Optimal impulsive closed-form control for spacecraft formation flying and rendezvous

This paper addresses the design of novel optimal closed-form multi-impulsive maneuvers for satellite formation-flying and rendezvous. A new method to derive the state transition matrix for the relative motion in J2-perturbed eccentric orbits is shown and used to compute (semi-)analytical solutions for formation control. In addition, a delta-v lower bound for eccentric orbits is formulated which provides direct insight into the optimality of the control solutions. The functionality and performance of the resulting maneuvering schemes are numerically analyzed through comparisons with state-of-the-art optimal control. The results of this paper show how closed-form maneuver solutions have the potential to fulfil the requirements posed by future distributed space systems at a fraction of the computational cost and overall complexity.