We study the optimal control of an arbitrarily large constellation of smallsatellites operating in low Earth orbit. Simulating the lack of on-boardpropulsion, we limit our actuation to the use of differential drag maneuvers tomake in-plane changes to the satellite orbits. We propose an efficient methodto separate a cluster of satellites into a desired constellation shape whilerespecting actuation constraints and maximizing the operational lifetime of theconstellation. By posing the problem as a linear program, we solve for theoptimal drag commands for each of the satellites on a daily basis with ashrinking-horizon model predictive control approach. We then apply this controlstrategy in a nonlinear orbital dynamics simulation with a simple, varyingatmospheric density model. We demonstrate the ability to control a cluster of100+ satellites starting at the same initial conditions in a circular low Earthorbit to form an equally spaced constellation (with a relative angularseparation error tolerance of one-tenth a degree). The constellation separationtask can be executed in 71 days, a time frame that is competitive for thestate-of-the-practice. This method allows us to trade the time required toconverge to the desired constellation with a sacrifice in the overallconstellation lifetime, measured as the maximum altitude loss experienced byone of the satellites in the group after the separation maneuvers.
展开▼
