Extension of the Cucker-Smale Control Law to Space Flight Formations

We designed a spacecraft control law for autonomous formation acquisition and formation keeping. This control law extends the ideas on flight formation for flocks first introduced by Cucker and Smale [Cucker, F., and Smale, S., Emergent Behavior in Flocks, IEEE Transactions on Automatic Control, Vol. 52, 2007, pp. 852-862] 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 the 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.