Consensus algorithms on Riemannian manifolds
Given a group of agents which move in Euclidean space and communicate according to a given communication graph, standard consensus algorithms provide a protocol which, as time passes, brings all the agents to a common location. The key aspect here is that only local communications are used. These algorithms, however, do not apply when the agents evolve on a manifold (for instance, imagine a group of satellites synchronizing their poses). Using my theoretical work, I proposed a natural extension for this case, and characterized its convergence for a large class of manifolds.
This work was awarded Best Student Paper and Best Student Paper Runner-up at the IEEE Conference for Decision and Control (CDC) in 2012 and 2011, respectively.