ABSTRACT
We envision programmable matter consisting of systems of computationally limited devices (which we call particles) that are able to self-organize in order to achieve a desired collective goal without the need for central control or external intervention. Central problems for these particle systems are shape formation and coating problems. In this paper, we present a universal shape formation algorithm which takes an arbitrary shape composed of a constant number of equilateral triangles of unit size and lets the particles build that shape at a scale depending on the number of particles in the system. Our algorithm runs in O(√n) asynchronous execution rounds, where $n$ is the number of particles in the system, provided we start from a well-initialized configuration of the particles. This is optimal in a sense that for any shape deviating from the initial configuration, any movement strategy would require Ω(√n) rounds in the worst case (over all asynchronous activations of the particles). Our algorithm relies only on local information (e.g., particles do not have ids, nor do they know n, or have any sort of global coordinate system), and requires only a constant-size memory per particle.
- D. Angluin, J. Aspnes, Z. Diamadi, M. J. Fischer, and R. Peralta. Computation in networks of passively mobile finite-state sensors. Distributed Computing, 18(4):235--253, 2006. Google ScholarDigital Library
- D. Arbuckle and A. Requicha. Self-assembly and self-repair of arbitrary shapes by a swarm of reactive robots: algorithms and simulations. Autonomous Robots, 28(2):197--211, 2010. Google ScholarDigital Library
- Z. J. Butler, K. Kotay, D. Rus, and K. Tomita. Generic decentralized control for lattice-based self-reconfigurable robots. International Journal of Robotics Research, 23(9):919--937, 2004.Google ScholarCross Ref
- A. Chavoya and Y. Duthen. Using a genetic algorithm to evolve cellular automata for 2d/3d computational development. In 8th annual conference on genetic and evolutionary computation, pages 231--232, 2006. Google ScholarDigital Library
- M. Chen, D. Xin, and D. Woods. Parallel computation using active self-assembly. In DNA Computing and Molecular Programming, pages 16--30. Springer, 2013. Google ScholarDigital Library
- G. Chirikjian. Kinematics of a metamorphic robotic system. In Proceedings of ICRA '94, volume 1, pages 449--455, 1994.Google ScholarCross Ref
- S. Das, P. Flocchini, N. Santoro, and M. Yamashita. On the computational power of oblivious robots: forming a series of geometric patterns. In Proceedings of PODC 2010, pages 267--276, 2010. Google ScholarDigital Library
- X. Defago and S. Souissi. Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity. Theoretical Computer Science, 396(1--3):97--112, 2008. Google ScholarDigital Library
- E. D. Demaine, M. J. Patitz, R. T. Schweller, and S. M. Summers. Self-assembly of arbitrary shapes using RNAse enzymes: Meeting the kolmogorov bound with small scale factor (extended abstract). In Proceedings of STACS '11, pages 201--212, 2011.Google Scholar
- Z. Derakhshandeh, R. Gmyr, A. W. Richa, C. Scheideler, and T. Strothmann. An algorithmic framework for shape formation problems in self-organizing particle systems. In Proceedings of NANOCOM 2015, 2015. Google ScholarDigital Library
- Z. Derakhshandeh, R. Gmyr, T. Strothmann, R. A. Bazzi, A. W. Richa, and C. Scheideler. Leader election and shape formation with self-organizing programmable matter. In DNA Computing and Molecular Programming (DNA 21), pages 117--132, 2015.Google Scholar
- P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theoretical Computer Science, 407(1):412--447, 2008. Google ScholarDigital Library
- K. Imai, Y. Kasai, Y. Sonoyama, C. Iwamoto, and K. Morita. Self-reproduction and shape formation in two and three dimensional cellular automata with conservative constraints. In Proceedings of the Eighth International Symposium on Artificial Life and Robotics, pages 377--380, 2003.Google Scholar
- O. Michail. Terminating distributed construction of shapes and patterns in a fair solution of automata. In Proceedings of PODC 2015, pages 37--46, 2015. Google ScholarDigital Library
- O. Michail and P. G. Spirakis. Simple and efficient local codes for distributed stable network construction. In Proceedings of PODC 2014, pages 76--85, 2014. Google ScholarDigital Library
- M. J. Patitz. An introduction to tile-based self-assembly and a survey of recent results. Natural Computing, 13(2):195--224, 2014.Google ScholarCross Ref
- P. W. Rothemund. Folding DNA to create nanoscale shapes and patterns. Nature, 440(7082):297--302, 2006.Google ScholarCross Ref
- M. Rubenstein, A. Cornejo, and R. Nagpal. Programmable self-assembly in a thousand-robot swarm. Science, 345(6198):795--799, 2014.Google ScholarCross Ref
- M. Rubenstein and W.-M. Shen. Automatic scalable size selection for the shape of a distributed robotic collective. In Proceedings of IROS 2010, pages 508--513. IEEE, 2010.Google ScholarCross Ref
- N. Schiefer and E. Winfree. Universal computation and optimal construction in the chemical reaction network-controlled tile assembly model. In DNA Computing and Molecular Programming (DNA 21), pages 34--54, 2015.Google Scholar
- J. L. Schiff. Cellular automata: a discrete view of the world, volume 45. John Wiley & Sons, 2011. Google ScholarDigital Library
- J. E. Walter, J. L. Welch, and N. M. Amato. Distributed reconfiguration of metamorphic robot chains. Distributed Computing, 17(2):171--189, 2004. Google ScholarDigital Library
- D. Woods. Intrinsic universality and the computational power of self-assembly. In Proceedings of MCU 2013, pages 16--22, 2013.Google ScholarCross Ref
- D. Woods, H.-L. Chen, S. Goodfriend, N. Dabby, E. Winfree, and P. Yin. Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In ITCS, pages 353--354, 2013. Google ScholarDigital Library
- K. Yeom. Bio-inspired automatic shape formation for swarms of self-reconfigurable modular robots. In Proceedings of BIC-TA 2010, pages 469--476, 2010.Google Scholar
- K. Yeom and B.-J. You. Agent based morphological approach for collaborative shape formation of self-organizable unmanned aerial vehicles. In Proceedings of HPCC_EUC 2013, pages 85--92, 2013.Google Scholar
- M. Yim, W.-M. Shen, B. Salemi, D. Rus, M. Moll, H. Lipson, E. Klavins, and G. S. Chirikjian. Modular self-reconfigurable robot systems. IEEE Robotics Automation Magazine, 14(1):43--52, 2007.Google ScholarCross Ref
Index Terms
- Universal Shape Formation for Programmable Matter
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