Design of Minimum Time Maneuvers for Multi- Spacecraft Interferometric Imaging Systems

In this paper, we consider the design of minimum time maneuvers for multi-spacecraft interferometric imaging systems. We show that the process of image formation in a multispacecraft interferometric imaging system is analogous to painting a “large disk” with smaller “paintbrushes,” while satisfying a paint thickness constraint. We show that spiral maneuvers form the dominant set for the painting problem. Further, we frame the minimum time problem in the space of spiral maneuvers and obtain the Double Pantograph Problem. We show that the solution of a discretized version of the Double Pantograph Problem is given by the solution to two associated linear programming problems. We illustrate our results through an imaging example where the image of a fictitious exo-solar planet is formed using the maneuver prescribed by the Double Pantograph Problem.