Optimal Target States for Satellite Cluster Flight Control on Near-Circular Orbits

Abstract

One of the methods for maintaining a cluster of satellites in long-term bounded relative distances is keeping the satellites on near-circular orbits having the same mean semimajor axes and mean inclinations. This approach allows some freedom in determining the reference mean semimajor axis and reference mean inclination for the cluster. In this paper, this freedom is used to find the optimal target values of the mean semimajor axis and mean inclination, with the optimization criteria being either the total propellant consumption of the cluster or the fuel consumption differences among satellites. The optimization problems are solved analytically, assuming that a fixed-magnitude thruster is used for closed-loop orbit control, and new results are presented, providing simple closed-form expressions for the optimal target states. Simulations are used for validating the results, showing that much propellant can be saved by properly setting the cluster reference orbit. Nomenclature a, a = semimajor axis, mean semimajor axis, m a ⋆ η = optimal target semimajor axis, m C D = drag coefficient e, e = eccentricity, mean eccentricity f = true anomaly, rad h = orbital angular momentum, m 2 ∕s i, i = inclination, mean inclination, rad i ⋆ η = optimal target inclination, rad J 2 = second-order zonal harmonic M = mean anomaly, rad m = mass, kg n = mean motion, rad∕s r = magnitude of the position vector, m u h = acceleration in the cross-track direction, m∕s 2 u t = acceleration in the velocity direction, m∕s 2 v = speed, m∕s Δm = propellant consumption, kg ϵ = efficiency parameter θ = argument of latitude, rad μ = standard gravitational parameter, m 3 ∕s 2 ϒ = maximum propellant consumption difference, kg ω = argument of perigee, rad Ω = argument of the ascending node, rad

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