A Strategy for Maintaining Constant Distance between Satellites in an Elliptically Orbiting Constellation
A strategy for maintaining separation distances between several satellites in a coplanar elliptical orbiting constellation is developed. A possible scientific application of such a system would be in measuring the curl of the Earth's magnetic field by taking simultaneous measurements along the elliptical orbit. The strategy involves maneuvers that would cause small shifts in the direction of the four semi-major axes. With this approach for Keplerian type orbits, the separation distance between adjacent satellites remains within a few percent of the nominal separation distance. This paper emphasizes problems of implementation.
1. Initial deployment. It is assumed that the satellites are launched by a single vehicle. The method to distribute the satellites into their positions using the least maneuver energy is studied.
2. Maintenance of the separation distance. Since the mathematical model is nonlinear and time-variant, a nonlinear control law based on a Lyapunov function is applied to the osculating orbital elements of the daughter satellites. The simulation results with this control show that with perturbations (mainly caused by J2), the response to initial errors converges smoothly and the control energy spent is at a very low level.