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Resource-Aware Algorithms for Distributed Loop Closure Detection with Provable Performance Guarantees

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Algorithmic Foundations of Robotics XIII (WAFR 2018)

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 14))

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Abstract

Inter-robot loop closure detection, e.g., for collaborative simultaneous localization and mapping (CSLAM), is a fundamental capability for many multirobot applications in GPS-denied regimes. In real-world scenarios, this is a resource-intensive process that involves exchanging observations and verifying potential matches. This poses severe challenges especially for small-size and low-cost robots with various operational and resource constraints that limit, e.g., energy consumption, communication bandwidth, and computation capacity. This paper presents resource-aware algorithms for distributed inter-robot loop closure detection. In particular, we seek to select a subset of potential inter-robot loop closures that maximizes a monotone submodular performance metric without exceeding computation and communication budgets. We demonstrate that this problem is in general NP-hard, and present efficient approximation algorithms with provable performance guarantees. A convex relaxation scheme is used to certify near-optimal performance of the proposed framework in real and synthetic SLAM benchmarks.

Y. Tian and K. Khosoussi: Equal contribution.

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Notes

  1. 1.

    As the fidelity of metadata increases, the similarity score becomes more effective in identifying true loop closures. However, this typically comes at the cost of increased data transmission during metadata exchange. In this paper we do not take into account the cost of forming the exchange graph which is inevitable for optimal data exchange [10].

  2. 2.

    Selecting a vertex is equivalent to broadcasting the corresponding observation; see Fig. 1b.

  3. 3.

    This is a reasonable approximation when, e.g., b is sufficiently large (\(b \ge b_0\)) since \(k/(\varDelta b) - 1/b < {\lfloor k/\varDelta \rfloor }/{b} \le k/( \varDelta b)\) and thus the introduced error in the exponent will be at most \(1/b_0\).

  4. 4.

    Omitted due to space limitation.

  5. 5.

    For KITTI 00 we do not show UPT when using the D-criterion objective, because solving the convex relaxation in this case is too time-consuming.

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Acknowledgments

This work was supported in part by the NASA Convergent Aeronautics Solutions project Design Environment for Novel Vertical Lift Vehicles (DELIVER), by ONR under BRC award N000141712072, and by ARL DCIST under Cooperative Agreement Number W911NF-17-2-0181.

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Authors and Affiliations

  1. Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA, USA

    Yulun Tian, Kasra Khosoussi & Jonathan P. How

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  1. Yulun Tian
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  3. Jonathan P. How
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Corresponding author

Correspondence to Kasra Khosoussi .

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Editors and Affiliations

  1. Departamento de Sistemas Digitales, Instituto Tecnológico Autónomo de México, México, Mexico

    Marco Morales

  2. Department of Computer Science, University of New Mexico, Albuquerque, NM, USA

    Lydia Tapia

  3. Universidad Politécnica de Yucatán, Yucatán, Mexico

    Gildardo Sánchez-Ante

  4. Georgia Tech, Atlanta, GA, USA

    Seth Hutchinson

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Tian, Y., Khosoussi, K., How, J.P. (2020). Resource-Aware Algorithms for Distributed Loop Closure Detection with Provable Performance Guarantees. In: Morales, M., Tapia, L., Sánchez-Ante, G., Hutchinson, S. (eds) Algorithmic Foundations of Robotics XIII. WAFR 2018. Springer Proceedings in Advanced Robotics, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-44051-0_25

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