Collision-Geometry-Based Pulsed Guidance Law for Exoatmospheric Interception

Abstract

I N THE absence of aerodynamic control forces, divert thrusters are used to generate lateral acceleration required by interceptors in exoatmospheric engagements. The thrusters can be fired as pulses of constant lateral acceleration magnitude. The pulse width or duration is determined by the guidance law used. Several guidance laws based on the zero-effort miss (ZEM) have been proposed in the literature for exoatmospheric engagements. A ZEM-based midcourse guidance law for intercepting strategic targets and spacecraft is proposed by Newman [1,2]. Later, Hablani [3] proposed a ZEM-based pulsed guidance law with image processing delays for the endgame phase. Hablani [4] also demonstrated that zero-effort-miss guidance is superior to proportional navigation guidance in the endgame phase of an exoatmospheric interception using divert thrusters. Miss distance analysis of ZEM guidance with respect to various measurement errors is carried out by Hablani and Pearson [5]. Zarchan [6] has derived the ZEM-based pulsed guidance implemented with equally spaced pulses. ZEMcan be calculated from the instantaneous line-ofsight rate, the closing velocity, and the time to go. Lateral distance traveled by the interceptor depends on the width of the divert thruster pulse, which can be evaluated by equating the lateral distance to the ZEM. Because of the assumptions involved, interception cannot be guaranteed by firing a single pulse even for exact ZEM calculations. Subsequent pulses are fired to achieve a satisfactory miss distance. In this Note, an interceptor endgame pulsed guidance law is derived by attempting to attain the collision heading rather than negating ZEM. It is shown that this strategy is more effective than ZEM-based guidance for intercepting targets with higher heading angles off the nominal head-on case. The interceptor and the target are assumed to be constant speed lag free point masses. A planar engagement scenario is considered, assuming that the interceptor can perform uncoupled guidance commands in two perpendicular planes. The proposed guidance law, to determine the pulse width, is derived in steps by 1) obtaining the collision heading based on the collision triangle engagement geometry and parameters, and 2) computing the width of the pulse fired by the divert thruster to attain the collision heading. In the existing pulsed guidance laws, the pulses are fired either at fixed intervals [6] or every time the line-of-sight rate (or zero-effort miss) crosses a predefined threshold value [3]. In the present work, it is shown that firing pulses in quick succession results in minimum pulse widths and hence minimum control effort for interception. For comparative study, the derivation of pulsed guidance [6], based on ZEM steering, is described briefly in Sec. II. The proposed guidance law is derived in Sec. III, followed by some results on pulse firing sequence in Sec. IV. Simulation studies are carried out in Sec. V.