Optimal fuel-image motion planning for a class of dual spacecraft formations

In this paper we study a class of dual spacecraft formations for imaging applications. After motivating the problem, we discuss the general goals of an imaging formation. We then specialize the discussion to a class of dual spacecraft formations and introduce the geometric constraints imposed on the formation. The first main contribution of this paper is that we combine two ideas introduced separately in the literature and propose a maneuver that offers improved imaging performance. We then formulate an optimal control problem to minimize fuel consumption and further maximize image quality by minimizing the relative speed, which is proportional to the signal-to-noise ratio of the reconstructed image. We use the maximum principle to derive the necessary optimality conditions und show that they are also sufficient and that the resulting control law is unique. Finally, we apply a continuation method to solve for the unique optimal trajectory.