Triangular Networks for Resilient Formations

  • David Saldaña
  • Amanda Prorok
  • Mario F. M. Campos
  • Vijay Kumar
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 6)


Consensus algorithms allow multiple robots to achieve agreement on estimates of variables in a distributed manner, hereby coordinating the robots as a team, and enabling applications such as formation control and cooperative area coverage. These algorithms achieve agreement by relying only on local, nearest-neighbor communication. The problem with distributed consensus, however, is that a single malicious or faulty robot can control and manipulate the whole network. The objective of this paper is to propose a formation topology that is resilient to one malicious node, and that satisfies two important properties for distributed systems: (i) it can be constructed incrementally by adding one node at a time in such a way that the conditions for attachment can be computed locally, and (ii) its robustness can be verified through a distributed method by using only neighborhood-based information. Our topology is characterized by triangular robust graphs, consists of a modular structure, is fully scalable, and is well suited for applications of large-scale networks. We describe how our proposed topology can be used to deploy networks of robots. Results show how triangular robust networks guarantee asymptotic consensus in the face of a malicious agent.



We gratefully acknowledge the support of the Colombian Innovation Agency (COLCIENCIAS), and the Brazilian agencies CAPES, CNPq, FAPEMIG. We also acknowledge the support of ONR grants N00014-15-1-2115 and N00014-14-1-0510, ARL grant W911NF-08-2-0004, NSF grant IIS-1426840, and TerraSwarm, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • David Saldaña
    • 1
  • Amanda Prorok
    • 1
  • Mario F. M. Campos
    • 2
  • Vijay Kumar
    • 1
  1. 1.University of PennsylvaniaPhiladelphiaUSA
  2. 2.Universidade Federal de Minas GeraisBelo HorizonteBrazil

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