Self-organized aggregation without computation

This paper presents a solution to the problem of self-organized aggregation of embodied robots that requires no arithmetic computation. The robots have no memory and are equipped with one binary sensor, which informs them whether or not there is another robot in their line of sight. It is proven that the sensor needs to have a sufficiently long range; otherwise aggregation cannot be guaranteed, irrespective of the controller used. The optimal controller is found by performing a grid search over the space of all possible controllers. With this controller, robots rotate on the spot when they perceive another robot, and move backwards along a circular trajectory otherwise. This controller is proven to always aggregate two simultaneously moving robots in finite time, an upper bound for which is provided. Simulations show that the controller also aggregates at least 1000 robots into a single cluster consistently. Moreover, in 30 experiments with 40 physical e-puck robots, 98.6% of the robots aggregated into one cluster. The results obtained have profound implications for the implementation of multi-robot systems at scales where conventional approaches to sensing and information processing are no longer applicable.

[1]  Metin Sitti,et al.  Microscale and nanoscale robotics systems [Grand Challenges of Robotics] , 2007, IEEE Robotics & Automation Magazine.

[2]  Ali Jadbabaie,et al.  Decentralized Control of Connectivity for Multi-Agent Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[3]  P. Damasceno,et al.  Predictive Self-Assembly of Polyhedra into Complex Structures , 2012, Science.

[4]  Nick Jakobi,et al.  Half-baked, Ad-hoc and Noisy: Minimal Simulations for Evolutionary Robotics , 1993 .

[5]  Jeffrey L. Krichmar,et al.  Evolutionary robotics: The biology, intelligence, and technology of self-organizing machines , 2001, Complex..

[6]  R. A. Brooks,et al.  Intelligence without Representation , 1991, Artif. Intell..

[7]  TrianniVito,et al.  Evolving Self-Organizing Behaviors for a Swarm-Bot , 2004 .

[8]  Yves Métivier,et al.  The Power and the Limitations of Local Computations on Graphs , 1992, WG.

[9]  Olivier Michel,et al.  Cyberbotics Ltd. Webots™: Professional Mobile Robot Simulation , 2004, ArXiv.

[10]  W. McCarthy.  Programmable matter , 2000, Nature.

[11]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[12]  Luca Maria Gambardella,et al.  Evolving Self-Organizing Behaviors for a Swarm-Bot , 2004, Auton. Robots.

[13]  Guy Theraulaz,et al.  The Embodiment of Cockroach Aggregation Behavior in a Group of Micro-robots , 2008, Artificial Life.

[14]  N. J. A. Sloane,et al.  Penny-packing and two-dimensional codes , 1990, Discret. Comput. Geom..

[15]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[16]  Kevin M. Passino,et al.  Stability analysis of swarms , 2003, IEEE Trans. Autom. Control..

[17]  Giuseppe Oriolo,et al.  A swarm aggregation algorithm based on local interaction for multi-robot systems with actuator saturations , 2012, 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[18]  Wei Li.  Stability Analysis of Swarms With General Topology , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[19]  Serge Kernbach,et al.  Re-embodiment of Honeybee Aggregation Behavior in an Artificial Micro-Robotic System , 2009, Adapt. Behav..

[20]  Nazim Fatès.  Solving the decentralised gathering problem with a reaction–diffusion–chemotaxis scheme , 2010, Swarm Intelligence.

[21]  E. Klavins,et al.  Programmable Self-Assembly , 2007, IEEE Control Systems.

[22]  Tony J. Dodd,et al.  Evolving Aggregation Behaviors in Multi-Robot Systems with Binary Sensors , 2012, DARS.

[23]  Marco Dorigo,et al.  Self-Assembly at the Macroscopic Scale , 2008, Proceedings of the IEEE.

[24]  Lynne E. Parker,et al.  Multiple Mobile Robot Systems , 2008, Springer Handbook of Robotics.

[25]  Olivier Michel,et al.  Cyberbotics Ltd. Webots™: Professional Mobile Robot Simulation , 2004 .

[26]  Daniel Liberzon,et al.  Rendezvous Without Coordinates , 2012, IEEE Trans. Autom. Control..

[27]  Nicola Santoro,et al.  Gathering of asynchronous robots with limited visibility , 2005, Theor. Comput. Sci..

[28]  Wei Li,et al.  Clustering objects with robots that do not compute , 2014, AAMAS.

[29]  Israel A. Wagner,et al.  Gathering Multiple Robotic A(ge)nts with Limited Sensing Capabilities , 2004, ANTS Workshop.

[30]  J. Deneubourg,et al.  Kinetics of larval gregarious behavior in the bark beetleDendroctonus micans (Coleoptera: Scolytidae) , 1990, Journal of Insect Behavior.

[31]  Erol Sahin,et al.  Probabilistic aggregation strategies in swarm robotic systems , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[32]  Corel Corp.  Microscale and Nanoscale Robotics Systems , 2007 .

[33]  Aristides A. G. Requicha.  Nanorobots, NEMS, and nanoassembly , 2003 .

[34]  Serge Kernbach,et al.  Adaptive collective decision-making in limited robot swarms without communication , 2013, Int. J. Robotics Res..

[35]  J. Deneubourg,et al.  Self-organized aggregation in cockroaches , 2005, Animal Behaviour.

[36]  Timothy Y. Chow.  Penny-packings with minimal second moments , 1995, Comb..

[37]  Nikolaus Correll,et al.  Modeling and designing self-organized aggregation in a swarm of miniature robots , 2011, Int. J. Robotics Res..

[38]  Guy Theraulaz,et al.  Self-Organization in Biological Systems , 2001, Princeton studies in complexity.

[39]  Padmanabhan Pillai,et al.  Simulating multi-million-robot ensembles , 2011, 2011 IEEE International Conference on Robotics and Automation.

[40]  Zack J. Butler,et al.  Million Module March: Scalable Locomotion for Large Self-Reconfiguring Robots , 2008, Int. J. Robotics Res..

[41]  Andrea Gasparri,et al.  A swarm aggregation algorithm for multi-robot systems based on local interaction , 2012, 2012 IEEE International Conference on Control Applications.

[42]  Masafumi Yamashita,et al.  Distributed memoryless point convergence algorithm for mobile robots with limited visibility , 1999, IEEE Trans. Robotics Autom..

[43]  Francesco Mondada,et al.  The e-puck, a Robot Designed for Education in Engineering , 2009 .

[44]  Seth Copen Goldstein,et al.  Programmable Matter , 2005, Computer.

[45]  Vito Trianni,et al.  Evolutionary Swarm Robotics - Evolving Self-Organising Behaviours in Groups of Autonomous Robots , 2008, Studies in Computational Intelligence.

[46]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[47]  F Mondada,et al.  Social Integration of Robots into Groups of Cockroaches to Control Self-Organized Choices , 2007, Science.

[48]  Donald E. Knuth,et al.  The Art of Computer Programming, Volume I: Fundamental Algorithms, 2nd Edition , 1997 .

[49]  Alfred M. Bruckstein,et al.  Gathering Multiple Robotic Agents with Crude Distance Sensing Capabilities , 2008, ANTS Conference.

[50]  Erol Sahin,et al.  Modeling self-organized aggregation in swarm robotic systems , 2009, 2009 IEEE Swarm Intelligence Symposium.

[51]  Oussama Khatib,et al.  Springer Handbook of Robotics , 2007, Springer Handbooks.

[52]  James A. Yorke,et al.  No evidence of an association between mitochondrial DNA variants and osteoarthritis in 7393 cases and 5122 controls , 2012, Annals of the rheumatic diseases.

[53]  Pawel Zebrowski,et al.  Energy Efficient Robot Rendezvous , 2007, Fourth Canadian Conference on Computer and Robot Vision (CRV '07).

[54]  Eliseo Ferrante,et al.  Swarm robotics: a review from the swarm engineering perspective , 2013, Swarm Intelligence.

[55]  Daniel Merkle,et al.  Artificial Life 14 , 2014 .

[56]  Nicola Santoro,et al.  Solving the Robots Gathering Problem , 2003, ICALP.

[57]  L. Edelstein-Keshet,et al.  Complexity, pattern, and evolutionary trade-offs in animal aggregation. , 1999, Science.

[58]  Erol Sahin,et al.  Evolving aggregation behaviors for swarm robotic systems: a systematic case study , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..

[59]  Giuseppe Oriolo,et al.  A swarm aggregation algorithm based on local interaction with actuator saturations and integrated obstacle avoidance , 2013, 2013 IEEE International Conference on Robotics and Automation.

[60]  Michael R. M. Jenkin,et al.  Computational principles of mobile robotics , 2000 .