The NASA benchmark tetrahedron constellation is a proposed satellite formation
that requires a nominal separation distance at every apogee point. To maintain these
separation distance constraints between any pair of satellites within the constellation,
an open-loop scheme was developed based on the orbital elements. For a particular
size of the NASA benchmark tetrahedron problem, the constellation maintains the
separation distance conditions without perturbations. On the other hand, with
perturbations, the constellation maintains the separation distance criteria for a
limited number of orbits.
This scheme does not maintain the constellation together for the complete mission
period. For this reason, the Tschauner–Hempel (TH) equations are used to maintain
the separation distance criteria. Two control schemes are used to maintain the
separation distance conditions of the tetrahedron constellation and are compared
with each other to determine which one provides for minimum time and
consumption.
Keywords
tetrahedron constellation, linear quadratic regulator,
elliptical orbits