We consider a spacecraft formation reconfiguration problem in the case ofidentical spacecraft. This introduces in the optimal reconfiguration problem apermutational degree of freedom, in addition to the choice of individualspacecraft trajectories. We approach this using a coupled combinatorial andcontinuous optimization framework, in which the inner loop consists ofcomputing the costs associated with a particular assignment by using ageometrically exact and numerically efficient discrete optimal control methodbased on Lie group variational integrators. In the outer optimization loop,combinatorial techniques are used to determine the optimal assignments based onthe costs computed in the inner loop. The proposed method is demonstrated onthe optimal reconfiguration problem for 5 identical spacecraft to go from aninline configuration to one equally spaced on a circle.
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