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Bias-Shaping Method for Biased Proportional Navigation with Terminal-Angle Constraint

Authors: Tae-Hun Kim; Bong-Gyun Park; Min-Jea Tahk;

Bias-Shaping Method for Biased Proportional Navigation with Terminal-Angle Constraint

Abstract

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.

Country
Korea (Republic of)
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
158
Top 1%
Top 1%
Top 10%
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