Optimal continuous control for remote orbital capture

Optimal control histories are presented for the problem of detumbling (passivating) a satellite. It is proposed that this be done remotely by a robot spacecraft, sometimes referred to as a teleoperator or orbital maneuvering vehicle, in preparation for the return of both vehicles to low-Earth orbit. The dynamics of the coupled two-body system are described with equations of motion derived from an Eulerian formulation (the Hooker-Margulies equations). Two degrees of rotational freedom and one of translation are allowed at the joint that connects the orbital maneuvering vehicle and target spacecraft. The initial condition of the target satellite is free spin and precession. Representative masses and inertias are assumed for both bodies. Application of optimal control theory results in a nonsingular, two-point-boundary-value problem that is solved numerically for the controls, which are principally the external (thruster) and internal (joint) torques to be applied by the orbital maneuvering vehicle. Control histories and vehicle motion are found for both constrained and unconstrained fixed-time optimization. Constraint forces and torques at the joint are determined.