Capturability of 3D RTPN Against True-Arbitrarily Maneuvering Target with Maneuverability Limitation

Abstract

The capturability of the three-dimensional (3D) realistic true proportional navigation (RTPN) guidance law is thoroughly analyzed. The so-called true-arbitrarily maneuvering target is considered. The target maneuvering acceleration is along an arbitrary direction in 3D space while its magnitude is arbitrary but upper-bounded. At first, using a novel Lyapunov-like approach, the upper-bound of commanded acceleration of 3D RTPN is deduced. Then, the selection range of navigation gain is analyzed, when the maneuverability limitation of interceptor is considered. After that, utilizing the inequality analysis technique, the capture region of 3D RTPN is obtained, under a more practical definition of capture, i.e., the relative range is smaller than an allowable miss-distance while the approaching speed is larger than a required impact speed. Unlike previous researches which present two-dimensional (2D) capture regions, the obtained capture region of 3D RTPN is a 3D one, where the three coordinates are the closing speed, the transversal relative speed, and the relative range. The obtained capture region could be taken as the sufficient-but-unnecessary condition of capture. The new theoretical findings are all explicitly expressed and are more general than previous results. © 2022, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.