Small Satellite Constellation Separation using Linear Programming based Differential Drag Commands

TL;DR

This paper presents a linear programming-based control method for small satellite constellations using differential drag, enabling efficient in-plane separation and formation in low Earth orbit without onboard propulsion.

Contribution

It introduces a novel linear programming approach combined with model predictive control for optimal satellite separation using differential drag in large constellations.

Findings

Successfully controlled 100+ satellites to form an equally spaced constellation

Achieved constellation separation within 71 days, competitive with existing methods

Demonstrated effective trade-off between convergence time and constellation lifetime

Abstract

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 lifetime of the constellation. By posing the problem as a linear program, we solve for the optimal drag commands for each of the satellites on a daily basis with a shrinking-horizon model predictive control approach. We then apply this control strategy in a nonlinear orbital dynamics simulation with a simple, varying atmospheric density model. We demonstrate the ability to control a cluster of 100+ satellites starting at the same initial conditions in a circular low Earth orbit to form an equally spaced 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. This method allows us to trade the time required to converge to the desired constellation with a sacrifice in the overall constellation lifetime, measured as the maximum altitude loss experienced by one of the satellites in the group after the separation maneuvers.