Aas 05-338 Optimal Reconfiguration of a Tetrahedral Formation via a Gauss Pseudospectral Method

This paper addresses the problem of determining a minimum-fuel maneuver sequence to reconfigure a tetrahedral formation. The objective of this work is to develop a single orbit, minimum-fuel reconfiguration strategy such that, after reconfiguration, the four spacecraft are able to return to an acceptable tetrahe-dral configuration in a region of interest near apogee for a period of three weeks without any required propulsive maneuvers. In the design considered here, an acceptable tetrahedron is obtained by satisfying several constraints on the shape and size of the tetrahedron. The optimal reconfiguration problem is posed as a nonlinear optimal control problem and is solved via direct trajectory optimization using a method called the Gauss pseudospectral method. The results obtained in this study provide insight into the structure of the optimal mission design and demonstrate the generality, computational efficiency, and accuracy of the Gauss pseudospectral method.