Abstract
The design of control software for robot swarms is a challenging endeavour as swarm behaviour is the outcome of the entangled interplay between the dynamics of the individual robots and the interactions among them. Automatic design techniques are a promising alternative to classic ad-hoc design procedures and are especially suited to deal with the inherent complexity of swarm behaviours. In an automatic method, the design problem is cast into an optimisation problem: the solution space comprises instances of control software and an optimisation algorithm is applied to tune the free parameters of the architecture. Recently, some information theory and complexity theory measures have been proposed for the analysis of the behaviour of single autonomous agents; a similar approach may be fruitfully applied also to swarms of robots. In this work, we present a preliminary study on the applicability of complexity measures to robot swarm dynamics. The aim of this investigation is to compare and analyse prominent complexity measures when applied to data collected during the time evolution of a robot swarm, performing a simple stationary task. Although preliminary, the results of this study enable us to state that the complexity measures we used are able to capture relevant features of robot swarm dynamics and to identify typical patterns in swarm behaviour.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
Indeed, due to excessive computational resources required, for this preliminary step we did not applied measures of complexity based on model construction, such as the ones by Crutchfield et al. [7].
- 3.
Not to be confused with the excess entropy [26], which is defined for \(n \rightarrow \infty \).
- 4.
The name comes from the name initials of its inventors.
References
Ay, N., Bertschinger, N., Der, R., Güttler, F., Olbrich, E.: Predictive information and explorative behavior of autonomous robots. Eur. Phys. J. B - Condens. Matter Complex Syst. 63(3), 329–339 (2008)
Badii, R., Politi, A.: Complexity: Hierarchical Structures and Scaling in Physics, vol. 6. Cambridge University Press, Cambridge (1999)
Birattari, M., Delhaisse, B., Francesca, G., Kerdoncuff, Y.: Observing the effects of overdesign in the automatic design of control software for robot swarms. In: Dorigo, M., Birattari, M., Li, X., López-Ibáñez, M., Ohkura, K., Pinciroli, C., Stützle, T. (eds.) ANTS 2016. LNCS, vol. 9882, pp. 149–160. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44427-7_13
Brambilla, M., Ferrante, E., Birattari, M., Dorigo, M.: Swarm robotics: a review from the swarm engineering perspective. Swarm Intell. 7(1), 1–41 (2013)
http://www.bzip.org. Accessed 30 Nov 2016
Cover, T., Thomas, J.: Elements of Information Theory. Wiley, Hoboken (2012)
Crutchfield, J.: The calculi of emergence: computation, dynamics, and induction. Physica D 75, 11–54 (1994)
Edlund, J., Chaumont, N., Hintze, A., Koch, C., Tononi, G., Adami, C.: Integrated information increases with fitness in the evolution of animats. PLoS Comput. Biol. 7(10), e1002236 (2011)
Francesca, G., Birattari, M.: Automatic design of robot swarms: achievements and challenges. Front. Rob. AI 3, 29 (2016)
Francesca, G., Brambilla, M., Brutschy, A., Trianni, V.: AutoMoDe: a novel approach to the automatic design of control software for robot swarms. Swarm Intell. 8(2), 89–112 (2014)
Galas, D., Nykter, M., Carter, G., Price, N.: Biological information as set-based complexity. IEEE Trans. Inf. Theory 56, 667–677 (2010)
Gell-Mann, M., Lloyd, S.: Information measures, effective complexity, and total information. Complexity 2(1), 44–52 (1996)
Grassberger, P.: How to measure self-generated complexity. Phys. A: Stat. Mech. Appl. 140(1–2), 319–325 (1986)
Kolmogorov, A.: Three approaches to the quantitative definition of information. Prob. Inf. Transm. 1(1), 1–7 (1965)
Lempel, A., Ziv, J.: On the complexity of finite sequences. IEEE Trans. Inf. Theory 22(1), 75–81 (1976)
Li, W.: On the relationship between complexity and entropy for Markov chains and regular languages. Complex Syst. 5(4), 381–399 (1991)
Lindgren, K.: Information theory for complex systems - an information perspective on complexity in dynamical systems, physics, and chemistry. Chalmers (2014). http://studycas.com/c/courses/it
Lindgren, K., Nordahl, M.: Complexity measures and cellular automata. Complex Syst. 2(4), 409–440 (1988)
Lizier, J.: The Local Information Dynamics of Distributed Computation in Complex Systems. Springer Theses Series. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-32952-4
Lloyd, S.: Measures of complexity: a nonexhaustive list. IEEE Control Syst. Mag. 21(4), 7–8 (2001)
Lopez-Ruiz, R., Mancini, H., Calbet, X.: A statistical measure of complexity. Phys. Lett. A 209, 321–326 (1995)
Nicolis, G., Nicolis, C.: Foundations of Complex Systems: Emergence, Information and Predicition. World Scientific, Singapore (2012)
Pinciroli, C., Trianni, V., O’Grady, R., Pini, G., Brutschy, A., Brambilla, M., Mathews, N., Ferrante, E., Di Caro, G., Ducatelle, F., Birattari, M., Gambardella, L., Dorigo, M.: ARGoS: a modular, multi-engine simulator for heterogeneous swarm robotics. Swarm Intell. 6(4), 271–295 (2012)
Prokopenko, M., Boschetti, F., Ryan, A.: An information-theoretic primer on complexity, self-organization, and emergence. Complexity 15(1), 11–28 (2009)
Prokopenko, M.: Guided Self-Organization: Inception, vol. 9. Springer Science & Business Media, Heidelberg (2013). https://doi.org/10.1007/978-3-642-53734-9
Shalizi, C., Crutchfield, J.: Computational mechanics: pattern and prediction, structure and simplicity. J. Stat. Phys. 104(3), 817–879 (2001)
Shannon, C.: A mathematical theory of communication. Bell Syst. Tech. J. 27(1, 2), 379–423, 623–656 (1948)
Sperati, V., Trianni, V., Nolfi, S.: Evolving coordinated group behaviours through maximisation of mean mutual information. Swarm Intell. 2(2), 73–95 (2008)
Trianni, V.: Evolutionary Swarm Robotics: Evolving Self-Organising Behaviours in Groups of Autonomous Robots, vol. 108. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-77612-3
Utro, F., Di Benedetto, V., Corona, D., Giancarlo, R.: The intrinsic combinatorial organization and information theoretic content of a sequence are correlated to the DNA encoded nucleosome organization of eukaryotic genomes. Bioinformatics 32(6), 835–842 (2015)
Villani, M., Roli, A., Filisetti, A., Fiorucci, M., Poli, I., Serra, R.: The search for candidate relevant subsets of variables in complex systems. Artif. Life 21(4), 412–431 (2015)
Acknowledgements
Andrea Roli acknowledges the support of Université libre de Bruxelles as visiting professor in the “Chaire internationale” programme. Mauro Birattari acknowledges support from the Belgian Fonds de la Recherche Scientifique – FNRS. The project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 681872).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Roli, A., Ligot, A., Birattari, M. (2018). Complexity Measures in Automatic Design of Robot Swarms: An Exploratory Study. In: Pelillo, M., Poli, I., Roli, A., Serra, R., Slanzi, D., Villani, M. (eds) Artificial Life and Evolutionary Computation. WIVACE 2017. Communications in Computer and Information Science, vol 830. Springer, Cham. https://doi.org/10.1007/978-3-319-78658-2_18
Download citation
DOI: https://doi.org/10.1007/978-3-319-78658-2_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78657-5
Online ISBN: 978-3-319-78658-2
eBook Packages: Computer ScienceComputer Science (R0)