Low-Thrust Spacecraft Formation Keeping

Abstract

Replacing large and costly satellites with formations of smaller satellites, flying in close proximity, is a current subject of interest. One of the keys to successful formation flying is the control system that maintains the formation geometry and provides proper positioning of each member of the formation. This study compares two active control system designs that can be used to maintain a formation composed of microsatellites with limited on-off thrusting capabilities in low Earth orbit. The two evaluated designs are based on a linear approach using optimal control theory and on a nonlinear approach based on Lyapunov stability concepts. In assessing the effectiveness of each controller, the performance criteria were the accuracy with which the formation is maintained and the propellant consumption. The final selection is a tradeoff between fuel consumption and controller robustness based on model uncertainties. Nomenclature amrs = semimajor axis of leader orbit Co = controllability matrix e3 = unit vector fixed in the Earth along the direction of the north pole axis Fx , Fy, Fz = components of the control force along the rotating x, y, and z axes, respectively f = control force vector (force applied by the onboard propulsion system) J = cost function associated with the optimal control J2 = Earth oblateness harmonic coefficient Kglobal, = positive gains associated with the nonlinear