
doi: 10.2514/1.59252
handle: 10203/190212
F OR decades, many advanced guidance laws with terminalimpact-angle constraints have been devised to maximize the warhead effect of antiship or antitank missiles and to ensure a high kill probability. The proposed suboptimal guidance with a terminal body-attitude constraint for reentry vehicles in [1] appears to be the first attempt to design an impact-angle-constrained guidance. In [2], an energy-optimal impact-angle control lawwas proposed by solving the linear quadratic optimal control problem with arbitrary missile dynamics. As an extension of this study, the authors also proposed an optimal impact-angle controller that can minimize the time-to-go weighted energy-cost function [3]. Using the Schwartz inequality and differential game theory, terminal-impact-angle-constrained guidance laws for maneuvering targets were developed in [4,5], respectively. To intercept a stationary target with zero terminal acceleration as well as a specified impact angle, the guidance law called the time-to-go polynomial guidance law was suggested in [6], where the acceleration command was assumed initially as a polynomial function of the time-to-go with two unknown coefficients. In [7], a modified proportional navigation (PN) guidancewith a time-varying bias, which is a function of relative range, was proposed using a nonlinear planar engagement and Lyapunov-like function. Although various guidance laws to control the impact angle have been developed so far, most of these laws are difficult to implement, especially for a passive homing missile equipped with an infrared seeker, because an accurate time-to-go estimation or range information is required. The authors of [8–10] proposed two-phase guidance schemes with terminal-angle constraints on the basis of the conventional PN guidance. The guidance scheme suggested in [8] comprises PN guidance with a navigation gainN < 2 for covering all impact angles from 0 to −π and PN with N 2 for intercepting stationary targets with a desired impact angle in surface-to-surface engagements. This guidance scheme was further extended to the case of moving targets in [9]. Using the biased PN (BPN) guidance, the authors of [10] developed a similar two-phase scheme in which the missile follows BPN with a constant bias for the initial homing phase and then switches to PN (i.e., BPN with zero bias) when the integral value of the bias satisfies a certain value calculated from initial engagement conditions and desired impact angle. Because these two-phase guidance schemes only use the line-of-sight (LOS) rate information for the impact-angle control, they can be applied to passive homingmissile systems. However, these guidance schemes have some drawbacks. 1) If the limitation of missile acceleration capability exists, a large miss distance or impact-angle error is generated. 2) A higher look angle, which may result in seeker lock-on failure or instability, is produced in the first-phase guidance. To overcome the drawbacks resulting from the look angle and acceleration limits, we first propose a bias-shaping method based on the two-phase BPNguidance scheme of [10], which can achieve both the terminal-angle constraint and look-angle limitation to maintain the seeker lock-on condition. Next, we investigate analytically the guidance performance of BPN with the proposed bias-shaping method in consideration of the limited acceleration capability. The proposed bias-shaping method consists of two time-varying biases and switching logic similar to the proposed logic of [11] and only requires the LOS rate information to generate the guidance command, thereby easily implementing the proposed law in practical passive homing missiles.
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