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Pattern Formation

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Distributed Computing by Mobile Entities

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11340))

Abstract

The Pattern Formation problem is one of the most important coordination problem for robotic systems. Initially the entities are in arbitrary positions; within finite time they must arrange themselves in the space so to form a pattern given in input. In this chapter, we will mainly deal with the problem in the \(\mathcal{OBLOT}\) model.

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Notes

  1. 1.

    Note that, since at this time the robots still do not have a common agreement on the direction of the X axis, for some robots \({\mathcal M} _\mathbb D \) and \({\mathcal L} _\mathbb D \) might be different. All of them, however, agree on \(K _m\).

  2. 2.

    Note that, since \(\mathbb P _R\) is symmetric, nothing changes if the topmost point on the leftmost vertical axis tangent to \(\mathbb P\) is mapped onto \({ Out} \), and the topmost point on the rightmost vertical axis tangent to \(\mathbb P\) is mapped onto \({ Out}' \).

  3. 3.

    Equivalently, the position of the landmarks is known a priori to all robots.

  4. 4.

    For a plane graph, the periphery is the boundary of the exterior face.

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Author information

Authors and Affiliations

  1. University of Pisa, Pisa, Italy

    Giuseppe Prencipe

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  1. Giuseppe Prencipe
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Correspondence to Giuseppe Prencipe .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, ON, Canada

    Paola Flocchini

  2. University of Pisa, Pisa, Italy

    Giuseppe Prencipe

  3. Carleton University, Ottawa, ON, Canada

    Nicola Santoro

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Prencipe, G. (2019). Pattern Formation. In: Flocchini, P., Prencipe, G., Santoro, N. (eds) Distributed Computing by Mobile Entities. Lecture Notes in Computer Science(), vol 11340. Springer, Cham. https://doi.org/10.1007/978-3-030-11072-7_3

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  • DOI: https://doi.org/10.1007/978-3-030-11072-7_3

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  • Online ISBN: 978-3-030-11072-7

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