Fuel equalized retargeting for separated spacecraft interferometry

Motivated by NASA's proposed Deep Space 3 interferometer mission, the paper considers the problem of reorienting a constellation of spacecraft such that the total fuel distributed across the constellation is both conserved and expended uniformly. The spacecraft constellation is controlled to reorient as if it were a rigid body. Two approaches to fuel equalization are investigated. The first approach picks a point of rotation a priori that optimizes an objective function that trades off minimum-fuel maneuvers and maneuvers that equalize the fuel. Since the point of rotation is selected a priori and is fixed during the rotation, this approach is open-loop in that it cannot adjust to unpredicted, or inaccurately modeled fuel use. The second approach is closed-loop in that the point of rotation is caused to have second-order dynamics that track the center of unavailable fuel mass. Intuitively, the center of fuel mass will dynamically change to be close to spacecraft that are low on fuel. Simulation results for a four-spacecraft constellation restricted to a plane are given.