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Arbitrary Pattern Formation on Infinite Grid by Asynchronous Oblivious Robots [article]

Kaustav Bose, Ranendu Adhikary, Manash Kumar Kundu, Buddhadeb Sau
2018 arXiv   pre-print
The Arbitrary Pattern Formation problem asks to design a distributed algorithm that allows a set of autonomous mobile robots to form any specific but arbitrary geometric pattern given as input.  ...  The robots do not agree on any common global coordinate system or chirality. We have shown that a set of robots can form any arbitrary pattern, if their starting configuration is asymmetric.  ...  Combined with the result in [8] , they deduced that ARBITRARY PATTERN FORMATION and LEADER ELECTION are equivalent, i.e., it is possible to solve ARBITRARY PATTERN FORMATION for n ≥ 4 with chirality (  ... 
arXiv:1811.00834v1 fatcat:4xoff7uzhjgqbaem5a2kjmtfmy

Leader Election Problem versus Pattern Formation Problem [chapter]

Yoann Dieudonné, Franck Petit, Vincent Villain
2010 Lecture Notes in Computer Science  
Leader election and arbitrary pattern formation are fundammental tasks for a set of autonomous mobile robots. The former consists in distinguishing a unique robot, called the leader.  ...  In such a system, we show that both problems are equivalent, that is it is possible to solve the pattern formation problem for n = 2 if and only if the leader election is solvable too.  ...  The Arbitrary Pattern Formation Problem In the Arbitrary Pattern Formation Problem, the robots are given in input the same pattern, described as a set of points in the plane (each robot sees the same pattern  ... 
doi:10.1007/978-3-642-15763-9_26 fatcat:e3emxqvrurbblfwxwrc6s2fdxa

Leader Election Problem Versus Pattern Formation Problem [article]

Yoann Dieudonné
2012 arXiv   pre-print
Leader election and arbitrary pattern formation are funda- mental tasks for a set of autonomous mobile robots. The former consists in distinguishing a unique robot, called the leader.  ...  In such a system, Flochini et al. proved in [11] that it is possible to elect a leader for n \geq 3 robots if it is possible to form any pattern for n \geq 3.  ...  Arbitrary Pattern Formation Problem In the Arbitrary Pattern Formation Problem, the robots have in input the same pattern, called the target pattern P, described as a set of positions in the plane given  ... 
arXiv:0902.2851v3 fatcat:7cyt7nouczhdvlyllps65vbdaa

Multi-robot system for artistic pattern formation

Javier Alonso-Mora, Andreas Breitenmoser, Martin Rufli, Roland Siegwart, Paul Beardsley
2011 2011 IEEE International Conference on Robotics and Automation  
This paper describes work on multi-robot pattern formation. Arbitrary target patterns are represented with an optimal robot deployment, using a method that is independent of the number of robots.  ...  Experimental results are provided for a representative set of patterns, for a swarm of up to ten physical robots, and for fifty virtual robots in simulation.  ...  The presented multi-robot system is capable of creating multi-pattern formations as well as transitions between arbitrary patterns, involving filling and non-filling patterns likewise.  ... 
doi:10.1109/icra.2011.5980269 dblp:conf/icra/Alonso-MoraBRSB11 fatcat:e7pttzwaqjboreubeqbh5bzhk4

Exploration of Finite 2D Square Grid by a Metamorphic Robotic System [article]

Keisuke Doi, Yukiko Yamauchi, Shuji Kijima, Masafumi Yamashita
2019 arXiv   pre-print
We consider exploration of finite 2D square grid by a metamorphic robotic system consisting of anonymous oblivious modules.  ...  We show that if the modules agree on the directions (north, south, east, and west), three modules are necessary and sufficient for exploration from an arbitrary initial configuration, otherwise five modules  ...  They pointed out that the pattern formation problem is essentially related to the agreement problem because once the robots agree on a global coordinate system, they can form any arbitrary pattern [19  ... 
arXiv:1808.00214v2 fatcat:c22yxb7lsjcp7i6rtn6vtazdi4

On the computational power of oblivious robots

Shantanu Das, Paola Flocchini, Nicola Santoro, Masafumi Yamashita
2010 Proceeding of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing - PODC '10  
The robots are endowed with visual perception but do not have any means of explicit communication with each other, and have no memory of the past.  ...  In the extensive literature it has been shown how such simple robots can form a single geometric pattern (e.g., a line, a circle, etc), however arbitrary, in spite of their obliviousness.  ...  The arbitrary pattern formation problem, that of forming any pattern given in input, has also been studied [2, 16, 21, 22] .  ... 
doi:10.1145/1835698.1835761 dblp:conf/podc/DasFSY10 fatcat:gdqmz4xkyjbcdpwlhbffvjtv6a

Pattern Formation Problem for Synchronous Mobile Robots in the Three Dimensional Euclidean Space [article]

Yukiko Yamauchi, Taichi Uehara, Masafumi Yamashita
2016 arXiv   pre-print
For solvable instances, we present a pattern formation algorithm for oblivious FSYNC robots.  ...  We show the following necessary and sufficient condition for the pattern formation problem which is a natural extension of the existing results of the pattern formation problem in 2D-space: FSYNC robots  ...  Yamauchi et al. showed a randomized pattern formation algorithm for oblivious ASYNC robots that breaks the symmetricity of the initial configuration and forms any target pattern with probability 1 [20  ... 
arXiv:1509.09207v2 fatcat:tbaqjczb4bcwzeexywpftqun3u

Conic Formation in Presence of Faulty Robots [article]

Debasish Pattanayak, Klaus-Tycho Foerster, Partha Sarathi Mandal, Stefan Schmid
2020 arXiv   pre-print
In this paper, we initiate the study of distributed pattern formation in situations when some robots can be faulty.  ...  In particular, we consider the well-established look-compute-move model with oblivious, anonymous robots.  ...  Hence the configuration in the next step becomes an arbitrary configuration. We thus need three steps to achieve pattern formation instead of two.  ... 
arXiv:2003.01914v2 fatcat:rkg6xwpclfbgng3y2atc62wwoi

Arbitrary Pattern Formation by Asynchronous Opaque Robots with Lights [article]

Kaustav Bose, Manash Kumar Kundu, Ranendu Adhikary, Buddhadeb Sau
2020 arXiv   pre-print
The Arbitrary Pattern Formation problem asks for a distributed algorithm that moves a set of autonomous mobile robots to form any arbitrary pattern given as input.  ...  In both settings, we have provided a full characterization of initial configurations from where any arbitrary pattern can be formed.  ...  Combined with the result in [18] , it follows that Arbitrary Pattern Formation and Leader election are equivalent, i.e., it is possible to solve Arbitrary Pattern Formation for n ≥ 4 with chirality (resp  ... 
arXiv:1902.04950v4 fatcat:uugo7fr57ff2xlflwnlivoby3y

Plane Formation by Synchronous Mobile Robots in the Three Dimensional Euclidean Space [article]

Yukiko Yamauchi, Taichi Uehara, Shuji Kijima, Masafumi Yamashita
2016 arXiv   pre-print
Though there are plenty of results on the agreement problem for robots in the two dimensional plane, for example, the point formation problem, the pattern formation problem, and so on, this is the first  ...  The robots are fully synchronous and endowed with visual perception.  ...  Das et al. considered formation of a sequence of patterns by oblivious SSYNC robots with rigid movement [11] .  ... 
arXiv:1505.04546v3 fatcat:632vg2iavffvfer7eog56napty

Forming sequences of geometric patterns with oblivious mobile robots

Shantanu Das, Paola Flocchini, Nicola Santoro, Masafumi Yamashita
2014 Distributed computing  
This paper aims to understand the computational limits imposed by the obliviousness of the robots by studying the formation of a series of geometric patterns instead of a single pattern.  ...  We show that, under particular conditions, oblivious robot systems can indeed form a given series of geometric patterns starting from any arbitrary configuration.  ...  The arbitrary pattern formation problem, that is forming any pattern given in input, has also been studied [3, 16, 17, 20, 25, 26, 28] .  ... 
doi:10.1007/s00446-014-0220-9 fatcat:yqrwa2js3ba7jk3jtvh6l3usk4

Arbitrary pattern formation by asynchronous, anonymous, oblivious robots

Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, Peter Widmayer
2008 Theoretical Computer Science  
If the robots have no common agreement about their environment, they cannot form an arbitrary pattern.  ...  We therefore study a hard task for a set of weak robots. The task is for the robots in the plane to form any arbitrary pattern that is given in advance.  ...  The Arbitrary Pattern Formation Problem We study the problem of forming an arbitrary geometric pattern, where a pattern P is a set of points p 0 , . . . , p n (given by their Cartesian coordinates) in  ... 
doi:10.1016/j.tcs.2008.07.026 fatcat:re2rv2vmhzf3ro5u5hunlk5giu

Teach Me What You Want to Play: Learning Variants of Connect Four through Human-Robot Interaction [article]

Ali Ayub, Alan R. Wagner
2020 arXiv   pre-print
Our results show that the robot can learn arbitrary win conditions for the game with little prior knowledge of the win conditions and then play the game with a human utilizing the learned win conditions  ...  The paper demonstrates a method for teaching a robot the win conditions of the game Connect Four and its variants using a single demonstration and a few trial examples with a question and answer session  ...  Learning Variants of Connect Four through HRI  ... 
arXiv:2001.01004v3 fatcat:lzlcn4bujfcodornciiu3ibsdq

Autonomous Mobile Robots: A Distributed Computing Perspective [chapter]

Giuseppe Prencipe
2013 Lecture Notes in Computer Science  
In this paper we describe the current investigations on the algorithmic limitations of what autonomous mobile robots can do with respect to different coordination problems, and overview the main research  ...  The distributed coordination and control of a team of autonomous mobile robots is a problem widely studied in a variety of fields, such as engineering, artificial intelligence, artificial life, robotics  ...  In its most general definition, the robots are required to form an arbitrary pattern.  ... 
doi:10.1007/978-3-642-45346-5_2 fatcat:4ngp6gsko5fh5lc4n2hljihvs4

A General Approach to Swarm Coordination using Circle Formation [chapter]

Swaminathan Karthikeyan, Minai A. Ali
2006 Studies in Computational Intelligence  
This involves identifying specific robots to achieve different geometric patterns like lines, semicircles, triangles and squares, and dividing the robots into subgroups, which can then perform specific  ...  The idea behind this approach is that circle formation can be seen as a method of organizing the robots in a regular formation which can then be exploited.  ...  In the circle formation algorithm, the robots are initially in arbitrary positions.  ... 
doi:10.1007/978-3-540-34690-6_3 fatcat:pqubm34gtzgcdgubv4yh4vrmjy
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