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Distributed Localization

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Parallel and Distributed Map Merging and Localization

Part of the book series: SpringerBriefs in Computer Science ((BRIEFSCOMPUTER))

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Abstract

In this chapter we study the problem of distributed localization, which consists of establishing a common frame and computing the robots’ localization relative to this frame. Each robot is capable of measuring the relative pose of its neighboring robots. However, it does not know the poses of far robots, and it can only exchange data with neighbors using the range-limited communication network. The analyzed algorithms have the interesting property that can be executed in a distributed fashion. They allow each robot to recover localization using exclusively local information and local interactions with its neighbors. Besides, they only require each robot to maintain an estimate of its own pose. Thus, the memory load of the algorithm is low compared to methods where each robot must also estimate the poses of any other robot. We analyze two different scenarios and study distributed algorithms for them. In the first scenario each robot measures the noisy planar position and orientation of nearby robots to estimate its own full localization with respect to an anchor node. In the second case, robots take noisy measurements of the relative three-dimensional positions of their neighbors, which is used to estimate their three-dimensional positions with respect to the simultaneously computed centroid reference. When the centroid of the team is selected as common frame, the estimates are more precise than with any anchor selection.

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Notes

  1. 1.

    \(A \succ B\) (\(A \succeq B\)) represent that matrix \(A-B\) is positive-definite (positive-semidefinite). Equivalently, \(\prec \), \(\preceq \) are used for negative-definite and negative-semidefinite matrices.

  2. 2.

    The block-trace of a matrix defined by blocks \(P=[P_{ij}]\) with \(i,j\in \{1,\dots ,n\}\) is the sum of its diagonal blocks, \(\mathrm {blkTr}(P)=\mathop {\sum }_{i=1}^n P_{ii}\).

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Author information

Authors and Affiliations

  1. Instituto de Investigación en Ingeniería de Aragón , University of Zaragoza, Saragossa, Spain

    Rosario Aragues & Carlos Sagues

  2. Institut Pascal, CNRS, Clermont Université, IFMA, Clermont-Ferrand, France

    Youcef Mezouar

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  1. Rosario Aragues
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  2. Carlos Sagues
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  3. Youcef Mezouar
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Correspondence to Rosario Aragues .

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Aragues, R., Sagues, C., Mezouar, Y. (2015). Distributed Localization. In: Parallel and Distributed Map Merging and Localization. SpringerBriefs in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-319-25886-7_3

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  • DOI: https://doi.org/10.1007/978-3-319-25886-7_3

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