Document

**Published in:** LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

We consider a distributed system of n identical mobile robots operating in the two dimensional Euclidian plane. As in the previous studies, we consider the robots to be anonymous, oblivious, dis-oriented, and without any communication capabilities, operating based on the Look-Compute-Move model where the next location of a robot depends only on its view of the current configuration. Even in this seemingly weak model, most formation problems which require constructing specific configurations, can be solved quite easily when the robots are fully synchronized with each other. In this paper we introduce and study a new class of problems which, unlike the studied formation problems, cannot always be solved even in the fully synchronous model with atomic and rigid moves. This class of problems requires the robots to permute their locations in the plane. In particular, we are interested in implementing two special types of permutations - permutations without any fixed points and permutations of order n. The former (called Move-All) requires each robot to visit at least two of the initial locations, while the latter (called Visit-All) requires every robot to visit each of the initial locations in a periodic manner. We provide a characterization of the solvability of these problems, showing the main challenges in solving this class of problems for mobile robots. We also provide algorithms for the feasible cases, in particular distinguishing between one-step algorithms (where each configuration must be a permutation of the original configuration) and multi-step algorithms (which allow intermediate configurations). These results open a new research direction in mobile distributed robotics which has not been investigated before.

Shantanu Das, Giuseppe A. Di Luna, Paola Flocchini, Nicola Santoro, Giovanni Viglietta, and Masafumi Yamashita. Oblivious Permutations on the Plane. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 24:1-24:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{das_et_al:LIPIcs.OPODIS.2019.24, author = {Das, Shantanu and Di Luna, Giuseppe A. and Flocchini, Paola and Santoro, Nicola and Viglietta, Giovanni and Yamashita, Masafumi}, title = {{Oblivious Permutations on the Plane}}, booktitle = {23rd International Conference on Principles of Distributed Systems (OPODIS 2019)}, pages = {24:1--24:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-133-7}, ISSN = {1868-8969}, year = {2020}, volume = {153}, editor = {Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.24}, URN = {urn:nbn:de:0030-drops-118103}, doi = {10.4230/LIPIcs.OPODIS.2019.24}, annote = {Keywords: Distributed Algorithms, Mobile Robots, Fully synchronous, Oblivious, Permutations, Chirality, Sequence of configurations} }

Document

**Published in:** LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Consider a set of n mobile computational entities, called robots, located and operating on a continuous cycle C (e.g., the perimeter of a closed region of R^2) of arbitrary length l. The robots are identical, can only see their current location, have no location awareness, and cannot communicate at a distance. In this weak setting, we study the classical problems of gathering (GATHER), requiring all robots to meet at a same location; and election (ELECT), requiring all robots to agree on a single one as the "leader". We investigate how to solve the problems depending on the amount of knowledge (exact, upper bound, none) the robots have about their number n and about the length of the cycle l. Cost of the algorithms is analyzed with respect to time and number of random bits. We establish a variety of new results specific to the continuous cycle - a geometric domain never explored before for GATHER and ELECT in a mobile robot setting; compare Monte Carlo and Las Vegas algorithms; and obtain several optimal bounds.

Paola Flocchini, Ryan Killick, Evangelos Kranakis, Nicola Santoro, and Masafumi Yamashita. Gathering and Election by Mobile Robots in a Continuous Cycle. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{flocchini_et_al:LIPIcs.ISAAC.2019.8, author = {Flocchini, Paola and Killick, Ryan and Kranakis, Evangelos and Santoro, Nicola and Yamashita, Masafumi}, title = {{Gathering and Election by Mobile Robots in a Continuous Cycle}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {8:1--8:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.8}, URN = {urn:nbn:de:0030-drops-115044}, doi = {10.4230/LIPIcs.ISAAC.2019.8}, annote = {Keywords: Cycle, Election, Gathering, Las Vegas, Monte Carlo, Randomized Algorithm} }

Document

**Published in:** LIPIcs, Volume 95, 21st International Conference on Principles of Distributed Systems (OPODIS 2017)

We consider a distributed system consisting of autonomous mobile computing entities called robots moving in the three-dimensional space (3D-space). The robots are anonymous, oblivious, fully-synchronous and have neither any access to the global coordinate system nor any explicit communication medium. Each robot cooperates with other robots by observing the positions of other robots in its local coordinate system. One of the most fundamental agreement problems in 3D-space is the plane formation problem that requires the robots to land on a common plane, that is not predefined. This problem is not always solvable because of the impossibility of symmetry breaking. While existing results assume that the robots agree on the handedness of their local coordinate systems, we remove the assumption and consider the robots without chirality. The robots without chirality can never break the symmetry consisting of rotation symmetry and reflection symmetry. Such symmetry in 3D-space is fully described by 17 symmetry types each of which forms a group. We extend the notion of symmetricity [Suzuki and Yamashita, SIAM J. Compt. 1999] [Yamauchi et al., PODC 2016] to cover these 17 symmetry groups. Then we give a characterization of initial configurations from which the fully-synchronous robots without chirality can form a plane in terms of symmetricity.

Yusaku Tomita, Yukiko Yamauchi, Shuji Kijima, and Masafumi Yamashita. Plane Formation by Synchronous Mobile Robots without Chirality. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{tomita_et_al:LIPIcs.OPODIS.2017.13, author = {Tomita, Yusaku and Yamauchi, Yukiko and Kijima, Shuji and Yamashita, Masafumi}, title = {{Plane Formation by Synchronous Mobile Robots without Chirality}}, booktitle = {21st International Conference on Principles of Distributed Systems (OPODIS 2017)}, pages = {13:1--13:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-061-3}, ISSN = {1868-8969}, year = {2018}, volume = {95}, editor = {Aspnes, James and Bessani, Alysson and Felber, Pascal and Leit\~{a}o, Jo\~{a}o}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2017.13}, URN = {urn:nbn:de:0030-drops-86337}, doi = {10.4230/LIPIcs.OPODIS.2017.13}, annote = {Keywords: Autonomous mobile robots, plane formation problem, symmetry breaking, group theory} }

Document

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

The Meeting problem for k>=2 searchers in a polygon P (possibly with holes) consists in making the searchers move within P, according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of P, we minimize the number of searchers k for which the Meeting problem is solvable. Specifically, if P has a rotational symmetry of order sigma (where sigma=1 corresponds to no rotational symmetry), we prove that k=sigma+1 searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with k=2 searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations (provided that the coordinates of the polygon's vertices are algebraic real numbers in some global coordinate system), and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.

Giuseppe A. Di Luna, Paola Flocchini, Nicola Santoro, Giovanni Viglietta, and Masafumi Yamashita. Meeting in a Polygon by Anonymous Oblivious Robots. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{diluna_et_al:LIPIcs.DISC.2017.14, author = {Di Luna, Giuseppe A. and Flocchini, Paola and Santoro, Nicola and Viglietta, Giovanni and Yamashita, Masafumi}, title = {{Meeting in a Polygon by Anonymous Oblivious Robots}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {14:1--14:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.14}, URN = {urn:nbn:de:0030-drops-79833}, doi = {10.4230/LIPIcs.DISC.2017.14}, annote = {Keywords: Meeting problem, Oblivious robots, Polygon, Self-stabilization} }

X

Feedback for Dagstuhl Publishing

Feedback submitted

Please try again later or send an E-mail