Attitude synchronization of spacecraft formation with adaptation of consensus penalty terms

The main thrust of this work is on the time variation of the consensus weights used to enforce agreement (synchronization) amongst a network of spacecraft. The main idea is to allow a flexibility in the consensus gains to adapt in proportion to the Euclidean distance of the spacecraft states. A prelude to the time adaptation of the consensus controllers is also provided and takes the form of considering different gains in the synchronization signal thereby arriving in two cases: node-dependent and edge-dependent synchronization gains. A way to choose these fixed gains is in terms of the initial mismatch between the pairwise difference of the spacecraft states. Further, an adaptation of the synchronizing controllers is proposed and compared to the fixed gains. Extensive numerical studies are provided to further support the theoretical predictions and provide insights on the choice of consensus gains in synchronization control used for spacecraft formation.