Time-optimal control of axisymmetric rigid spacecraft using two controls

In this paper, we consider the minimum-time reorientation problem of an axi symmetric rigid spacecraft with two independent control torques mounted per pendicular to the spacecraft symmetry axis. The objective is to reorient th e spacecraft from an initial attitude, with some angular velocity, to a fin al attitude with a certain angular velocity in minimum time. All possible c ontrol structures, including both singular and nonsingular arcs, are studie d completely by deriving the corresponding formulas and the necessary optim ality conditions. It is shown that a second-order singular control can be p art of the optimal trajectory. It is also shown that for an inertially symm etric and a nonspinning axisymmetric rigid body, it is possible for infinit e-order singular controls to be part of or the whole optimal trajectory. In particular, for a nonspinning axisymmetric rigid body, the second order si ngular trajectory is shown to be an eigenaxis rotation. An efficient method for numerically solving the optimal control problem, based on a cascaded c omputational scheme that uses both a direct method and an indirect method, is also presented. Numerical examples demonstrate optimal reorientation man euvers with both nonsingular and singular subarcs, and comparisons are made between eigenaxis rotations and the true time-optimal rotations.