Partial attitude consensus for underactuated satellite clusters

In this paper, we consider two problems dealing with the partial attitude synchronization of a multi-satellite system in which the satellites, modeled as rigid bodies, are underactuated. Having control authority about only two of the three principal axes, the objective is to align the uncontrolled third axis of all satellites such that they point along the same direction. Two control laws are proposed, one which aligns two satellites towards the same direction in inertial space, and another one which synchronizes an N-satellite system such that the satellites align their underactuated axes towards a fixed inertial direction. The synchronization discrepancy between the satellites is expressed in a unique parameterization that describes the uncontrolled axis of one satellite in the frame of the other via a stereographic projection, while the velocity discrepancy is described using a partial angular velocity difference.