Small Satellite Constellation Separation using Linear Programming based Differential Drag Commands

We study the optimal control of an arbitrarily large constellation of small satellites operating in low Earth orbit. Simulating the lack of on-board propulsion, we limit our actuation to the use of differential drag maneuvers to make in-plane changes to the satellite orbits. We propose an efficient method to separate a cluster of satellites into a desired constellation shape while respecting actuation constraints and maximizing the operational life of the constellation. By posing the problem as a linear program, we determine the optimal drag commands for each satellite on a daily basis with a shrinking-horizon model predictive control approach. We then apply this control strategy to a nonlinear orbital dynamics simulation with a simple, varying atmospheric density model. We demonstrate the ability to separate a cluster of 100+ satellites, starting at the same initial conditions in a circular low Earth orbit, into an equally-spaced, single-plane constellation (with a relative angular separation error tolerance of one-tenth a degree). The constellation separation task can be executed in 71 days, a time frame that is competitive for the state-of-the-practice. We show that there exists a trade-off between minimizing the time used to conduct the separation maneuvers and maximizing the operational life of the constellation. Finally, we show that the control strategy can be used not only to initially acquire but also to maintain the constellation throughout its total lifetime.