New differential geometric guidance strategies for impact-time control problem

This paper presents a new differential geometric guidance design methodology applied to an impact-time control (ITC) problem of constant-speed missiles subject to lateral control acceleration. For such an ITC problem, a simple circular arc guidance equation of desired heading angle is derived, its approximate closed-form solutions are obtained, and a circular predictive guidance (CPG) law is developed. Furthermore, a new dual-virtual-target (DVT) concept is incorporated into the CPG law to guide a missile along a straight-line flight path (with zero lateral acceleration) during its terminal gliding phase toward a stationary target. The integrated CPG-DVT strategy does not involve any form of time-to-go estimation or numerical iterations, and it can be easily employed to accommodate a variety of practical missile engagement requirements.