard optimal control is leveraged to develop an analytical guidance command that drives the missile to converge to the desired collision course. Numerical simulations are conducted to validate the proposed guidance law.