Abstract
In swarm robotics, behaviors requiring consensus, meaning having the robots agree on a set of variables, have attracted great attention over the years. Determining the robustness and applicability of these behaviors in harsh communication environments is an open area of research. In this paper, we propose the use of a formal software engineering technique, statistical model checking, to model and assess the robustness of consensus-based behaviors from a communication standpoint. We validate our approach on two common scenarios for a robot swarm: the election of a leader and the allocation of a set of tasks. With the proposed model, we verify the functional correctness of these consensus-based algorithms, as well as assessing their robustness to communication loss and robot failures.
Similar content being viewed by others
References
Agha, G., & Palmskog, K. (2018). A survey of statistical model checking. ACM Transactions on Modeling and Computer Simulation (TOMACS), 28(1), 6.
Amin, S., Elahi, A., Saghar, K., & Mehmood, F. (2017). Formal modelling and verification approach for improving probabilistic behaviour of robot swarms. In 2017 14th international Bhurban conference applied sciences and technology (IBCAST) (pp. 392–400). IEEE.
Armando, A., Mantovani, J., & Platania, L. (2009). Bounded model checking of software using smt solvers instead of sat solvers. International Journal on Software Tools for Technology Transfer, 11(1), 69–83.
Barringer, H., Fisher, M., Gabbay, D. M., & Gough, G. (2013). Advances in temporal logic. Berlin: Springer.
Behrmann, G., Larsen, K. G., & Rasmussen, J. I. (2004). Priced timed automata: Algorithms and applications. In International symposium on formal methods for components and objects (pp. 162–182). Springer.
Behrmann, G., David, A., Larsen, K. G., Hakansson, J., Petterson, P., Yi, W., & Hendriks, M. (2006). Uppaal 4.0. In Third international conference quantitative evaluation of systems, 2006. QEST 2006 (pp. 125–126). IEEE.
Brambilla, M., Ferrante, E., Birattari, M., & Dorigo, M. (2013). Swarm robotics: A review from the swarm engineering perspective. Swarm Intelligence, 7(1), 1–41.
Brunet, L., Choi, H. L., & How, J. P. (2008). Consensus-based auction approaches for decentralized task assignment. In AIAA guidance, navigation, and control conference (p. 6839). Honolulu, Hawaii.
Bulychev, P. E, David, A., Larsen, K. G., Legay, A., Li, G., Poulsen, D. B., & Stainer, A. (2012). Monitor-based statistical model checking for weighted metric temporal logic. In LPAR (pp. 168–182). Springer.
Cimatti, A., Clarke, E., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., Sebastiani, R., & Tacchella, A. (2002). Nusmv 2: An opensource tool for symbolic model checking. In: International conference on computer aided verification (pp. 359–364). Springer.
Clarke, E., Grumberg, O., Jha, S., Lu, Y., & Veith, H. (2001). Progress on the state explosion problem in model checking. In Informatics (pp. 176–194). Springer.
Clarke, E. M., Grumberg, O., & Long, D. E. (1994). Model checking and abstraction. ACM Transactions on Programming Languages and Systems (TOPLAS), 16(5), 1512–1542.
Clarke, E. M., Grumberg, O., & Peled, D. (1999). Model checking. Cambridge: MIT Press.
Das, G. P., McGinnity, T. M., Coleman, S. A., & Behera, L. (2015). A distributed task allocation algorithm for a multi-robot system in healthcare facilities. Journal of Intelligent and Robotic Systems, 80(1), 33–58.
David, A., Larsen, K. G., Legay, A., Mikučionis, M., Poulsen, D. B., Van Vliet, J., & Wang, Z. (2011). Statistical model checking for networks of priced timed automata. In International conference on formal modeling and analysis of timed systems (pp. 80–96). Springer.
De Nicola, R., Ferrari, G. L., & Pugliese, R. (1998). Klaim: A kernel language for agents interaction and mobility. IEEE Transactions on Software Engineering, 24(5), 315–330.
De Nicola, R., & Kühn, E. (2016). Software engineering and formal methods. In Proceedings 14th international conference SEFM 2016. Springer.
Dixon, C., Winfield, A. F., Fisher, M., & Zeng, C. (2012). Towards temporal verification of swarm robotic systems. Robotics and Autonomous Systems, 60(11), 1429–1441.
Dorigo, M., Birattari, M., & Brambilla, M. (2014). Swarm robotics. Scholarpedia, 9(1), 1463.
Fainekos, G. E., Kress-Gazit, H., & Pappas, G. J. (2005). Temporal logic motion planning for mobile robots. In Proceedings of the 2005 IEEE international conference on robotics and automation (pp. 2020–2025). IEEE.
Fernandez, J. C., Mounier, L., & Pachon, C. (2005). A model-basedapproach for robustness testing. IFIP international conference on testing of communicating systems (pp. 333–348).
Gjondrekaj, E., Loreti, M., Pugliese, R., Tiezzi, F., Pinciroli, C., Brambilla, M., Birattari, M., & Dorigo, M. (2012). Towards a formal verification methodology for collective robotic systems. In International conference on formal engineering methods (pp. 54–70). Springer.
Grassé, P. P. (1959). La reconstruction du nid et les coordinations interindividuelles chezbellicositermes natalensis etcubitermes sp. la théorie de la stigmergie: Essai d’interprétation du comportement des termites constructeurs. Insectes sociaux, 6(1), 41–80.
Hessel, A., Larsen, K.G., Mikucionis, M., Nielsen, B., Pettersson, P., & Skou, A. (2008). Testing real-time systems using uppaal. In Formal methods and testing (pp. 77–117). Springer.
Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58(301), 13–30.
Holzmann, G. (2003). Spin model checker: The primer and referencemanual. Boston: Addison-Wesley Professional.
Konur, S., Dixon, C., & Fisher, M. (2012). Analysing robot swarm behaviour via probabilistic model checking. Robotics and Autonomous Systems, 60(2), 199–213.
Kouvaros, P., & Lomuscio, A. (2016). Formal verification of opinion formation in swarms. In Proceedings of the 2016 international conference on autonomous agents and multiagent systems (pp. 1200–1208). International Foundation for Autonomous Agents and Multiagent Systems.
Kouvaros, P., & Lomuscio, A. (2017). Verifying fault-tolerance in parameterised multi-agent systems. In IJCAI (pp. 288–294).
Kuriki, Y., & Namerikawa, T. (2015). Experimental validation of cooperative formation control with collision avoidance for a multi-uav system. In Automation, robotics and applications (ICARA) (pp. 531–536). IEEE.
Kwiatkowska, M., Norman, G., & Parker, D. (2011). Prism 4.0: Verification of probabilistic real-time systems. In Computer aided verification (pp 585–591). Springer.
Mikaël, L. (2012). Formal verification of flexibility in swarm robotics. Ph.D. thesis, Citeseer.
Otte, M., Kuhlman, M., & Sofge, D. (2017). Multi-robot task allocation with auctions in harsh communication environments. In Multi-robot and multi-agent systems (MRS) (pp. 32–39). IEEE.
Pinciroli, C., Lee-Brown, A., & Beltrame, G. (2015) A tuple space for data sharing in robot swarms. In BICT 2015, proceedings of the 9th EAI international conference on bio-inspired information and communications technologies (formerly BIONETICS) (pp. 287–294).
Pinciroli, C., Lee-Brown, A., & Beltrame, G. (2016). Buzz: An extensible programming language for self-organizing heterogeneous robot swarms. In 2016 IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 3794–3800). IEEE.
Pinciroli, C., Trianni, V., O’Grady, R., Pini, G., Brutschy, A., Brambilla, M., et al. (2012). ARGoS: A modular, parallel, multi-engine simulator for multi-robot systems. Swarm Intelligence, 6(4), 271–295.
Reina, A., Valentini, G., Fernández-Oto, C., Dorigo, M., & Trianni, V. (2015). A design pattern for decentralised decision making. PloS ONE, 10(10), e0140950.
Robin, C., & Lacroix, S. (2016). Multi-robot target detection and tracking: taxonomy and survey. Autonomous Robots, 40(4), 729–760.
Rossi, F., Bandyopadhyay, S., Wolf, M., & Pavone, M. (2018). Review of multi-agent algorithms for collective behavior: A structural taxonomy. IFAC-Papers OnLine, 51(12), 112–117.
Rubinstein, R. Y., & Kroese, D. P. (2016). Simulation and the Monte Carlo method (p. 10). New York: Wiley.
Ruiz, M. C., Macià, H., Mateo, J. A., & Calleja, J. (2016). Formal analysis of an energy-aware collision resolution protocol for wireless sensor networks. Procedia Computer Science, 80, 1191–1201.
Saghar, K., Henderson, W., Kendall, D., Bouridane, A. (2010). Formal modelling of a robust wireless sensor network routing protocol. In 2010 NASA/ESA conference on adaptive hardware and systems (pp. 281–288). IEEE.
Senanayake, M., Senthooran, I., Barca, J. C., Chung, H., Kamruzzaman, J., & Murshed, M. (2016). Search and tracking algorithms for swarms of robots: A survey. Robotics and Autonomous Systems, 75, 422–434.
St-Onge, D., Varadharajan, V.S., Li, G., Svogor, I., & Beltrame, G. (2017). Ros and buzz: Consensus-based behaviors for heterogeneous teams. arXiv preprint arXiv:171008843
Strobel, V., Castelló Ferrer, E., & Dorigo, M. (2018). Managing byzantine robots via blockchain technology in a swarm robotics collective decision making scenario. In Proceedings of the 17th international conference on autonomous agents and multiagent systems (pp. 541–549). International foundation for autonomous agents and multiagent systems.
Tartakovsky, A., Nikiforov, I., & Basseville, M. (2014). Sequential analysis: Hypothesis testing and changepoint detection. Boca Raton: CRC Press.
Tripakis, S., & Yovine, S. (2001). Analysis of timed systems using time-abstracting bisimulations. Formal Methods Syst Des, 18(1), 25–68.
Valentini, G. (2017). Achieving consensus in robot swarms. Design and analysis of strategies for the best-of-n-problem. In Studies in computational intelligence (Vol. 706). Springer.
Wald, A. (1945). Sequential tests of statistical hypotheses. The Annals of Mathematical Statistics, 16(2), 117–186.
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of small-world networks. Nature, 393(6684), 440.
Wei, X., Fengyang, D., Qingjie, Z., Bing, Z., & Hongchang, S. (2015). A new fast consensus algorithm applied in rendezvous of multi-uav. In Control and decision conference (CCDC (pp. 55–60). IEEE.
Winfield, A. F., Sa, J., Fernández-Gago, M. C., Dixon, C., & Fisher, M. (2005). On formal specification of emergent behaviours in swarm robotic systems. International Journal of Advanced Robotic Systems, 2(4), 39.
Yang, B., Bryant, R. E., OHallaron, D. R, Biere, A., Coudert, O., Janssen, G., Ranjan, R. K., & Somenzi, F. (1998). A performance study of bdd-based model checking. In International conference on formal methods in computer-aided design (pp. 255–289). Springer.
Funding
Funded was provided by NSERC Strategic Partnership (Grant 479149-2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Moussa, M., Beltrame, G. On the robustness of consensus-based behaviors for robot swarms. Swarm Intell 14, 205–231 (2020). https://doi.org/10.1007/s11721-020-00183-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11721-020-00183-1