Performance Analysis of Generating Function Approach for Optimal Reconfiguration of Formation Flying

The use of generating functions for solving optimal rendezvous problems has an advantage in the sense that it does not require one to guess and iterate the initial costate. This paper presents how to apply generating functions to analyze spacecraft optimal reconfiguration between projected circular orbits. The series-based solution obtained by using generating functions demonstrates excellent convergence and approximation to the nonlinear reference solution obtained from a numerical shooting method. These favorable properties are expected to hold for analyzing optimal formation reconfiguration under perturbations and non-circular reference orbits.