# Almost global consensus on the n-sphere

arXiv: https://arxiv.org/abs/1609.04885 · HTML: https://mlsanity.com/paper/1609.04885/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2016.

## Built on by (most cited first, 1 of 1)

- [On the Local Linear Rate of Consensus on the Stiefel Manifold](https://mlsanity.com/paper/2101.09346/) (2021)

## Abstract (arXiv)

This paper establishes novel results regarding the global convergence properties of a large class of consensus protocols for multi-agent systems that evolve in continuous time on the n-dimensional unit sphere or n-sphere. For any connected, undirected graph and all n in N1, each protocol in said class is shown to yield almost global consensus. The feedback laws are negative gradients of Lyapunov functions and one instance generates the canonical intrinsic gradient descent protocol. This convergence result sheds new light on the general problem of consensus on Riemannian manifolds; the n-sphere for n in N1 differs from the circle and SO(3) where the corresponding protocols fail to generate almost global consensus. Moreover, we derive a novel consensus protocol on SO(3) by combining two almost globally convergent protocols on the n-sphere for n in 1,2. Theoretical and simulation results suggest that the combined protocol yields almost global consensus on SO(3).