Paper Info
Title
Distributed Laplacian Eigenvalue and Eigenvector Estimation in Multi-robot Systems
Abstract
In many multi-robot systems applications, obtaining the spectrum and the eigenvectors of the Laplacian matrix provides very useful information. For example, the second smallest eigenvalue, and the corresponding eigenvector, can be used for connectivity maintenance (see for example Freeman et al., Stability and convergence properties of dynamic average consensus estimators, 2006, [5]). Moreover, as shown in Zareh et al. (Decentralized biconnectivity conditions in multi-robot systems, 2016, [22], Enforcing biconnectivity in multi-robot systems, 2016, [23]), the third smallest eigenvalue provides a metric for ensuring robust connectivity in the presence of single robot failures. In this paper, we introduce a novel decentralized gradient based protocol to estimate the eigenvalues and the corresponding eigenvectors of the Laplacian matrix. The most significant advantage of this method is that there is no limit on the multiplicity of the eigenvalues. Simulations show the effectiveness of the theoretical findings.
Year
DOI
Venue
2016
10.1007/978-3-319-73008-0_14
Springer Proceedings in Advanced Robotics
Field
DocType
Volume
Convergence (routing),Robotic systems,Applied mathematics,Laplacian matrix,Computer science,Multiplicity (mathematics),Robot,Eigenvalues and eigenvectors,Laplace operator,Estimator,Distributed computing
Conference
6
ISSN
Citations 
PageRank 
2511-1256
0
0.34
References 
Authors
0
3
Name
Order
Citations
PageRank
Mehran Zareh1142.68
Lorenzo Sabattini239336.65
Cristian Secchi397781.94