Results on an Intrinsic Consensus Algorithm on SO(3) with Almost-Global Convergence

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Date
2012
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Department of Electrical and Computer Engineering, Johns Hopkins University
Abstract
In this paper we propose a discrete time protocol to align the states of a network of agents evolving in the space of rotations SO(3). The starting point of our work is Riemannian consensus, a general and intrinsic extension of classical consensus algorithms to Riemannian manifolds. Unfortunately, this algorithm is guaranteed to align the states only when the initial states are not too far apart. We show how to modify this algorithm so that the states of the agents can be aligned, in practice, from almost any initial condition. While we focus on the specific case of SO(3), we hope that this work will represent the first step toward more general results.
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Keywords
Riemannian geometry, Distributed optimization, Distributed coordination, Almost-global convergence, Consensus algorithms
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