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Given any multiset F of points in the Euclidean plane and a set R of robots such that |R|=|F|, the Arbitrary Pattern Formation (APF) problem asks for a distributed algorithm that moves robots so as to reach a configuration similar to F.…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-02-07 Serafino Cicerone , Gabriele Di Stefano , Alfredo Navarra

Arbitrary pattern formation ($\mathcal{APF}$) by mobile robots is studied by many in literature under different conditions and environment. Recently it has been studied on an infinite grid network but with full visibility. In opaque robot…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-09 Manash Kumar Kundu , Pritam Goswami , Satakshi Ghosh , Buddhadeb Sau

Arbitrary Pattern Formation (APF) is a fundamental coordination problem in swarm robotics. It requires a set of autonomous robots (mobile computing units) to form an arbitrary pattern (given as input) starting from any initial pattern. This…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-03-28 Avisek Sharma , Satakshi Ghosh , Pritam Goswami , Buddhadeb Sau

In the field of distributed system, Arbitrary Pattern Formation (APF) problem is an extensively studied problem. The purpose of APF is to design an algorithm to move a swarm of robots to a particular position on an environment (discrete or…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-07-17 Brati Mondal , Pritam Goswami , Avisek Sharma , Buddhadeb Sau

Arbitrary Pattern formation ($\mathcal{APF}$) by a swarm of mobile robots is a widely studied problem in the literature. Many works regarding $\mathcal{APF}$ have been proposed on plane and infinite grid by point robots. But in practical…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-07-01 Manash Kumar Kundu , Pritam Goswami , Satakshi Ghosh , Buddhadeb Sau

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 problem has been extensively studied in…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-11-05 Kaustav Bose , Ranendu Adhikary , Manash Kumar Kundu , Buddhadeb Sau

The \textsc{Arbitrary Pattern Formation} (\textsc{Apf}) is a widely studied in distributed computing for swarm robots. This problem asks to design a distributed algorithm that allows a team of identical, autonomous mobile robots to form any…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-05-30 Satakshi Ghosh , Pritam Goswami , Avisek Sharma , Buddhadeb Sau

Arbitrary Pattern Formation is a widely studied problem in autonomous robot systems. The problem asks to design a distributed algorithm that moves a team of autonomous, anonymous and identical mobile robots to form any arbitrary pattern…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-10-08 Kaustav Bose , Ranendu Adhikary , Manash Kumar Kundu , Buddhadeb Sau

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. The robots are assumed to be autonomous, anonymous and identical. They…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-10-08 Kaustav Bose , Manash Kumar Kundu , Ranendu Adhikary , Buddhadeb Sau

Arbitrary pattern formation (\textsc{Apf}) is a well-studied problem in swarm robotics. To the best of our knowledge, the problem has been considered in two different settings: one in a euclidean plane and another in an infinite grid. This…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-08-29 Avisek Sharma , Satakshi Ghosh , Pritam Goswami , Buddhadeb Sau

\textsc{Arbitrary Pattern Formation} is a fundamental problem in autonomous mobile robot systems. The problem asks to design a distributed algorithm that moves a team of autonomous, anonymous and identical mobile robots to form any…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-02-17 Kaustav Bose , Archak Das , Buddhadeb Sau

Two fundamental problems of distributed computing are Gathering and Arbitrary pattern formation (\textsc{Apf}). These two tasks are different in nature as in gathering robots meet at a point but in \textsc{Apf} robots form a fixed pattern…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-08-28 Satakshi Ghosh , Avisek Sharma , Pritam Goswami , Buddhadeb Sau

A fundamental problem in Distributed Computing is the Pattern Formation problem, where some independent mobile entities, called robots, have to rearrange themselves in such a way as to form a given figure from every possible…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-05-23 Marcello Mamino , Giovanni Viglietta

Given a set of $n\geq 1$ autonomous, anonymous, indistinguishable, silent, and possibly disoriented mobile unit disk (i.e., fat) robots operating following Look-Compute-Move cycles in the Euclidean plane, we consider the Pattern Formation…

Computational Geometry · Computer Science 2025-03-20 Rusul J. Alsaedi , Joachim Gudmundsson , André van Renssen

In the arbitrary pattern formation problem, $n$ autonomous, mobile robots must form an arbitrary pattern $P \subseteq \mathbb{R}^2$. The (deterministic) robots are typically assumed to be indistinguishable, disoriented, and unable to…

Robotics · Computer Science 2024-04-05 Christopher Hahn , Jonas Harbig , Peter Kling

Pattern formation is one of the most fundamental problems in distributed computing, which has recently received much attention. In this paper, we initiate the study of distributed pattern formation in situations when some robots can be…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-08-28 Debasish Pattanayak , Klaus-Tycho Foerster , Partha Sarathi Mandal , Stefan Schmid

We study the computational power that oblivious robots operating in the plane have under sequential schedulers. We show that this power is much stronger than the obvious capacity these schedulers offer of breaking symmetry, and thus to…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-03-06 Paola Flocchini , Alfredo Navarra , Debasish Pattanayak , Francesco Piselli , Nicola Santoro

The dispersion problem on graphs asks $k\leq n$ robots placed initially arbitrarily on the nodes of an $n$-node anonymous graph to reposition autonomously to reach a configuration in which each robot is on a distinct node of the graph. This…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-09-05 Ajay D. Kshemkalyani , Anisur Rahaman Molla , Gokarna Sharma

This paper presents a deterministic algorithm for forming a given asymmetric pattern in finite time by a set of autonomous, homogeneous, oblivious mobile robots under the CORDA model. The robots are represented as points on the 2D plane.…

Distributed, Parallel, and Cluster Computing · Computer Science 2014-03-12 Sruti Gan Chaudhuri , Swapnil Ghike , Shrainik Jain , Krishnendu Mukhopadhyaya

Consider a set of $n$ simple autonomous mobile robots (asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, non-rigid, deterministic) initially in distinct…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-30 Paola Flocchini , Giuseppe Prencipe , Nicola Santoro , Giovanni Viglietta
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