Distributed Orientation Localization of Multi-agent Systems in 3-dimensional Space with Direction-only Measurements

When a group of agents such as unmanned aerial vehicles are operating in 3-dimensional space, their coordinated action in pursuit of some group objective generally requires all agents to share a common coordinate frame or orientations of the coordinate axes of agents up to an unknown coordinate rotation common to all agents, which are simply referred to as having common coordinate axis orientations. Given coordinate axes that are initially unaligned, this paper considers the process of using direction measurements between agent pairs (obtained in their own coordinate frames) to achieve orientation localization, i.e. determination of common coordinate axis orientations, the calculations all being distributed. The process builds on the initial determination of relative orientations of agent pairs in a common coordinate basis. Distributed differential equations then allow determination of a common set of coordinate axis orientations, uniquely up to a common rotation transformation, which can itself be determined if and only if one or more agents have access to global coordinates.