Self-Organization as Phase Transition in Decentralized Groups of Robots: A Study Based on Boltzmann Entropy

Part of the Advanced Information and Knowledge Processing book series (AI&KP)


Decentralized coordination is usually based on self-organizing principles. Very often research on decentralized multi-robot systems makes a general claim on the presence of these principles underlying the success of the studied systems, but it does not conduct a detailed analysis of which specific principles are at work, nor it attempts to measure their effects in terms of the evolution of the system’s organization in time or to analyze the robustness of its operation versus noise (e.g. see Holland and Melhuish in Artif. Life 5:173–202, 1999; Krieger et al. in Nature 406:992–995, 2000; Kube and Bonabeau in Robot. Auton. Syst. 30:85–101, 2000; Quinn et al. in Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 361:2321–2344, 2003). This chapter studies some of these issues in a multi-robot system presented in detail elsewhere (Baldassarre et al. in Applications of evolutionary computing—proceedings of the second European workshop on evolutionary robotics, pp. 581–592. Springer, Berlin, 2003; Artif. Life 12(3):289–311, 2006; Proceedings of the fifth international conference on complex systems (ICCS2004), 16–21 May 2004, Boston, MA, USA, pp. e1–e14, 2007a; IEEE Trans. Syst. Man Cybern. 37(1):244–239, 2007b). This system is formed by robots that are physically connected and have to coordinate their direction of motion to explore an open arena without relying on a centralized coordination. The robots are controlled by an identical neural network whose weights are evolved through a genetic algorithm. Through this algorithm the system develops the capacity to solve the task on the basis of self-organizing principles. The goal of this chapter is to present some preliminary results that show how such principles lead the organization of the system, measured through a suitable index based on Boltzmann entropy, to arise in a quite abrupt way if the noise/signal ratio related to the signal that allows the robots to coordinate is slowly decreased. With this respect, the chapter argues, on the basis of theoretical arguments and experimental evidence, that such sudden emergence of organization shares some properties with the phase transitions exhibited by some physical system studied in physics (Anderson in Basic notions of condensed matter physics. Perseus, Cambridge, 1997).


Genetic Algorithm Robotic System Random Fluctuation Collective Level Entropy Index 
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This research has been supported by the SWARM-BOTS project funded by the Future and Emerging Technologies program (IST-FET) of the European Commission under grant IST-2000-31010. I thank Stefano Nolfi and Domenico Parisi with which I designed, developed and studied extensively the robotic setup studied in the paper.


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© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Laboratory of Autonomous Robotics and Artificial Life, Istituto di Scienze e Tecnologie della CognizioneConsiglio Nazionale delle Ricerche (LARAL-ISTC-CNR)RomeItaly

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