Aas 05-103 Optimal Configuration of Spacecraft Formations via a Gauss Pseudospectral Method

The problem of determining minimum-fuel maneuver sequences for a four-spacecraft formation is considered. The objective of this paper is to determine fuel-optimal configuration trajectories that transfer a four spacecraft formation from an initial parking orbit to a desired terminal reference orbit while satisfying particular formation constraints. In this paper, the configuration problem is solved numerically using a newly developed direct transcription method called the Gauss pseudospectral method. Two versions of the minimum-fuel configuration problem are considered. In the first problem the trajectory is terminated upon satisfying the required terminal position constraints. In the second problem the trajectory is extended one full orbit beyond that of the first problem such that the terminal conditions are the same as those attained one period earlier. The results obtained in this paper illustrate the key features of the optimal configuration trajectories and controls, provide insight into the structure of the optimally controlled system, and demonstrate the applicability of the Gauss pseudospectral method to optimal formation flying trajectory design.