Composite Guidance Scheme for Impact Angle Control Against a Nonmaneuvering Moving Target

Abstract

I N ADVANCED guidance law designs, impact angle control has been widely required to maximize the effect of thewarhead and to achieve a high kill probability. Since the first paper for impact angle control [1] was published, to the best of our knowledge, many guidance laws with impact angle constraint have been studied. Ryoo et al. [2] proposed a pure energy optimal guidance law with impact angle constraint. As an extension of this work, Ryoo et al. [3] proposed an optimal impact angle control guidance law minimizing the time-to-go weighted energy cost function. Lu et al. [4] developed three-dimensional guidance laws, which were based on proportional navigation (PN) with adaptive guidance parameters, to achieve impact angle requirements. Ratnoo and Ghose proposed a two-phase guidance law for capturing all possible impact angles against a stationary target [5] and a nonstationary nonmaneuvering target [6]. The proposed guidance law used PN with N < 2 for the initial phase to cover impact angles from zero to −π through an orientation trajectory and PNwithN ≥ 2 for the final phase to intercept the target with the desired impact angle. Erer andMerttopcuoglu [7] proposed a similar two-phase guidance law switching from biased PN to PN when the integral value of the bias met a certain value determined by engagement conditions. Most of research mentioned has focused on the impact angle as well as a zero terminal miss distance. The impact angle control, however, made the missile trajectory highly curved, which might have then missed the target within the seeker’s lookangle limit. Since this leads to the mission failure, it is very important to consider the missile’s physical constraints, such as the seeker’s look-angle and maximum acceleration limits. Recently, studies considering the look-angle limits as well as the impact angle have been carried out. Park et al. [8] proposed a composite guidance law comprising PN with N 1 to maintain the constant look angle and PNwithN ≥ 2 to intercept the target with the desired impact angle. In [9], the error feedback loop of the look angle was included in PN with N 1 for robustness and converging from the arbitrary look angle to the desired one. In [10], a pure energy optimal guidance lawwith an impact angle constraint and the seeker’s look-angle limit was developed using optimal control theory with state variable inequality constraint. Kim et al. [11] proposed a biasshaping method, based on the work in [7], to consider the look-angle and acceleration limits. Tekin and Erer [12] presented a two-phase guidance law with a numerical process for calculating navigation gains to handle the look-angle limits and acceleration constraints. Also, Erer et al. [13] proposed another two-phase guidance scheme to address the look-angle constraint problem, which can select an initial phase guidance lawbetween PNandbiasedPN.Ratnoo [14] dealt with a similar problem to [8] and showed analytic guarantees for achieving all impact angles with any finite field-of-view (FOV) limit. These works have been studied against stationary targets, so the impact angle errors may appear at the instant of interception if the guidance laws presented in [8–14] are applied to the case of moving targets. In this Note, a composite guidance scheme, studied in [8,9], is extended to the case of a nonmaneuvering moving target. The proposed guidance scheme is composed of modified deviated pure pursuit (DPP) with the error feedback loop of the look angle for the initial guidance phase and PN with N ≥ 3 for the final guidance phase: the first phase is to maintain the constant look angle of the seeker, and the second is to intercept themoving targetwith a terminal angle constraint. The switching of guidance phases occurs when satisfying a specific line-of-sight (LOS) angle determined by engagement conditions. Guidelines on the gain tuning of modified DPP and calculation of themaximumachievable impact angle, which is calculated by taking into account the seeker’s look-angle and maximum acceleration limits, are also investigated for guidance designers.