Differential geometric guidance based on the involute of the target's trajectory: 2-D aspects

This paper presents a novel approach to missile guidance utilising the differential geometry of curves and not relying on the line of sight (LOS) information. The target's trajectory is treated as a smooth curve of known curvature and the new algorithm is based on the involute of the target's curve. The missile's trajectory uses the concept of virtual target to generate the correct involute trace. It is shown that the missile is either on the trace immediately or can reach it through a flying in procedure. Following the trace may require a 3-D manoeuvre, not described here, while the 2-D aspects of the algorithm lead to very simple formulae. The reference scenario is a planar air-to-air engagement of point masses with a manoeuvrable target of the F-16 fighter class. Simulations for perfect target information show intercepts both for the involute law and PN guidance. PN based intercepts occur quicker, but the involute based trajectories are more difficult to evade and always result in a side impact.