Propulsion-Free Cross-Track Control of a LEO Small-Satellite Constellation with Differential Drag

In this work, we achieve propellantless control of both cross-track and along-track separation of a satellite formation by manipulating atmospheric drag. Increasing the atmospheric drag of one satellite with respect to another directly introduces along-track separation, while cross-track separation can be achieved by taking advantage of higher-order terms in the Earth's gravitational field that are functions of altitude. We present an algorithm for solving a multi-satellite formation flying problem based on linear programming. We demonstrate this algorithm in a receding-horizon control scheme in the presence of disturbances and modeling errors in a high-fidelity closed-loop orbital-dynamics simulation. Results show that separation distances of hundreds of kilometers can be achieved by a small-satellite formation in low-Earth orbit over a few months.