Adaptation of consensus penalty terms for attitude synchronization of spacecraft formation with unknown parameters

The main concern of this work is on the temporal adjustment of the consensus weights, as applied to spacecraft formation control. Such an objective is attained by dynamically enforcing attitude synchronization via coupling terms included in each spacecraft controller. It is assumed that each spacecraft has identical dynamics but with unknown inertia parameters and external disturbances. By augmenting a standard adaptive controller that accounts for the unknown parameters, made feasible via an assumption on parametrization, with adaptation of the consensus weights, one opts to improve spacecraft synchronization. The coupling terms, responsible for enforcing synchronization amongst spacecraft, are weighted dynamically in proportion to the disagreement between the states of the spacecraft. The time adjustment of edge-dependent gains as well as the special cases of node-dependent and agent-independent constant gains are derived using Lyapunov redesign methods. The proposed adaptive control architecture which allows for adaptation of both parameter uncertainties and consensus penalty terms is demonstrated via extensive numerical studies of a four-spacecraft network with limited connectivity. By considering the sum of deviation-from-the-mean and rotational kinetic energy as appropriate metric for synchronization, the numerical studies also provide insights on the choice of optimal edge-dependent consensus gains.