Coordination of groups of mobile autonomous agents using nearest neighbor rules
- 27 August 2003
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- Vol. 3 (01912216), 2953-2958
- https://doi.org/10.1109/cdc.2002.1184304
Abstract
Vicsek et al. proposed (1995) a simple but compelling discrete-time model of n autonomous agents {i.e., points or particles} all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors". In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.Keywords
This publication has 21 references indexed in Scilit:
- Coordination of groups of mobile autonomous agents using nearest neighbor rulesIEEE Transactions on Automatic Control, 2003
- Modeling and control of formations of nonholonomic mobile robotsIEEE Transactions on Robotics and Automation, 2001
- Corrigendum/addendum to: Sets of matrices all infinite products of which convergeLinear Algebra and its Applications, 2001
- Stability and paracontractivity of discrete linear inclusionsLinear Algebra and its Applications, 2000
- On the maximum of ergodicity coefficients, the Dobrushin ergodicity coefficient, and products of stochastic matricesLinear Algebra and its Applications, 1997
- Infinite products and paracontracting matricesThe Electronic Journal of Linear Algebra, 1997
- Sets of matrices all infinite products of which convergeLinear Algebra and its Applications, 1992
- Matrix AnalysisPublished by Cambridge University Press (CUP) ,1985
- Non-negative Matrices and Markov ChainsPublished by Springer Nature ,1981
- Products of Indecomposable, Aperiodic, Stochastic MatricesProceedings of the American Mathematical Society, 1963