Formation Flying Control Implementation in Highly Elliptical Orbits

Abstract

The Tschauner-Hempel equations are widely used to correct the separation distance drifts between a pair of satellites within a constellation in highly elliptical orbits [1]. This set of equations was discretized in the true anomaly angle [1] to be used in a digital steady-state hierarchical controller [2]. This controller [2] performed the drift correction between a pair of satellites within the constellation. The objective of a discretized system is to develop a simple algorithm to be implemented in the computer onboard the satellite. The main advantage of the discrete systems is that the computational time can be reduced by selecting a suitable sampling interval. For this digital system, the amount of data will depend on the sampling interval in the true anomaly angle [3]. The purpose of this paper is to implement the discrete Tschauner-Hempel equations and the steady-state hierarchical controller in the computer onboard the satellite. This set of equations is expressed in the true anomaly angle in which a relation will be formulated between the time and the true anomaly angle domains.