ABSTRACT
We revisit the problem of gathering autonomous robots in the plane. In particular, we consider non-transparent unit-disc robots (i.e., fat) in an asynchronous setting with vision as the only means of coordination and robots only make local decisions. We use a state-machine representation to formulate the gathering problem and develop a distributed algorithm that solves the problem for any number of fat robots. The main idea behind the algorithm is to enforce the robots to reach a configuration in which all the following hold:
(i) The robots' centers form a convex hull in which all robots are on the convex hull's boundary;
(ii) Each robot can see all other robots;
(iii) The configuration is connected: every robot touches another robot and all robots form together a connected formation.
We show that starting from any initial configuration, the fat robots eventually reach such a configuration and terminate yielding a solution to the gathering problem.
- Ch. Agathangelou, Ch. Georgiou, and M. Mavronicolas. A distributed algorithm for gathering many fat robots in the plane. In arXiv:1209.3904, 2012.Google Scholar
- N. Agmon and D. Peleg. Fault-tolerant gathering algorithms for autonomous mobile robots. In Proc. of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pages 1070--1078. Google ScholarDigital Library
- H. Ando, Y. Oasa, I. Suzuki, and M. Yamashita. Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transactions on Robotics and Automation, 15(5):818--828, 1999.Google ScholarCross Ref
- H. Attiya and J. Welch. Distributed Computing: Fundamentals, Simulationsand Advanced Topics. Second edition, Wiley & Sons, 2004. Google ScholarDigital Library
- A. Bandettini, F. Luporini, G. Viglietta. A survey on open problems for mobile robots. In arXiv:1111.2259v1, 2011.Google Scholar
- K. Bolla, T. Kovacs, and G. Fazekas. Gathering of fat robots with limited visibility and without global navigation. In Proc. of ICAISC/SIDE-EC 2012, pages 30--38. Google ScholarDigital Library
- S. G. Chaudhuri and K. Mukhopadhyaya. Gathering asynchronous transparent fat robots. In Proc. of the 6th International Conference on Distributed Computing and Internet Technology (ICDCIT 2010), pages 170--175. Google ScholarDigital Library
- A. Cord-Landwehr, B. Degener, M. Fischer, M. Hüllmann, B. Kempkes, A. Klaas, P. Kling, S. Kurras, M. Märtens, F. M. A Der Heide, C. Raupach, K. Swierkot, D. Warner, C. Weddemann, and D. Wonisch. Collisionless gathering of robots with an extent. In Proc. of SOFSEM 2011, pages 178--189. Google ScholarDigital Library
- J. Czyzowicz, L. Gasieniec, and A. Pelc. Gathering few fat mobile robots in the plane. Theoretical Computer Science, 410(6-7):481--499, 2009. Google ScholarDigital Library
- A. Dutta, S. G. Chaudhuri, S. Datta, and K. Mukhopadhyaya. Circle formation by asynchronous fat robots with limited visibility. In Proc. of ICDCIT 2012, pages 83--93. Google ScholarDigital Library
- P. Flocchini, G. Prencipe, N. Santoro. Distributed Computing by Oblivious Mobile Robots.Synthesis Lectures on Distributed Computing Theory, Morgan & Claypool, 2012. Google ScholarDigital Library
- P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer. Gathering of asynchronous robots with limited visibility. Theoretical Computer Science, 337(1-3):147--168, 2005. Google ScholarDigital Library
- R. L. Graham. An efficient algorithm for determining the convex hull of a finite planar set. Information Processing Letters, 1(4):132--133, 1972.Google ScholarCross Ref
- S. Kamei, A. Lamani, F. Ooshita, and S. Tixeuil. Gathering an even number of robots in an odd ring without global multiplicity detection. In Proc. of the 37th International Symposium on Mathematical Foundations of Computer Science (MFCS 2012), pages 542--553. Google ScholarDigital Library
- S. Souissi, T. Izumi, and K. Wada. Distributed algorithms for cooperative mobile robots: A survey. In Proc. of the 2nd Second International Conference on Networking and Computing (ICNC 2011), pages 364--371. Google ScholarDigital Library
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- A distributed algorithm for gathering many fat mobile robots in the plane
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