Long-distance Formation Flying of Spacecraft in Elliptic Orbits

Abstract

This paper presents relative position control of spacecraft formation flying. A control law based on the Tschauner-Hempel (TH) equation is usually used to reconfigure a spacecraft formation. However, the solution of the TH equation is not valid when the formation size is large. This paper focuses on the effects of the relatively long distance between two spacecraft. By taking the differences in orbital elements between two spacecraft as state variables, a state equation is obtained with long-distance effects as perturbations. Then, the optimal control input is derived by the Hamiltonian perturbation theory, including the long-distance effects. Numerical simulations show the usefulness of the control input from the perspective of the accuracy of the relative position and velocity. The obtained control input is also compared with the optimal control input numerically obtained by nonlinear programming.