Leader Election and Shape Formation with Self-organizing Programmable Matter

In this paper we consider programmable matter consisting of simple computational elements, called particles, that can establish and release bonds and can actively move in a self-organized way, and we investigate the feasibility of solving fundamental problems relevant for programmable matter. As a model for such self-organizing particle systems, we will use a generalization of the geometric amoebot model first proposed ini¾?[21]. Based on the geometric model, we present efficient local-control algorithms for leader election and line formation requiring only particles with constant size memory, and we also discuss the limitations of solving these problems within the general amoebot model.

[1]  Nicola Santoro,et al.  On the computational power of oblivious robots: forming a series of geometric patterns , 2010, PODC '10.

[2]  Lali Barrière,et al.  Uniform Scattering of Autonomous Mobile Robots in a Grid , 2011, Int. J. Found. Comput. Sci..

[3]  Nancy M. Amato,et al.  Distributed reconfiguration of metamorphic robot chains , 2004, PODC '00.

[4]  Ke Li,et al.  Slime Mold Inspired Path Formation Protocol for Wireless Sensor Networks , 2010, ANTS Conference.

[5]  Leonid A. Levin,et al.  Fast and lean self-stabilizing asynchronous protocols , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[6]  Damien Woods,et al.  Intrinsic universality and the computational power of self-assembly , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[7]  Matthew Cook,et al.  Proceedings Machines, Computations and Universality 2013: Preface , 2013 .

[8]  Nicola Santoro,et al.  Arbitrary pattern formation by asynchronous, anonymous, oblivious robots , 2008, Theor. Comput. Sci..

[9]  S. Griffis.  EDITOR , 1997, Journal of Navigation.

[10]  M. Buss,et al.  Self Organizing Robots Based on Cell Structures - CKBOT , 2002, IEEE International Workshop on Intelligent Robots.

[11]  Aristides A. G. Requicha,et al.  Self-assembly and self-repair of arbitrary shapes by a swarm of reactive robots: algorithms and simulations , 2010, Auton. Robots.

[12]  Alon Itai,et al.  Symmetry breaking in distributive networks , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[13]  David Doty,et al.  Theory of algorithmic self-assembly , 2012, CACM.

[14]  Bernard Chazelle,et al.  Natural algorithms , 2009, SODA.

[15]  Hermann Wagner.  Auf der Heide , 1876 .

[16]  Jacob Hendricks,et al.  Replication of Arbitrary Hole-Free Shapes via Self-assembly with Signal-Passing Tiles , 2015, UCNC.

[17]  N. Seeman,et al.  Design and self-assembly of two-dimensional DNA crystals , 1998, Nature.

[18]  Erik D. Demaine,et al.  Self-Assembly of Arbitrary Shapes Using RNAse Enzymes: Meeting the Kolmogorov Bound with Small Scale Factor (extended abstract) , 2010, STACS.

[19]  Gregory S. Chirikjian,et al.  Kinematics of a metamorphic robotic system , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[20]  Rafail Ostrovsky,et al.  Memory-efficient and self-stabilizing network RESET (extended abstract) , 1994, PODC '94.

[21]  Zack J. Butler,et al.  Generic Decentralized Control for Lattice-Based Self-Reconfigurable Robots , 2004, Int. J. Robotics Res..

[22]  Erik Winfree,et al.  Active self-assembly of algorithmic shapes and patterns in polylogarithmic time , 2013, ITCS '13.

[23]  Radhika Nagpal,et al.  Programmable self-assembly in a thousand-robot swarm , 2014, Science.

[24]  Serge Kernbach,et al.  Handbook of Collective Robotics: Fundamentals and Challenges , 2013 .

[25]  Nicola Santoro,et al.  Distributed Computing by Mobile Robots: Gathering , 2012, SIAM J. Comput..

[26]  Nicola Santoro,et al.  Computing Without Communicating: Ring Exploration by Asynchronous Oblivious Robots , 2007, OPODIS.

[27]  Erik D. Demaine,et al.  Programmable Assembly With Universally Foldable Strings (Moteins) , 2011, IEEE Transactions on Robotics.

[28]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

[29]  Esther M. Arkin,et al.  Algorithms for Rapidly Dispersing Robot Swarms in Unknown Environments , 2002, WAFR.

[30]  James McLurkin,et al.  Analysis and implementation of distributed algorithms for multi-robot systems , 2008 .

[31]  Reuven Cohen,et al.  Local spreading algorithms for autonomous robot systems , 2008, Theor. Comput. Sci..

[32]  Chryssis Georgiou,et al.  A distributed algorithm for gathering many fat mobile robots in the plane , 2013, PODC '13.

[33]  Gregory S. Chirikjian,et al.  Modular Self-Reconfigurable Robot Systems [Grand Challenges of Robotics] , 2007, IEEE Robotics & Automation Magazine.

[34]  Friedhelm Meyer auf der Heide,et al.  Convergence of local communication chain strategies via linear transformations: or how to trade locality for speed , 2011, SPAA '11.

[35]  Gregory S. Chirikjian,et al.  Modular Self-Reconfigurable Robot Systems , 2007 .

[36]  Kurt Mehlhorn,et al.  Physarum can compute shortest paths , 2011, SODA.

[37]  Matthew J. Patitz.  An introduction to tile-based self-assembly and a survey of recent results , 2014, Natural Computing.

[38]  Michael J. Fischer,et al.  Computation in networks of passively mobile finite-state sensors , 2004, PODC '04.

[39]  Richard J. Lipton,et al.  On the Computational Power of DNA , 1996, Discret. Appl. Math..

[40]  Christian Scheideler,et al.  Amoebot - a new model for programmable matter , 2014, SPAA.

[41]  Mark Braverman,et al.  On the convergence of the Hegselmann-Krause system , 2012, ITCS '13.

[42]  Xavier Défago,et al.  Non-uniform circle formation algorithm for oblivious mobile robots with convergence toward uniformity , 2008, Theor. Comput. Sci..

[43]  Ho-Lin Chen,et al.  Fast Algorithmic Self-assembly of Simple Shapes Using Random Agitation , 2014, DNA.

[44]  Damien Woods,et al.  Parallel computation using active self-assembly , 2014, Natural Computing.