Prescribed-time control for spacecraft formation flying with uncertainties and disturbances

The prescribed-time spacecraft formation flying problem with uncertainties and unknown disturbances is investigated. First, based on Lie group SE(3), the coupled 6-degrees-of-freedom kinematics and dynamics for spacecraft with uncertainties and unknown disturbances are introduced. Second, with the aid of some key properties of a class of parametric Lyapunov equations, novel prescribed-time control laws are designed. It is proved that the proposed control laws can drive the relative motion between the leader spacecraft and follower spacecraft to zero in any prescribed time and are bounded. Finally, numerical simulations verify the effectiveness of the proposed control scheme.