# Riemannian Consensus for Manifolds With Bounded Curvature

@article{Tron2013RiemannianCF, title={Riemannian Consensus for Manifolds With Bounded Curvature}, author={Roberto Tron and Bijan Afsari and Ren{\'e} Vidal}, journal={IEEE Transactions on Automatic Control}, year={2013}, volume={58}, pages={921-934} }

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…

## 89 Citations

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It turns out, convergence can be guaranteed as soon as the data lie in a small enough ball of a mere CAT(k) metric space, and linear rates of convergence are established.

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A local consensus protocol is provided for connected compact Riemannian manifolds, where communication network can be directed and dynamically switching and a global consensus algorithm is proposed for such manifolds.

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- Mathematics, Computer ScienceArXiv
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This work proposes Distributed Riemannian Consensus on Stiefel Manifold (DRCS) and proves that it enjoys a local linear convergence rate to global consensus, which is the first work showing the equality of the two rates.

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We study optimization problems over Riemannian manifolds using Stochastic Derivative-Free Optimization (SDFO) algorithms. Riemannian adaptations of SDFO in the literature use search information…

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- 2018

Multi-agent systems on nonlinear spaces sometimes fail to synchronize. This is usually attributed to the initial configuration of the agents being too spread out, the graph topology having certain…

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- Mathematics, Computer ScienceSyst. Control. Lett.
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The main result is that the synchronization manifold is asymptotically stable even for drift vector fields which are only locally Lipschitz continuous, as long as the algebraic connectivity of the underlying graph is sufficiently large.

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