A Numerical Optimization Method for Quickly Determining Energy Optimal Interception Prediction Hit Points

Abstract

The invention discloses a numerical optimization method capable of rapidly determining energy optimal interception predicated hit points. The method specifically comprises the following steps: (1) giving a test value of independent variable X, and setting coefficient matrixes u and v; (2) calculating a partial derivative matrix FF' (X) by a formula (22) and a formula (24); (3) calculating a new independent variable value X(k+1) by a formula (25); and (4) judging whether convergence exists or not; if delta XX=XX(k+1)-XX(k) is smaller than limits of error, ending the calculation; otherwise transferring to step (2), and repeating steps (2)-(4). According to the numerical optimization method, on the basis of a Kepler track theory and P iterative method-based Gauss problem, the problem of the minimum velocity correction of intercepted orbital transferring of orbital maneuvering for a target is converted into an optimal planning problem; through an optimal planning theory, KKT condition corresponding to delta vmin is obtained, and meanwhile, Newton iteration is further designed for rapidly solving KKT condition, so that analytical gradient information can be obtained. Compared with a common search algorithm, the method has the advantages of high calculation precision, high speed and insensitivity to an initial value.

Description

technical field [0001] The invention relates to the field of spacecraft interception and rendezvous control, in particular to a numerical optimization method for quickly determining energy optimal interception prediction hit points. Background technique [0002] In the general orbital interception problem, a basic problem that needs to be solved is how to reach another point from one point in space within a predetermined time. The two-point boundary value problem in this kind of aerospace dynamics is called the Lambert problem. The mathematician Gauss gave the classical solution to the Lambert problem, such as figure 1 As shown, the Gauss problem is defined as: given the initial position vector r 1 , terminal position vector r 2 , and from r 1 to r 2 flight time t F and motion direction, find the initial and terminal velocity vector ν 1 and ν 2 . [0003] Under the precondition of Kepler orbital motion, the position vector r 1 、r 2 , and the velocity vector ν 1 、ν...

AI Technical Summary

Problems solved by technology

[0044] Although this type of search algorithm has a simple idea and the calculation accuracy can meet the actual engineering, it takes a long time. Even if the half-division method is used to speed up the search, it is not conducive to online solution

Images