Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm
This paper addresses the problem of monocular Simultaneous Localization And Mapping on Lie groups using fiducial patterns. For that purpose, we propose a reformulation of the classical camera model as a model on matrix Lie groups. Thus, we define an original-state vector containing the camera pose a...
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| Format: | Article |
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MDPI AG
2022-01-01
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| Series: | Remote Sensing |
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| Online Access: | https://www.mdpi.com/2072-4292/14/3/571 |
| _version_ | 1797485098256302080 |
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| author | Samy Labsir Gaël Pages Damien Vivet |
| author_facet | Samy Labsir Gaël Pages Damien Vivet |
| author_sort | Samy Labsir |
| collection | DOAJ |
| description | This paper addresses the problem of monocular Simultaneous Localization And Mapping on Lie groups using fiducial patterns. For that purpose, we propose a reformulation of the classical camera model as a model on matrix Lie groups. Thus, we define an original-state vector containing the camera pose and the set of transformations from the world frame to each pattern, which constitutes the map’s state. Each element of the map’s state, as well as the camera pose, are intrinsically constrained to evolve on the matrix Lie group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>E</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>. Filtering is then performed by an extended Kalman filter dedicated to matrix Lie groups to solve the visual SLAM process (LG-EKF-VSLAM). This algorithm has been evaluated in different scenarios based on simulated data as well as real data. The results show that the LG-EKF-VSLAM can improve the absolute position and orientation accuracy, compared to a classical EKF visual SLAM (EKF-VSLAM). |
| first_indexed | 2024-03-09T23:13:55Z |
| format | Article |
| id | doaj.art-a7c138cd9e904327bd036db355d6ae79 |
| institution | Directory Open Access Journal |
| issn | 2072-4292 |
| language | English |
| last_indexed | 2024-03-09T23:13:55Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj.art-a7c138cd9e904327bd036db355d6ae792023-11-23T17:39:55ZengMDPI AGRemote Sensing2072-42922022-01-0114357110.3390/rs14030571Lie Group Modelling for an EKF-Based Monocular SLAM AlgorithmSamy Labsir0Gaël Pages1Damien Vivet2Thales LAS France, Rue Pierre Gilles de Gennes, 91470 Limours, FranceInstitut Supérieur de l’Aéronautique et de l’Espace (ISAE-SUPAERO), University of Toulouse, 31400 Toulouse, FranceInstitut Supérieur de l’Aéronautique et de l’Espace (ISAE-SUPAERO), University of Toulouse, 31400 Toulouse, FranceThis paper addresses the problem of monocular Simultaneous Localization And Mapping on Lie groups using fiducial patterns. For that purpose, we propose a reformulation of the classical camera model as a model on matrix Lie groups. Thus, we define an original-state vector containing the camera pose and the set of transformations from the world frame to each pattern, which constitutes the map’s state. Each element of the map’s state, as well as the camera pose, are intrinsically constrained to evolve on the matrix Lie group <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>E</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>. Filtering is then performed by an extended Kalman filter dedicated to matrix Lie groups to solve the visual SLAM process (LG-EKF-VSLAM). This algorithm has been evaluated in different scenarios based on simulated data as well as real data. The results show that the LG-EKF-VSLAM can improve the absolute position and orientation accuracy, compared to a classical EKF visual SLAM (EKF-VSLAM).https://www.mdpi.com/2072-4292/14/3/571visual SLAMcoded patternscamera modelKalman filteringoptimizationLie groups |
| spellingShingle | Samy Labsir Gaël Pages Damien Vivet Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm Remote Sensing visual SLAM coded patterns camera model Kalman filtering optimization Lie groups |
| title | Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm |
| title_full | Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm |
| title_fullStr | Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm |
| title_full_unstemmed | Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm |
| title_short | Lie Group Modelling for an EKF-Based Monocular SLAM Algorithm |
| title_sort | lie group modelling for an ekf based monocular slam algorithm |
| topic | visual SLAM coded patterns camera model Kalman filtering optimization Lie groups |
| url | https://www.mdpi.com/2072-4292/14/3/571 |
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