Analytical Approach for Orbital Evasion with Space Geometry Considered

Abstract

This paper researches an optimal problem of orbital evasion with considering space geometry by using an analytical approach. Firstly, an angles-only relative navigation model is built and the definition of completely nonobservable maneuver is proposed. After algebraic analysis of relative space geometry, it is proved that the completely nonobservable maneuver is nonexistent. Based on this, the angle measurements of orbit without evasion are set as reference measurements and an analytical solution is derived to find the minimum difference between measurements and the reference measurements in a constant measuring time. Then, an object function using vector multiplication is designed and an optimization model is established so as to prove the optimality of analytical solution. At last, several numerical simulations are performed with different maneuver directions, which verify the effectiveness of the analytical method of this paper for orbital evasion problem. This method offers a new viewpoint for orbital evasion problem.

Capturability Analysis of TPN Guidance Law for Circular Orbital Pursuit-Evasion

“…Isaacs 1,2) initially proposed this problem, and then Berkovitz 3) and Friedman 4) proposed the saddle point existence theorem of the differential game and proofed the necessary conditions. The differential game method has been widely used to solve the pursuit-evasion problem of aircraft, 5) spacecraft, [6][7][8] and missiles. [9][10][11] This kind of differential game problem is usually converted into a two-point boundary-value problem, after which the respective method can be used.…”