---
_id: '5960'
abstract:
- lang: eng
  text: In this paper we present a reliable method to verify the existence of loops
    along the uncertain trajectory of a robot, based on proprioceptive measurements
    only, within a bounded-error context. The loop closure detection is one of the
    key points in simultaneous localization and mapping (SLAM) methods, especially
    in homogeneous environments with difficult scenes recognitions. The proposed approach
    is generic and could be coupled with conventional SLAM algorithms to reliably
    reduce their computing burden, thus improving the localization and mapping processes
    in the most challenging environments such as unexplored underwater extents. To
    prove that a robot performed a loop whatever the uncertainties in its evolution,
    we employ the notion of topological degree that originates in the field of differential
    topology. We show that a verification tool based on the topological degree is
    an optimal method for proving robot loops. This is demonstrated both on datasets
    from real missions involving autonomous underwater vehicles and by a mathematical
    discussion.
article_processing_charge: No
arxiv: 1
author:
- first_name: Simon
  full_name: Rohou, Simon
  last_name: Rohou
- first_name: Peter
  full_name: Franek, Peter
  id: 473294AE-F248-11E8-B48F-1D18A9856A87
  last_name: Franek
  orcid: 0000-0001-8878-8397
- first_name: Clément
  full_name: Aubry, Clément
  last_name: Aubry
- first_name: Luc
  full_name: Jaulin, Luc
  last_name: Jaulin
citation:
  ama: Rohou S, Franek P, Aubry C, Jaulin L. Proving the existence of loops in robot
    trajectories. <i>The International Journal of Robotics Research</i>. 2018;37(12):1500-1516.
    doi:<a href="https://doi.org/10.1177/0278364918808367">10.1177/0278364918808367</a>
  apa: Rohou, S., Franek, P., Aubry, C., &#38; Jaulin, L. (2018). Proving the existence
    of loops in robot trajectories. <i>The International Journal of Robotics Research</i>.
    SAGE Publications. <a href="https://doi.org/10.1177/0278364918808367">https://doi.org/10.1177/0278364918808367</a>
  chicago: Rohou, Simon, Peter Franek, Clément Aubry, and Luc Jaulin. “Proving the
    Existence of Loops in Robot Trajectories.” <i>The International Journal of Robotics
    Research</i>. SAGE Publications, 2018. <a href="https://doi.org/10.1177/0278364918808367">https://doi.org/10.1177/0278364918808367</a>.
  ieee: S. Rohou, P. Franek, C. Aubry, and L. Jaulin, “Proving the existence of loops
    in robot trajectories,” <i>The International Journal of Robotics Research</i>,
    vol. 37, no. 12. SAGE Publications, pp. 1500–1516, 2018.
  ista: Rohou S, Franek P, Aubry C, Jaulin L. 2018. Proving the existence of loops
    in robot trajectories. The International Journal of Robotics Research. 37(12),
    1500–1516.
  mla: Rohou, Simon, et al. “Proving the Existence of Loops in Robot Trajectories.”
    <i>The International Journal of Robotics Research</i>, vol. 37, no. 12, SAGE Publications,
    2018, pp. 1500–16, doi:<a href="https://doi.org/10.1177/0278364918808367">10.1177/0278364918808367</a>.
  short: S. Rohou, P. Franek, C. Aubry, L. Jaulin, The International Journal of Robotics
    Research 37 (2018) 1500–1516.
date_created: 2019-02-13T09:36:20Z
date_published: 2018-10-24T00:00:00Z
date_updated: 2023-09-19T10:41:59Z
day: '24'
department:
- _id: UlWa
doi: 10.1177/0278364918808367
external_id:
  arxiv:
  - '1712.01341'
  isi:
  - '000456881100004'
intvolume: '        37'
isi: 1
issue: '12'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1712.01341
month: '10'
oa: 1
oa_version: Preprint
page: 1500-1516
publication: The International Journal of Robotics Research
publication_identifier:
  eissn:
  - 1741-3176
  issn:
  - 0278-3649
publication_status: published
publisher: SAGE Publications
quality_controlled: '1'
scopus_import: '1'
status: public
title: Proving the existence of loops in robot trajectories
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 37
year: '2018'
...