Abstract
Designing teams of autonomous robots that can create target structures or repair damage to those structures on either a one-off or ongoing basis is an important problem in distributed robotics. However, it is not known if a team design algorithm for any of these tasks can both have low runtime and produce teams that will always perform their specified tasks quickly and correctly. In this article, we give the first computational and parameterized complexity analyses of several robot team design problems associated with creating, repairing, and maintaining target structures in given environments. Our goals are to establish whether efficient design algorithms exist that operate reliably on all possible inputs and, if not, under which restrictions such algorithms are and are not possible. We prove that all of our design problems are not efficiently solvable in general for heterogeneous robot teams and remain so under a number of plausible restrictions on robot controllers, environments, and target structures. We also give the first restrictions relative to which some of these problems may be efficiently solvable and discuss how theoretical results like those derived here can be combined with physical experiments to derive the best possible algorithms for real-world robot team design.
- Scott Aaronson. 2005. Complexity theory column 46: NP-complete problems and physical reality. ACM SIGACT News 36, 1 (2005), 30--52. Google ScholarDigital Library
- Len Adleman, Qi Cheng, Ashish Goel, Ming-Deh Huang, David Kempe, Pablo De Espanes, and Paul Rothemund. 2002. Combinatorial optimization problems in self-assembly. In Proceedings of the 34th Annual ACM Symposium on Theory of Computing. 23--32. Google ScholarDigital Library
- Hadi Ardiny, Stefan Witwicki, and Francesco Mondada. 2015. Are autonomous mobile robots able to take over construction? A review. Int. J. Rob. Theory Appl. 4, 3 (2015), 10--21.Google Scholar
- Carlos Balaguer and Mohamed Abderrahim. 2008. Trends in robotics and automation in construction. In Robotics and Automation in Construction, Carlos Balaguer and Mohamed Abderrahim (Eds.). InTech, 1--20.Google Scholar
- Levent Bayındır. 2016. A review of swarm robotics tasks. Neurocomput. 172, 8 January (2016), 292--321. Google ScholarDigital Library
- Mauro Birattari, Brian Delhaisse, Gianpiero Francesca, and Yvon Kerdoncuff. 2016. Observing the effects of overdesign in the automatic design of control software for robot swarms. In Proceedings of ANTS 2016 (Lecture Notes in Computer Science), Vol. 9882. Springer, 149--160.Google ScholarCross Ref
- Eric Bonabeau, Marco Dorigo, and Guy Theraulaz. 1999. Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press. Google ScholarCross Ref
- Eric Bonabeau, Sylvain Guérin, Dominique Snyers, Pascale Kuntz, and Guy Theraulaz. 2000. Three-dimensional architectures grown by simple “stigmergic” agents. Biosyst. 56, 1 (2000), 13--32.Google ScholarCross Ref
- Manuele Brambilla, Eliseo Ferrante, Mauro Birattari, and Marco Dorigo. 2013. Swarm robotics: A review from the swarm engineering perspective. Swarm Intell. 7, 1 (2013), 1--41.Google ScholarCross Ref
- Rodney A. Brooks. 1992. Artificial life and real robots. In Towards a Practice of Autonomous Systems: Proceedings of the 1st European Conference on Artificial Life, Francisco J. Varella and Paul Bourgine (Eds.). MIT Press, 3--10.Google Scholar
- Marek Cygan, Fedor V Fomin, Lukasz Kowalik, Daniel Lokshtanov, Daniel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. 2015. Parameterized Algorithms. Springer. Google ScholarDigital Library
- Erik Demaine, Mohammad Hajiaghayi, and Dániel Marx. 2014. Minimizing movement: Fixed-parameter tractability. ACM Trans. Alg. 11, 2 (2014), 1--29. Google ScholarDigital Library
- Rod Downey and Michael R. Fellows. 2013. Fundamentals of Parameterized Complexity. Springer, Berlin. Google ScholarDigital Library
- Paul E. Dunne, Michael Laurence, and Michael Wooldridge. 2003. Complexity results for agent design. Ann. Math., Comput. Teleinformatics 1, 1 (2003), 19--36.Google Scholar
- Henning Fernau, Torben Hagerup, Naomi Nishimura, Prabhakar Ragde, and Klaus Reinhardt. 2003. On the parameterized complexity of the generalized Rush Hour puzzle. In Proceedings of the 15th Canadian Conference on Computational Geometry. 6--9.Google Scholar
- Lance Fortnow. 2009. The status of the P versus NP problem. Commun. ACM 52, 9 (2009), 78--86. Google ScholarDigital Library
- Gianpiero Francesa and Mauro Birattari. 2016. Automatic design of robot swarms: Achievements and challenges. Front. Rob. AI 3, 29 (2016), 1--8.Google Scholar
- Michael R. Garey and David S. Johnson. 1979. Computers and Intractability. W.H. Freeman.Google ScholarDigital Library
- Victor Gerling and Sebastian Von Mammen. 2016. Robotics for self-organised construction. In IEEE International Worksop on Foundations and Applications of Self* Systems. IEEE, 162--167.Google Scholar
- Alexander Grushin and James A. Reggia. 2008. Automated design of distributed control rules for the self-assembly of prespecified artificial structures. Rob. Auton. Syst. 56, 4 (2008), 334--359. Google ScholarDigital Library
- Heiko Hamann, Yara Khaluf, Jean Botev, M. Divband Soorati, Eliseo Ferrante, Oliver Kosak, Jean-Marc Montanier, Sanaz Mostaghim, Richard Redpath, Jon Timmis, et al. 2016. Hybrid societies: Challenges and perspectives in the design of collective behavior in self-organizing systems. Front. Rob. AI 3, 11 April (2016), 1--8.Google Scholar
- John E. Hopcroft, Jacob Theodore Schwartz, and Micha Sharir. 1984. On the complexity of motion planning for multiple independent objects: PSPACE-hardness of the “warehouseman’s problem”. Int. J. Rob. Res. 3, 4 (1984), 76--88.Google ScholarCross Ref
- Nick Jakobi. 1997. Evolutionary robotics and the radical envelope-of-noise hypothesis. Adapt. Behav. 6, 2 (1997), 325--368. Google ScholarDigital Library
- Nick Jakobi, Phil Husbands, and Inman Harvey. 1995. Noise and the reality gap: The use of simulation in evolutionary robotics. In Advances in Artificial Life, F. Morán (Ed.). Lecture Notes in Computer Science, Vol. 929. Springer, 704--720. Google ScholarDigital Library
- Narendra Karmarkar. 1984. A new polynomial-time algorithm for linear programming. Combinatorica 4, 4 (1984), 373--395. Google ScholarDigital Library
- Andreas Kolling, Phillip Walker, Nilanjan Chakraborty, Katia Sycara, and Michael Lewis. 2016. Human interaction with robot swarms: A survey. IEEE Trans. Hum.-Mach. Syst. 46, 1 (2016), 9--26.Google ScholarCross Ref
- Christian Komusiewicz and Rolf Niedermeier. 2012. New races in parameterized algorithmics. In International Symposium on Mathematical Foundations of Computer Science (Lecture Notes in Computer Science), Branislav Rovan, Vladimiro Sassone, and Peter Widmayer (Eds.), Vol. 7464. Springer, 19--30. Google ScholarDigital Library
- Sylvain Koos, Jean-Baptiste Mouret, and Stéphane Doncieux. 2013. The transferability approach: Crossing the reality gap in evolutionary robotics. IEEE Trans. Evol. Comput. 17, 1 (2013), 122--145. Google ScholarDigital Library
- Quentin Lindsey, Daniel Mellinger, and Vijay Kumar. 2011. Construction of cubic structures with quadrotor teams. In Robotics: Science 8 Systems VII, Hugh F. Durrant-Whyte, Nicholas Roy, and Pieter Abbeel (Eds.). MIT Press, 177--184.Google Scholar
- Rolf Niedermeier. 2006. Invitation to Fixed-Parameter Algorithms. Oxford University Press.Google Scholar
- Lynne E. Parker and John V. Draper. 1998. Robotics applications in maintenance and repair. In Handbook of Industrial Robotics (2nd ed.), S. Nof (Ed.). Wiley, 1023--1036.Google Scholar
- Eric S. Ristad. 1993. The Language Complexity Game. MIT Press. Google ScholarDigital Library
- Kamel S. Saidi, Thomas Bock, and Christos Georgoulas. 2016. Robotics in construction. In Handbook of Robotics. Springer, 1493--1520.Google Scholar
- Touraj Soleymani, Vito Trianni, Michael Bonani, Francesco Mondada, and Marco Dorigo. 2015. Bio-inspired construction with mobile robots and compliant pockets. Rob. Auton. Syst. 74, December (2015), 340--350. Google ScholarDigital Library
- Ulrike Stege. 2012. The impact of parameterized complexity to interdisciplinary problem solving. In The Multivariate Algorithmic Revolution and Beyond. Number 7370 in Lecture Notes in Computer Science. Springer, Berlin, 56--68. Google ScholarDigital Library
- Ian A. Stewart. 2003. The complexity of achievement and maintenance problems in agent-based systems. Artif. Intell. 2, 146 (2003), 175--191. Google ScholarDigital Library
- Ashley Stroupe, Avi Okon, Matthew Robinson, Terry Huntsberger, Hrand Aghazarian, and Eric Baumgartner. 2006. Sustainable cooperative robotic technologies for human and robotic outpost infrastructure construction and maintenance. Auton. Rob. 20, 2 (2006), 113--123. Google ScholarDigital Library
- Guy Theraulaz and Eric Bonabeau. 1995. Coordination in distributed building. Sci. 269, 5224 (1995), 686.Google Scholar
- Guy Theraulaz, Jacques Gautrais, Scott Camazine, and Jean-Louis Deneubourg. 2003. The formation of spatial patterns in social insects: From simple behaviours to complex structures. Philos. Trans. R. Soc. London, Ser. A 361, 1807 (2003), 1263--1282.Google ScholarCross Ref
- Mesam Timmar. 2018. The Computational Complexity of Controller-Environment Co-design Using Library Selection for Distributed Construction. M.Sc. thesis, Memorial University of Newfoundland.Google Scholar
- Mesam Timmar and Todd Wareham. 2019. The computational complexity of controller-environment co-design using library selection for distributed construction. In Distributed Autonomous Robotic Systems: The 14th International Symposium (Springer Proceedings in Advanced Robotics), N. Correll, M. Schwager, and M. Otte (Eds.), Vol. 9. Springer Nature Switzerland AG, 51--63.Google ScholarCross Ref
- Iris van Rooij and Todd Wareham. 2008. Parameterized complexity in cognitive modeling: Foundations, applications, and opportunities. Comput. J. 51, 3 (2008), 385--404. Google ScholarDigital Library
- Sebastian Von Mammen, Christian Jacob, and Gabriella Kókai. 2005. Evolving swarms that build 3D structures. In 2005 IEEE Congress on Evolutionary Computation, Vol. 2. IEEE, 1434--1441.Google ScholarCross Ref
- Todd Wareham. 1999. Systematic Parameterized Complexity Analysis in Computational Phonology. Ph.D. Dissertation. University of Victoria. Google ScholarDigital Library
- Todd Wareham. 2015. 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. ICST, Brussels, 295--302. Google ScholarDigital Library
- Todd Wareham, Johan Kwisthout, Pim Haselager, and Iris van Rooij. 2011. 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. 1--5.Google ScholarCross Ref
- Todd Wareham and Andrew Vardy. 2018. Putting it together: The computational complexity of designing robot controllers and environments for distributed construction. Swarm Intell. 12, 2 (2018), 111--128.Google ScholarCross Ref
- Todd Wareham and Andrew Vardy. 2018. Viable algorithmic options for designing reactive robot swarms. ACM Trans. Auton. Adapt. Syst. 13, 1 (2018), 5:1--5:22. Google ScholarDigital Library
- Justin Werfel and Radhika Nagpal. 2008. Three-dimensional construction with mobile robots and modular blocks. Int. J. Rob. Res. 27, 3--4 (2008), 463--479. Google ScholarDigital Library
- Justin Werfel, Kirstin Petersen, and Radhika Nagpal. 2014. Designing collective behavior in a termite-inspired robot construction team. Sci. 343, 6172 (2014), 754--758.Google Scholar
- Stefan Wismer, Gregory Hitz, Michael Bonani, Alexey Gribovskiy, and Stéphane Magnenat. 2012. Autonomous construction of a roofed structure: Synthesizing planning and stigmergy on a mobile robot. In 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 5436--5437.Google ScholarCross Ref
- Michael Wooldridge and Paul E. Dunne. 2002. The computational complexity of agent verification. In Intelligent Agents VIII. Springer, 115--127. Google ScholarDigital Library
- Seung-kook Yun, Mac Schwager, and Daniela Rus. 2011. Coordinating construction of truss structures using distributed equal-mass partitioning. In Robotics Research, C. Pradalier, R. Siegwart, and G. Hirzinger (Eds.). STAR, Vol. 70. Springer, Berlin, 607--623.Google Scholar
Index Terms
- Designing Robot Teams for Distributed Construction, Repair, and Maintenance
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