Control of impact angle using generalized biased proportional navigation against higher-speed targets

In this paper, a generalized biased proportional navigation (PN) guidance law to intercept higher-speed nonmaneuvering targets at a desired impact angle is presented. Inspired by controlling the turn rate of the relative velocity vector, the biased relative PN is introduced to design the relative heading angular rate, which is required to be proportional to the LOS rate as in the case of PN but with an extra bias term. Then the impact angle constrained interception for higher-speed nonmaneuvering targets is controlled through adding a time-varying term to the designed biased relative PN. Analysis of the time-varying term shows that the generalized biased PN has two guidance mode (PN mode and retro-PN mode), so that the useful features of the classical PN and the retro-PN guidance laws can be synthesized in the guidance design. In order to avoid the singularity of the guidance command, the impact angles are divided into two groups. The impact angle can be achieved by selecting appropriate guidance mode to determine the right direction of the trajectory. Extensive simulations are conducted to verify the design features of the algorithm.

I. Introduction

Capturing higher-speed targets is a challenging task, where the target speed is higher than the missile. When conventional guidance laws, designed for lower speed target interception, are used for interception of higher-speed targets, they may result in sharply degraded performance. However, there are very few papers that address this problem in the available literature. When the guidance laws are used to intercept the higher-speed target without impact angle constraint, they can be classified into two modes: proportional navigation (PN) mode and retro-PN mode. The trajectory guided by the PN mode terminates in a head-on engagement, while the trajectory guided by the retro-PN mode terminates in a head-pursuit engagement. The head-pursuit engagement defined in this paper mainly means the method, where high-speed targets are intercepted by placing the missile ahead of the target on the target trajectory. In case of the PN mode, a 3-D pure PN guidance law was given with the aid of a modified polar coordinate system in [1]. The 3-D pure PN can achieve global capturability by selecting an appropriate navigation gain. However, it is sensitive to the target maneuver and disturbance. In case of the retro-PN mode, a retro-PN guidance law in a 2-D engagement scenario is given in [2]. Analysis of the retro-PN guidance law against higher-speed targets showed that even though retro-PN takes more time than PN in achieving successful interception, it performs better than the classical PN law, in terms of capturability, lateral acceleration, and closing velocity [3]. Later the retro-PN guidance law was further extended to a 3-D engagement scenario [4].