Stability and Performance of Orbital Elements Feedback for Cluster Keeping Using Differential Drag

Differential drag (DD) as a means for fuelless satellite cluster keeping is an old idea, but so far using DD-based cluster keeping while relying on mean orbital elements feedback has not been proposed. This paper develops a DD-based maximum distance keeping method that uses Brouwer-Lyddane differential mean elements feedback for long-term control of the secular drift among satellites. The stability of the maximum distance keeping controller is proven using finite-time stability theory, and high-precision simulation results confirm that the new controller is able to arrest satellite relative drift for mission lifetimes exceeding a year. The maximum distance controller is automatically activated, and does not require a pre-determined activation time. Moreover, as a part of a complete DD-based solution for cluster keeping, a collision-avoidance method based on the same controller structure, albeit with differential osculating elements feedback, is developed and validated. Finally, the possibility to regulate cross-track drift with DD is examined, but it is shown that DD can only provide weak controllability in this case.