Intrinsic tetrahedron formation of reduced attitude

In this paper, formation control for reduced attitude is studied, in which a regular tetrahedron formation can be achieved and shown to be asymptotically stable under a large family of gain functions in the control. Moreover, by further restriction on the control gain, almost global stability of the desired formation is obtained. In addition, the control proposed is an intrinsic protocol that only uses relative information and does not need to contain any information of the desired formation beforehand. The constructed formation pattern is totally attributed to the geometric properties of the space and the designed inter-agent connection topology. Besides, a novel coordinates transformation is proposed to represent the relative reduced attitudes in S², which is shown to be an efficient approach to reduced attitude formation problems.