Distributed hybrid unit quaternion localisation of camera networks

Several dynamical systems evolve on angular type of variables, such as the pose of rigid bodies or optimization techniques applied to variables of unitary norms. Perhaps the most suitable mathematical tool for describing such dynamics corresponds to the n-dimensional sphere, that is the manifold of dimension n embedded in the (n+1) dimensional Euclidean space and corresponding to all the vectors having unit norm. A relevant example corresponds to the 3-sphere and the ensuing quaternion-based coordinate system, which is largely used for describing the pose of rigid bodies. One of the challenges in describing dynamics evolving on the n-dimensional sphere is the fact that global robust stabilization of a point cannot be accomplished with continuous feedback laws. It is then necessary to resort to alternative solutions, for wanting robustness of the closed-loop stability properties. Hybrid dynamical systems are a possible answer to this, where existing works on the distributed calibration of camera networks will be first overviewed, and hybrid solutions will be proposed and tested.