Maintenance of the tetrahedral satellite configuration with single-input control

The paper discusses the problem of maintenance of the tetrahedral configuration of four satellites. The main goal is to control satellites so that the formed tetrahedron preserved volume and quality according to certain criterion. The relative orbits preserving the quality in linear HCW model of motion without any control are constructed in the paper. Then in linear SS model and in nonlinear model of motion the algorithms enable single-input control along the geomagnetic field are described. This control is able to maintain the reference orbit, and therefore to preserve volume and quality of the tetrahedron.