The Computational Complexity of Controller-Environment Co-design Using Library Selection for Distributed Construction

  • Mesam TimmarEmail author
  • Todd Wareham
Conference paper
Part of the Springer Proceedings in Advanced Robotics book series (SPAR, volume 9)


Creating specified structures through the coordinated efforts of teams of simple autonomous robots is a very important problem in distributed robotics. All previous effort, both empirical and theoretical, has focused on the problems of designing either controllers or environments which, in tandem with given environments or controllers, built the specified structures. In this paper, we give the results of the first computational and parameterized complexity analyses of the controller-environment co-design problem in the simple case where robot teams are designed by selecting controllers from a given library. We show that this problem cannot be solved efficiently in general or under a number of restrictions, and give the first restrictions under which this problem is efficiently solvable.


Swarm robotics Construction Computational complexity Parameterized complexity 



The authors would like to thank the MUN Writing Center, Rory Campbell, Caroline Strickland, and the three anonymous reviewers for comments that helped to significantly improve the presentation of this paper. MT was supported by funds from the MUN School of Graduate Studies and National Science and Engineering Research Council (NSERC) Discovery Grant 228104-2015 held by TW; TW was also supported by the latter.


  1. 1.
    Allwright, M., Bhalla, N., Dorigo, M.: Structure and markings as stimuli for autonomous construction. In: Proceedings of the 2017 18th International Conference on Advanced Robotics, pp. 296–302. IEEE (2017)Google Scholar
  2. 2.
    Ardiny, H., Witwicki, S., Mondada, F.: Are autonomous mobile robots able to take over construction? A review. Int. J. Robot.: Theory Appl. 4(3), 10–21 (2015)Google Scholar
  3. 3.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press (1999)Google Scholar
  4. 4.
    Bonabeau, E., Guérin, S., Snyers, D., Kuntz, P., Theraulaz, G.: Three-dimensional architectures grown by simple ‘stigmergic’ agents. BioSystems 56(1), 13–32 (2000)Google Scholar
  5. 5.
    Brambilla, M., Ferrante, E., Birattari, M., Dorigo, M.: Swarm robotics: a review from the swarm engineering perspective. Swarm Intell. 7(1), 1–41 (2013)Google Scholar
  6. 6.
    Clementi, A.E.F., Rolim, J.D.P., Trevisan, L.: The computational complexity column: recent advances towards proving \(P = BPP\). Bull. Eur. Assoc. Theoret. Comput. Sci. 64, 96–103 (1998)zbMATHGoogle Scholar
  7. 7.
    Cygan, M., Fomin, F.V., Kowalik, L., Lokshtanov, D., Marx, D., Pilipczuk, M., Pilipczuk, M., Saurabh, S.: Parameterized Algorithms. Springer (2015)Google Scholar
  8. 8.
    Downey, R., Fellows, M.: Fundamentals of Parameterized Complexity. Springer, Berlin (2013)zbMATHGoogle Scholar
  9. 9.
    Dunne, P., Laurence, M., Wooldridge, M.: Complexity results for agent design. Ann. Math. Comput. Teleinform. 1(1), 19–36 (2003)Google Scholar
  10. 10.
    Fortnow, L.: The status of the P versus NP problem. Commun. ACM 52(9), 78–86 (2009)Google Scholar
  11. 11.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, W.H (1979)zbMATHGoogle Scholar
  12. 12.
    Gerling, V., Von Mammen, S.: Robotics for self-organised construction. In: IEEE International Workshop on Foundations and Applications of Self* Systems, pp. 162–167. IEEE (2016)Google Scholar
  13. 13.
    Grushin, A., Reggia, J.A.: Automated design of distributed control rules for the self-assembly of prespecified artificial structures. Robot. Auton. Syst. 56(4), 334–359 (2008)Google Scholar
  14. 14.
    Khaluf, Y.: Adaptive construction behavior in robot swarms. In: Proceedings of the Eighth International Conference on Adaptive and Self-Adaptive Systems and Applications, pp. 34–39. IARIA (2016)Google Scholar
  15. 15.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
  16. 16.
    Nolfi, S., Floreano, D.: Evolutionary Robotics. MIT Press (2000)Google Scholar
  17. 17.
    Soleymani, T., Trianni, V., Bonani, M., Mondada, F., Dorigo, M.: Bio-inspired construction with mobile robots and compliant pockets. Robot. Auton. Syst. 74, 340–350 (2015)Google Scholar
  18. 18.
    Stewart, I.A.: The complexity of achievement and maintenance problems in agent-based systems. Artif. Intell. 2(146), 175–191 (2003)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Stewart, R.L., Russell, R.A.: Building a loose wall structure with a robotic swarm using a spatio-temporal varying template. In: Proceedings of the 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 1, pp. 712–716. IEEE (2004)Google Scholar
  20. 20.
    Sugawara, K., Doi, Y.: Collective construction of dynamic equilibrium structure through interaction of simple robots with semi-active blocks. In: Proceedings of the 12th International Symposium on Distributed Autonomous Robotic Systems, pp. 165–176. Springer (2016)Google Scholar
  21. 21.
    Theraulaz, G., Bonabeau, E.: Coordination in distributed building. Science 269(5224), 686 (1995)Google Scholar
  22. 22.
    Von Mammen, S., Jacob, C., Kókai, G.: Evolving swarms that build 3D structures. In: 2005 IEEE Congress on Evolutionary Computation, vol. 2, pp. 1434–1441. IEEE (2005)Google Scholar
  23. 23.
    Wareham, T.: Exploring algorithmic options for the efficient design and reconfiguration of reactive robot swarms. In: Proceedings of the 9th EAI International Conference on Bio-inspired Information and Communication Technologies, pp. 295–302. ICST, Brussels (2015)Google Scholar
  24. 24.
    Wareham, T., Vardy, A.: Viable algorithmic options for designing reactive robot swarms. ACM Trans. Auton. Adapt. Syst. 13(1), 5:1–5:23 (2018)Google Scholar
  25. 25.
    Wareham, T.: Systematic parameterized complexity analysis in computational phonology. Ph.D. thesis, University of Victoria, Canada (1999)Google Scholar
  26. 26.
    Wareham, T., Kwisthout, J., Haselager, P., van Rooij, I.: Ignorance is bliss: a complexity perspective on adapting reactive architectures. In: Proceedings of the 1st Joint IEEE International Conference on Development and Learning and on Epigenetic Robotics, vol. 2, pp. 1–5 (2011)Google Scholar
  27. 27.
    Wareham, T., Vardy, A.: Putting it together: the computational complexity of designing robot controllers and environments for distributed construction. Swarm Intell. 12(2), 111–128 (2018)Google Scholar
  28. 28.
    Wawerla, J., Sukhatme, G.S., Mataric, M.J.: Collective construction with multiple robots. In: Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, pp. 2696–2701. IEEE (2002)Google Scholar
  29. 29.
    Werfel, J., Petersen, K., Nagpal, R.: Designing collective behavior in a termite-inspired robot construction team. Science 343, 754–758 (2014)Google Scholar
  30. 30.
    Werfel, J., Nagpal, R.: Three-dimensional construction with mobile robots and modular blocks. Int. J. Robot. Res. 27(3–4), 463–479 (2008)Google Scholar
  31. 31.
    Wooldridge, M., Dunne, P.E.: The computational complexity of agent verification. In: Intelligent Agents VIII, pp. 115–127. Springer (2002)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer ScienceMemorial University of NewfoundlandSt. John’sCanada

Personalised recommendations