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)

Abstract

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).

Keywords

Entropy Vortex Torque Assure Arena 

Notes

Acknowledgements

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.

References

  1. Anderson, P. (1997). Basic notions of condensed matter physics. Cambridge: Perseus. Google Scholar
  2. Anderson, C., Theraulaz, G., & Deneubourg, J.-L. (2002). Self-assemblages in insect societies. Insectes Sociaux, 49, 1–12. CrossRefGoogle Scholar
  3. Baldassarre, G. (2008). Self-organization as phase transition in decentralized groups of robots: a study based on Boltzmann entropy. In M. Prokopenko (Ed.), Advances in applied self-organizing systems (1st ed.). London: Springer. Google Scholar
  4. Baldassarre, G., & Nolfi, S. (2009). Strengths and synergies of evolved and designed controllers: a study within collective robotics. Artificial Intelligence, 173, 857–875. CrossRefGoogle Scholar
  5. Baldassarre, G., Nolfi, S., & Parisi, D. (2003). Evolution of collective behaviour in a group of physically linked robots. In G. Raidl, A. Guillot, & J.-A. Meyer (Eds.), Applications of evolutionary computing—proceedings of the second European workshop on evolutionary robotics (pp. 581–592). Berlin: Springer. Google Scholar
  6. Baldassarre, G., Parisi, D., & Nolfi, S. (2006). Distributed coordination of simulated robots based on self-organization. Artificial Life, 12(3), 289–311. CrossRefGoogle Scholar
  7. Baldassarre, G., Parisi, D., & Nolfi, S. (2007a). Measuring coordination as entropy decrease in groups of linked simulated robots. In A. Minai & Y. Bar-Yam (Eds.), Proceedings of the fifth international conference on complex systems (ICCS2004), Boston, MA, USA, 16–21 May 2004 (pp. e1–e14). http://www.necsi.edu/events/iccs/2004proceedings.html. Google Scholar
  8. Baldassarre, G., Trianni, V., Bonani, M., Mondada, F., Dorigo, M., & Nolfi, S. (2007b). Self-organised coordinated motion in groups of physically connected robots. IEEE Transactions on Systems, Man and Cybernetics, 37(1), 224–239. CrossRefGoogle Scholar
  9. Beckers, R., Holland, O. E., & Deneubourg, J.-L. (1994). From local actions to global tasks: stigmergy and collective robotics. In R. A. Brooks & P. Maes (Eds.), Proceedings of the 4th international workshop on the synthesis and simulation of living systems (Artificial Life IV) (pp. 181–189). Cambridge: MIT Press. Google Scholar
  10. Bonabeau, E., Dorigo, M., & Theraulaz, G. (1999). Swarm intelligence: from natural to artificial systems. New York: Oxford University Press. MATHGoogle Scholar
  11. Camazine, S., Deneubourg, J. L., Franks, N. R., Sneyd, J., Theraulaz, G., & Bonabeau, E. (2001). Self-organization in biological systems. Princeton: Princeton University Press. Google Scholar
  12. Cao, Y. U., Fukunaga, A. S., & Kahng, A. B. (1997). Cooperative mobile robotics: antecedents and directions. Autonomous Robots, 4, 1–23. CrossRefGoogle Scholar
  13. Dorigo, M., & Sahin, E. (2004). Swarm robotics—special issue editorial. Autonomous Robots, 17(2–3), 111–113. CrossRefGoogle Scholar
  14. Dorigo, M., Trianni, V., Sahin, E., Gross, R., Labella, T. H., Baldassarre, G., Nolfi, S., Denebourg, J.-L., Floreano, D., & Gambardella, L. M. (2004). Evolving self-organizing behavior for a swarm-bot. Autonomous Robots, 17(2–3), 223–245. CrossRefGoogle Scholar
  15. Dudek, G., Jenkin, M., Milios, E., & Wilkes, D. (1996). A taxonomy for multi-agent robotics. Autonomous Robots, 3, 375–397. CrossRefGoogle Scholar
  16. Feldman, P. D. (1998). A brief introduction to: Information theory, excess entropy and computational mechanics (Technical report). Department of Physics, University of California. Google Scholar
  17. Ferrauto, T., Parisi, D., Di Stefano, G., & Baldassarre, G. (2013, in press). Different genetic algorithms and the evolution of specialisation: a study with groups of simulated neural robots. Artificial Life. Google Scholar
  18. Holland, O., & Melhuish, C. (1999). Stimergy, self-organization, and sorting in collective robotics. Artificial Life, 5, 173–202. CrossRefGoogle Scholar
  19. Ijspeert, A. J., Martinoli, A., Billard, A., & Gambardella, L. M. (2001). Collaboration through the exploitation of local interactions in autonomous collective robotics: the stick pulling experiment. Autonomous Robots, 11, 149–171. MATHCrossRefGoogle Scholar
  20. Krieger, M. J. B., Billeter, J. B., & Keller, L. (2000). Ant-like task allocation and recruitment in cooperative robots. Nature, 406, 992–995. CrossRefGoogle Scholar
  21. Kube, R. C., & Bonabeau, E. (2000). Cooperative transport by ants and robots. Robotics and Autonomous Systems, 30, 85–101. CrossRefGoogle Scholar
  22. Kube, C. R., & Zhang, H. (1993). Collective robotics: from social insects to robots. Adaptive Behavior, 2(2), 189–219. CrossRefGoogle Scholar
  23. Mondada, F., Pettinaro, G., Guignard, A., Kwee, I., Floreano, D., Denebourg, J.-L., Nolfi, S., Gambardella, L. M., & Dorigo, M. (2004). Swarm-bot: a new distributed robotic concept. Autonomous Robots, 17(2–3), 193–221. CrossRefGoogle Scholar
  24. Nolfi, S., & Floreano, D. (2001). Evolutionary robotics. the biology, intelligence, and technology of self-organizing machines. Cambridge: MIT Press. Google Scholar
  25. Prokopenko, M. (2008). Design versus self-organization. In M. Prokopenko (Ed.), Advances in applied self-organizing systems (pp. 3–18). London: Springer. CrossRefGoogle Scholar
  26. Prokopenko, M., Gerasimov, V., & Tanev, I. (2006). Evolving spatiotemporal coordination in a modular robotic system. In S. Nolfi, G. Baldassarre, R. Calabretta, J. Hallam, D. Marocco, J.-A. Meyer, O. Miglino, & D. Parisi (Eds.), Lecture notes in computer science: Vol. 4095. From animals to animats 9: proceedings of the ninth international conference on the simulation of adaptive behavior (SAB-2006) (pp. 558–569). Berlin: Springer. CrossRefGoogle Scholar
  27. Prokopenko, M., Boschetti, F., & Ryan, A. J. (2009). An information-theoretic primer on complexity, self-organization, and emergence. Complexity, 15(1), 11–28. MathSciNetCrossRefGoogle Scholar
  28. Quinn, M., Smith, L., Mayley, G., & Husbands, P. (2003). Evolving controllers for a homogeneous system of physical robots: structured cooperation with minimal sensors. Philosophical Transactions - Royal Society. Mathematical, Physical and Engineering Sciences, 361, 2321–2344. MathSciNetCrossRefGoogle Scholar
  29. Reynolds, C. W. (1987). Flocks, herds, and schools: a distributed behavioral model. Computer Graphics, 21(4), 25–34. CrossRefGoogle Scholar
  30. Trianni, V., Nolfi, S., & Dorigo, M. (2006). Cooperative hole-avoidance in a swarm-bot. Robotics and Autonomous Systems, 54(2), 97–103. CrossRefGoogle Scholar
  31. Tsai, S., & Salinas, S. R. (1998). Fourth-order cumulants to characterize the phase transitions of a spin-1 Ising model. Brazilian Journal of Physics, 28(1), 58–65. CrossRefGoogle Scholar

Copyright information

© 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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