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