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.

Instantaneous Impact Point Guidance with Coast Arcs for Solid Rockets

“…The velocities v sub:x in the suborbital orbit and v orb:x in the target orbit can be calculated by Eqs. (24) and (25). Similarly, the velocity v sub:y and v orb:y can be obtained, according to the true anomaly f at the point P imp .…”

“…where the flight path angle ϑ l is used for parameterizing and updating. The main advantage of setting ϑ l as an iteration parameter over other variables lies in the fact that it is bounded [25,26]. In addition to the natural bound (−π∕ 2 < ϑ l < π∕ 2), additional bounds for the minimum and maximum values for flight path angle ϑ l can be obtained from the target missions and the engine energy.…”

Fast Trajectory Generation Method for Midcourse Guidance Based on Convex Optimization

“…Aiming at target maneuver and interceptor terminal constraints correction, Zhou et al [14] and Li et al [15] established a trajectory optimization and correction problem of midcourse guidance with path constraints. Du et al [16] presented a semianalytical method for solving the exoatmospheric midcourse guidance problem with minimum velocity increment. Li et al [17] designed an angleconstrained midcourse guidance trajectory according to the offline optimized trajectory information.…”