Sensor Localization by Few Distance Measurements via the Intersection of Implicit Manifolds

Michael M. Bilevich, Steven M. Lavalle, Dan Halperin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We present a general approach for determining the unknown (or uncertain) position and orientation of a sensor mounted on a robot in a known environment, using only a few distance measurements (between 2 to 6 typically), which is advantageous, among others, in sensor cost, and storage and information-communication resources. In-between the measurements, the robot can perform predetermined local motions in its workspace, which are useful for narrowing down the candidate poses of the sensor. We demonstrate our approach for planar workspaces, and show that, under mild transversality assumptions, already two measurements are sufficient to reduce the set of possible poses to a set of curves (one-dimensional objects) in the three-dimensional configuration space of the sensor R2×S1, and three or more measurements reduce the set of possible poses to a finite collection of points. However, analytically computing these potential poses for non-trivial intermediate motions between measurements raises substantial hardships and thus we resort to numerical approximation. We reduce the localization problem to a carefully tailored procedure of intersecting two or more implicitly defined two-manifolds, which we carry out to any desired accuracy, proving guarantees on the quality of the approximation. We demonstrate the real-time effectiveness of our method even at high accuracy on various scenarios and different allowable intermediate motions. We also present experiments with a physical robot. Our open-source software and supplementary materials are available at https://bitbucket.org/taucgl/vb-fdml-public.

Original languageEnglish
Title of host publicationProceedings - ICRA 2023
Subtitle of host publicationIEEE International Conference on Robotics and Automation
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1912-1918
Number of pages7
ISBN (Electronic)9798350323658
DOIs
StatePublished - 2023
Event2023 IEEE International Conference on Robotics and Automation, ICRA 2023 - London, United Kingdom
Duration: 29 May 20232 Jun 2023

Publication series

NameProceedings - IEEE International Conference on Robotics and Automation
Volume2023-May
ISSN (Print)1050-4729

Conference

Conference2023 IEEE International Conference on Robotics and Automation, ICRA 2023
Country/TerritoryUnited Kingdom
CityLondon
Period29/05/232/06/23

Funding

FundersFunder number
Blavatnik Computer Science Research Fund
US-Israel-BSF2019754
Yandex Machine Learning Initiative for Machine Learning
National Science Foundation
European Research Council101020977
Academy of FinlandPERCEPT 322637
Israel Science Foundation1736/19
Tel Aviv University
Ministry of Science and Technology, Israel103129

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