The Artistic Geometry of Consensus Protocols

  • Panagiotis Tsiotras
  • Luis Ignacio Reyes Castro


A large class of control problems in multi-agent systems use the so-called consensus protocol to achieve coordinated motion among a team of agents. Inspired by the “standard” consensus protocol = -Lx, in this paper we propose a decentralized control law for multi-agent formations in two dimensions that allows the participating vehicles to display intricate periodic and quasi-periodic geometric patterns. Similarly to the standard consensus protocol, these controls rely only on the relative position between the networked agents which are neighbors in the underlying communication graph. Several examples are presented, resulting in nontrivial geometric patterns described by trochoidal curves, similar to those generated using a spirograph. These paths can be useful for coordinated, distributed surveillance, and monitoring applications, as well as for the sake of their own esthetic beauty.


Consensus Protocols Pattern generation Multi-agent systems Esthetics Trochoids 



The authors would like to thank Magnus Egerstedt and Amy LaViers for organizing the session on “Controls and Art” during the 2011 American Control Conference and for inviting the authors of this paper to contribute to the session. The authors would also like to thank Prof. Athanassios Economou from the College of Architecture at Georgia Tech for several informative discussions over the use of group symmetries in art and architecture.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Panagiotis Tsiotras
    • 1
  • Luis Ignacio Reyes Castro
    • 2
  1. 1.Daniel Guggenheim School of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Currently a graduate student at the Department of Aeronautics and AstronauticsMassachusetts Institute of TechnologyCambridgeUSA

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