The Virtual Formation Method for Precise Autonomous Absolute Orbit Control

This paper analyzes the problem of precise autonomous orbit control of a spacecraft in a low Earth orbit. Autonomous onboard orbit control means that the spacecraft maintains its ground track close to a reference trajectory, without operator intervention. The problem is formulated as a specific case of two spacecraft in formation in which one, the reference, is virtual and affected only by the Earth’s gravitational field. A new parametrization, the relative Earth-fixed elements, is introduced to describe the relative motion of the two spacecraft’s subsatellite points on the Earth surface. These relative elements enable the translation of absolute-into-relative orbit-control requirements and the straightforward use of modern control-theory techniques for orbit control. As a demonstration, linear and quadratic optimum regulators are designed and compared, by means of numerical simulations, with an analytical autonomous orbit-control algorithm that has been validated in flight. The differences of the numerical and analytical control methods are identified and discussed