Dual quaternion-based adaptive iterative learning control for flexible spacecraft rendezvous

Spacecraft formation maneuvering will inevitably induce flexible vibration from flexible appendages of spacecraft such as solar array appendages or antennae, which leads to complex disturbances with unknown fundamental frequencies. To achieve high performance of spacecraft formation flying, a novel adaptive iterative learning disturbance observer based on adaptive notch filter is designed to estimate and compensate unknown multi-frequency disturbances. Different from existing results on iterative learning disturbance observer, the newly proposed observer can estimate effectively both low-frequency disturbances and high-frequency periodic disturbances. Based on the proposed observer, an output feedback pose tracking law is derived by combining the proposed velocity observer and a feedback controller in dual quaternions description. The stability of the closed-loop system is approved based on the Lyapunov framework. Finally, the effectiveness and accuracy of the proposed observer and controller are demonstrated successfully by numerical simulations.