Spherical formation of regular tetrahedra

In this paper, we study the problem of tracking and encircling a moving target by agents in the 3-dimensional space. Specifically, a group of agents are driven to a regular tetrahedron formation on a spherical surface and simultaneously keep the center of this spherical formation coinciding with the target to be tracked. In the proposed method, to avoid the singularity caused by spherical parameterisations in control, we directly consider the spherical formation in space S
²
. Besides, the protocol proposed does not contain any information of the desired formation beforehand. Rather the constructed formation pattern is attributed to the properties of space S
²
and the inter-agent topology.