Relative Motion of Formation Flying with Elliptical Reference Orbit

Abstract

In this paper we present the optimal control of the relative motion of formation flying consisting of two spacecrafts. One of the spacecraft is considered as the chief, orbiting the Earth on a Highly Elliptical Orbit(HEO), and the other ,orbiting the chief, is considered as the deputy. The Keplerian relative dyanmics of the formation as well as the the second zonal hamonics of the Earth’s gravitational field (J2) are studied. To study these perturbative effect the linearized true anomaly varying Tschauner-Hempel equations are augmented to include the effect of J2. We solve the nonlinear feedback optimal control of the relative motion using the state dependent Riccati Equation( SDRE). The results are validated through a nummerical example.