Bearing rigidity theory in SE(3)

Rigidity theory has recently emerged as an efficient tool in the control field of coordinated multi-agent systems, such as multi-robot formations and UAVs swarms, which are characterized by sensing, communication and movement capabilities. This work aims at describing the rigidity properties for frameworks embedded in the three-dimensional Special Euclidean space SE(3) wherein each agent has 6DoF. In such a scenario, it is assumed that the devices are able to gather bearing measurements w.r.t. their neighbors, expressing them into their own body frame. The goal is then to identify the framework transformations that allow to preserve such measurements maintaining it rigid. Rigidity properties are mathematically formalized in this work which differs from the related literature as it faces the extension in three-dimensional space dealing with the 3D rotations manifold. In particular, the attention is focused on the infinitesimal SE(3)-rigidity for which a necessary and sufficient condition is provided.