Three Dimensional Nonlinear Guidance Law for Exact Impact Time Control

Abstract

This paper presents a nonlinear guidance law for controlling the impact time of a missile-target engagement in three dimensions. The guidance law is initially formulated for a two-dimensional encounter before being extended to a three-dimensional scenario. The guidance law is constructed such that nonlinear kinematics are neither linearized nor approximated. The guidance law offers a precise closed-form expression for impact time, which is the principal contribution of this work. Choosing an integrable heading error profile is the central concept of this research for determining an accurate impact time. A two-step strategy is utilized to accomplish an interception at a predetermined time. Because the control parameter is related to the desired impact time with an exact expression, a simple and accurate control of impact time is attained. The method provides equations for calculating the minimum and maximum impact times, enabling the determination of the range of impact times that can be achieved. The proposed guidance law can ensure that the seeker field of view restriction is not violated, If the initial heading error is within this limit. The developed method is utilized in salvo attacks, in which multiple missiles simultaneously strike an enemy target, increasing the missiles’ effectiveness against the target’s self-defense mechanism. To validate the effectiveness of the proposed strategy, MATLAB-based numerical simulations of 2D and 3D engagements, including salvo attacks, are conducted.