Time-Optimal Control of Axisymmetric Rigid Spacecraft Using Two Controls

In this paper, we consider the minimum-time reorientation problem of an axisymmetric rigid spacecraft with two independent control torques mounted perpendicular to the spacecraft symmetry axis. The objective is to reorient the spacecraft from an initial attitude, with some angular velocity, to a e nal attitude with a certain angular velocity in minimum time. All possible control structures, including both singular and nonsingular arcs, arestudied completely byderivingthecorrespondingformulasand thenecessary optimality conditions. Itisshown that a second-order singular control can be part of the optimal trajectory. It is also shown that for an inertially symmetric and a nonspinning axisymmetric rigid body, it is possible for ine nite-order singular controls to be part of or the whole optimal trajectory. In particular, for a nonspinning axisymmetric rigid body, the second-order singular trajectory is shown to be an eigenaxis rotation. An efe cient method for numerically solving the optimal controlproblem,basedonacascadedcomputationalschemethatusesbotha directmethodand anindirectmethod, is also presented. Numerical examples demonstrate optimal reorientation maneuvers with both nonsingular and singular subarcs, and comparisons are made between eigenaxis rotations and the true time-optimal rotations.