by also allowing for particle accelerations, thus incorporating dynamics. When this control law is applied to a multispacecraft system, the resulting formation orbits as a rigid body driven by the natural dynamics of the centroid of the formation. We applied this law to the transfer orbit of a set of spacecraft that, in loose formation, follows a natural trajectory to a libration point orbit, as it is suggested for the Darwin mission. We used two standard metrics to evaluate the performance of this control law: the maximum variation in interspacecraft distance and the integral of the motor thrusts necessary to maintain the formation, or fuel expenditure. For the Darwin case study, the new control law outperforms the zero relative radial acceleration cone control. In particular, we find that the minimum fuel expenditure of the new control law can be 4 orders of magnitude less than the fuel expenditure of zero relative radial acceleration cone control.

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Nomenclature Roman Symbols a = Semimajor axis A = Plant matrix B = Deterministic matrix e = Eccentricity e c = Control error vector GM = Gravitational parameter i = Inclination K = Gain matrix l = Reference separation between the occulter and the coronagraph M = Mean anomaly Q = Control error weighting matrix R = Control input weighting matrix r = Position in Earth-Centered Inertial (ECI) u = Control input v = Velocity in ECI x = State vector in ECI Greek Symbols ω = Argument of perigee Ω = Right ascension of ascending node Subscripts cs = The coronagraph satellite cs, ref = Reference trajectory for the coronagraph max = Maximum value os = The occulter satellite ⊕ = The Earth = The Sun