Ramirez Riberos, Jaime Luis (2006-08). Design of fuel optimal maneuvers for multi-spacecraft interferometric imaging systems. Master's Thesis.
Multi-spacecraft interferometry imaging is an innovative concept intended to apply formations of satellites to obtain high resolution images allowing for the synthesis of a large size aperture through the combination of the signal from several sub-apertures. The design of such systems requires the design of trajectories that cover a specified region of the observation plane to obtain appropriate information to reconstruct an image of the source. A proposed configuration consists of symmetrical formations which use control thrust to actively follow spiral trajectories that would appropriately cover the specified regions. An optimization problem has to be solved to design the optimal trajectories with minimum fuel consumption. The present work introduces an algorithm to obtain near optimal maneuvers for multi-spacecraft interferometric imaging systems. Solutions to the optimization problem are obtained assuming the optimality of spiral coverage of the spatial frequency plane. The relationship between the error in the frequency content and the reliability of the image is studied to make a connection to the dynamics of the maneuver and define the parameters of the optimization problem. The solution to the problem under deep space dynamics is shown to be convex and is solved by discretization into a non-linear programing problem. Further, the problem is extended to include the effects of dynamical constraints and the effect of time varying relative position from the imaging system to the target. For the calculation of the optimal trajectories, a two-stage hierarchical controller is proposed that obtains acceleration requirements of near minimum fuel maneuvers for different target-system configurations. Several cases are simulated to apply the algorithm. From the obtained results some conclusions about the feasibility and dynamical requirements of these systems are described.