Riemannian consensus for manifolds with bounded curvature
Files
First author draft
Date
2013-04-01
Authors
Tron, Roberto
Afsari, Bijan
Vidal, Rene
Version
OA Version
Citation
Roberto Tron, Bijan Afsari, Rene Vidal. 2013. "Riemannian Consensus for Manifolds With Bounded Curvature." IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Volume 58, Issue 4, pp. 921 - 934 (14).
Abstract
Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in Euclidean space. In this work we propose Riemannian consensus, a natural extension of existing averaging consensus algorithms to the case of Riemannian manifolds. Unlike previous generalizations, our algorithm is intrinsic and, in principle, can be applied to any complete Riemannian manifold. We give sufficient convergence conditions on Riemannian manifolds with bounded curvature and we analyze the differences with respect to the Euclidean case. We test the proposed algorithms on synthetic data sampled from the space of rotations, the sphere and the Grassmann manifold.