The saturated quaternion control law with application for spacecraft formation flying

Rotation matrix parameterization using unit quaternion can represent attitude globally. However, it is not unique and may generates the unwinding phenomenon, besides the issue on the globally asymptotically stability guarantee. This paper proposes a piecewise-continuous scheme of quaternion-based control law that employs a saturation element such that would avoid the unwinding phenomenon. This paper also proposes a consensus control scheme based on the saturated quaternion control law that would show the property of the unwinding phenomenon avoidance and the corresponding graph only need to have a directed spanning tree.