Triangular Networks for Resilient Formations
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.
- 1.Ahmadi, M., Stone, P.: A distributed biconnectivity check. In: Distributed Autonomous Robotic Systems 7, pp. 1–10. Springer, Berlin (2006)Google Scholar
- 3.Haas, R., Orden, D., Rote, G., Santos, F., Servatius, B., Servatius, H., Souvaine, D., Streinu, I., Whiteley, W.: Planar minimally rigid graphs and pseudo-triangulations. In: Proceedings of the Nineteenth Annual Symposium On Computational Geometry, pp. 154–163. ACM (2003)Google Scholar
- 4.Hromkovič, J.: Dissemination Of Information In Communication Networks: Broadcasting, Gossiping, Leader Election, And Fault-tolerance. Springer Science & Business Media (2005)Google Scholar
- 5.Jadbabaie, A., Lin, J., Morse, A.S.: Coordination of groups of mobile autonomous agents using nearest neighbor rules. In: Proceedings of the 41st IEEE Conference on Decision and Control, 2002, vol. 3, pp. 2953–2958 (2002). https://doi.org/10.1109/CDC.2002.1184304
- 6.LeBlanc, H.J., Koutsoukos, X.D.: Algorithms for determining network robustness. In: Proceedings of the 2nd ACM International Conference On High Confidence Networked Systems, pp. 57–64. ACM (2013)Google Scholar
- 8.Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann (1996)Google Scholar
- 9.Murray, R.M, Olfati Saber, R.: Consensus protocols for networks of dynamic agents. In: Proceedings of the 2003 American Controls Conference (2003)Google Scholar
- 11.Park, H., Hutchinson, S.: A distributed robust convergence algorithm for multi-robot systems in the presence of faulty robots. In: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2980–2985. IEEE (2015)Google Scholar
- 12.Park, H., Hutchinson, S.: An efficient algorithm for fault-tolerant rendezvous of multi-robot systems with controllable sensing range. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), pp. 358–365. IEEE (2016)Google Scholar
- 14.Ren, W., Beard, R.W., Atkins, E.M.: A survey of consensus problems in multi-agent coordination. In: American Control Conference (ACC), pp. 1859–1864. IEEE (2005)Google Scholar
- 17.West, D.B., et al.: Introduction To Graph Theory. Prentice hall Upper Saddle River (2001)Google Scholar
- 20.Zhang, H., Sundaram, S.: Robustness of information diffusion algorithms to locally bounded adversaries. In: American Control Conference (ACC), pp. 5855–5861 (2012). https://doi.org/10.1109/ACC.2012.6315661