Theory in Biosciences

, Volume 131, Issue 3, pp 149–159 | Cite as

Perception–action loops of multiple agents: informational aspects and the impact of coordination

  • Philippe Capdepuy
  • Daniel Polani
  • Chrystopher L. Nehaniv
Original Paper


Embodied agents can be conceived as entities perceiving and acting upon an external environment. Probabilistic models of this perception–action loop have paved the way to the investigation of information-theoretic aspects of embodied cognition. This formalism allows (i) to identify information flows and their limits under various scenarios and constraints, and (ii) to use informational quantities in order to induce the self-organization of the agent’s behavior without any externally specified drives. This article extends the perception–action loop formalism to multiple agents. The multiple-access channel model is presented and used to identify the relationships between informational quantities of two agents interacting in the same environment. The central question investigated in this article is the impact of coordination. Information-theoretic limits on what can be achieved with and without coordination are identified. For this purpose, different abstract channels are studied, along with a concrete example of agents interacting in space. It is shown that, under some conditions, self-organizing systems based on information-theoretic quantities have a tendency to spontaneously generate coordinated behavior. Moreover, in the perspective of engineering such systems to achieve specific tasks, these information-theoretic limits put constraints on the amount of coordination that is required to perform the task, and consequently on the mechanisms that underlie self-organization in the system.


Information theory Perception–action loop Multiple agents Coordination 



The authors gratefully acknowledge the comments of reviewers and editors which considerably improved the article.


  1. Arimoto S (1972) An algorithm for computing the capacity of arbitrary discrete memoryless channels. IEEE Trans Inform Theor 18(1):14–20CrossRefGoogle Scholar
  2. Ay N, Polani D (2008) Information flows in causal networks. Adv Complex Syst 11(1):17–41Google Scholar
  3. Ay N, Bertschinger N, Der R, Güttler F, Olbrich E (2008) Predictive information and explorative behavior of autonomous robots. Eur Phys J B 63(3):329–339CrossRefGoogle Scholar
  4. Blahut R (1972) Computation of channel capacity and rate distortion functions. IEEE Trans Inform Theor 18(4):460–473CrossRefGoogle Scholar
  5. Capdepuy P, Polani D, Nehaniv CL (2007a) Constructing the basic umwelt of artificial agents: an information-theoretic approach. In: Proceedings of the ninth european conference on artificial life, vol 4648 of LNCS/LNAI. Springer, Lisbon, pp 375–383Google Scholar
  6. Capdepuy P, Polani D, Nehaniv CL (2007b) Maximization of potential information flow as a universal utility for collective behaviour. In: Proceedings of the first IEEE symposium on artificial life, IEEE, Hawaii, pp 207–213Google Scholar
  7. Cover TM, Thomas JA (2006) Elements of information theory, 2nd edn. Wiley Series in Telecommunications and Signal Processing. Wiley-Interscience, New YorkGoogle Scholar
  8. Klyubin A (2007) Organization of information flow through the perception–action loop. PhD Thesis, School of Computer Science, University of HertfordshireGoogle Scholar
  9. Klyubin AS, Polani D, Nehaniv CL (2007) Representations of space and time in the maximization of information flow in the perception–action loop. Neural Comput 19(9):2387–2432PubMedCrossRefGoogle Scholar
  10. Lungarella M, Sporns O (2006) Mapping information flow in sensorimotor networks. PLoS Comput Biol 2(10):e144+PubMedCrossRefGoogle Scholar
  11. Massey JL (1990) Causality, feedback and directed information. In: Proceedings of the international symposium on information theory and its applications, HawaiiGoogle Scholar
  12. Prokopenko M, Gerasimov V, Tanev I (2006) Evolving spatiotemporal coordination in a modular robotic system. In: From animals to animats 9: 9th international conference on the simulation of adaptive behavior (SAB 2006). Lecture notes in computer science, vol 4095. Springer, pp 558–569Google Scholar
  13. Rezaeian M, Grant A (2004) Computation of total capacity for discrete memoryless multiple-access channels. IEEE Trans Inform Theor 50(11):2779–2784CrossRefGoogle Scholar
  14. Still S (2009) Information-theoretic approach to interactive learning. EPL Europhys Lett 85(2):28005 (6 pp)Google Scholar
  15. Tatikonda S, Mitter S (2009) The capacity of channels with feedback. IEEE Trans Inform Theor 55(1):323–349CrossRefGoogle Scholar
  16. Thomas J (1987) Feedback can at most double gaussian multiple access channel capacity. IEEE Trans Inform Theor 33(5):711–716CrossRefGoogle Scholar
  17. Touchette H, Lloyd S (2000) Information-theoretic limits of control. Phys Rev Lett 84:1156PubMedCrossRefGoogle Scholar
  18. Touchette H, Lloyd S (2004) Information-theoretic approach to the study of control systems. Physica A 331:140CrossRefGoogle Scholar
  19. Zahedi K, Ay N, Der R (2009) Higher coordination with less control—a result of information maximisation in the sensori-motor loop. CoRR, abs/0910.2039Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Philippe Capdepuy
    • 1
  • Daniel Polani
    • 1
  • Chrystopher L. Nehaniv
    • 1
  1. 1.Adaptive Systems Research GroupUniversity of HertfordshireHatfield, HertsUK

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