Tetrahedron formation of nanosatellites with single-input control

The present paper studies the formation flight of four nanosatellites forming a tetrahedron. The main goal of this research is to find the relative orbits of these satellites that, at least in the linear Hill–Clohessy–Wiltshire model, ensure finite relative motion and keep the volume and shape of the tetrahedron configuration. Since real motions of these satellites will differ from the linear ones, especially under the influence of the (J_{2}) perturbation, active control is necessary. In addition, the limited size of the satellites does not allow us to use a complex 3-axis attitude control system. In the present paper we consider the passive magnetic attitude control system and suppose that the thrust direction is always aligned with the local geomagnetic field. In order to increase mission lifetime the control algorithm that minimizes the propellant consumption and keeps the tetrahedron volume and shape is investigated.