Optimal Midcourse Guidance Algorithm for Exoatmospheric Interception Using Analytical Gradients

Abstract

This paper is aimed at providing a semianalytical method to solve the optimal exoatmospheric interception problem with the minimum fuel consumption. A nonlinear programming (NLP) problem with the minimum velocity increment, which involves Lambert’s problem with unspecified time-of-flight, is firstly formulated. Then, a set of Karush-Kuhn-Tucker conditions and the Jacobian matrix corresponding to those conditions are derived in an analytical manner, even though the derivatives are mathematically complicated and computationally onerous. Therefore, the Newton-Raphson method can be used to efficiently solve this problem. To further decrease computational cost, a near-optimal initialization method reducing the dimension of the search space is presented to provide a better initial guess. The performance of the proposed method is assessed by numerical experiments and comparison with other methods. The results show that this method is not only of high computational efficiency and accuracy but also applicable to onboard guidance.