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.

A collision-free formation reconfiguration trajectory subject to the linearized Hill’s dynamics of relative motion is analytically developed by extending an algorithm for gravity-free space. Based on the initial solution without collision avoidance constraints, the final solution to minimize the designated performance index and avoid collision is found, based on a gradient method. Simple simulations confirm that satellites reconfigure their positions along the safe trajectories, while trying to spend minimum energies. The algorithm is applicable to wide range of formation flying under the Hill’s dynamics.