Differential Geometric Guidance Based on the Involute of the Target's Trajectory: 3-D Aspects

Abstract

This paper presents a novel approach to missile guidance utilising the differential geometry of curves that does not rely 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 is obtained by generating the trace of the correct involute. The missile is either on the trace immediately or can reach it through an alignment manoeuvre and both of these situations require only 2-D manoeuvring for planar targets. Following the trace may require a 3-D manoeuvre and this manoeuvre is the focus here. 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. Compared with PN, the missile trajectories generated by the involute law have unexpected, curved shapes. This results in longer engagement times than PN, but adds uncertainty to the evasion strategy.