Distributed stabilization of 3D circular formations

The paper presents distributed control design to stabilize circular formations of steered particles in three-dimensional space. In formation, the particles are required to follow equal radius circular paths with common orientation, but not necessarily common center. The formation is given by specifying desired separations of the centers of the circular paths and desired relative headings. The information exchange between the particles is modeled by a directed graph which is assumed to have a spanning tree. Control design is based on a hierarchical approach utilizing a reduction principle for asymptotic stability of closed sets.