A new guidance law for three-dimensional interception of a maneuvering target.

Abstract

For several decades, guidance problems for interception have been extensively studied, and some guidance laws have been proposed. Among them, proportional navigation and pursuit guidance have been widely used in practical implementation. But there is no previous work which treats a combination of proportional navigation and pursuit guidance with constant gains, let alone an analytical solution of this guidance problem. In this thesis, first, we propose a new guidance law, the combined guidance law, which is a combination of proportional navigation and pursuit guidance with constant parameters, with the aim of retaining the effectiveness of each guidance law and at the same time reducing the normal acceleration or the duration of the engagement. Furthermore, in the final and most important phase of the interception, when usually the engagement is a tail chase, the linearization of the dynamics yields a confluent hypergeometric equation which is solvable analytically when the heading angle of the target is a polynomial function of the independent variable. In the three-dimensional guidance problem, because of the non-linearity of the equations of relative motion, the analytical solution is generally expressed in the form of non-integrable quadratures. In this thesis, secondly, we propose another new guidance law, the generalized Cochran's law, which generates the generalized relative commanded acceleration with components along the line-of-sight direction and orthogonal to it. This has the advantages of adjusting the time for interception, modifying the velocity profile, and fixing the trajectory to match any other end condition required. The relative range, the line-of-sight angle and the flight time are expressible in terms of each other in closed-form. In particular, the flight time, as a function of the line-of-sight angle, is expressed through an incomplete beta function, which is a special case of hypergeometric function. This guidance law, with its explicit solution, is successfully applied to the following three-dimensional guidance problems of interception of a space vehicle: minimum fuel interception, quasi-ballistic interception, delayed launch and head-on interception. Practical aspects of the realization of the guidance law are studied.