Global Asymptotic Convergent Observer for SLAM
This paper investigates the global convergence problem of SLAM algorithms, a problem that has been subject to topological obstacles. This is due to the fact that state-space of attitude kinematics, <inline-formula> <tex-math notation="LaTeX">$SO(3)$ </tex-math></inline...
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| Format: | Article |
| Language: | English |
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IEEE
2022-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9945956/ |
| _version_ | 1811322177784381440 |
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| author | Seyed Hamed Hashemi Jouni Mattila |
| author_facet | Seyed Hamed Hashemi Jouni Mattila |
| author_sort | Seyed Hamed Hashemi |
| collection | DOAJ |
| description | This paper investigates the global convergence problem of SLAM algorithms, a problem that has been subject to topological obstacles. This is due to the fact that state-space of attitude kinematics, <inline-formula> <tex-math notation="LaTeX">$SO(3)$ </tex-math></inline-formula>, is a non-contractible manifold. Hence, <inline-formula> <tex-math notation="LaTeX">$SO(3)$ </tex-math></inline-formula> is not diffeomorphic to Euclidean space. Therefore, existing SLAM algorithms can only guarantee almost global convergence. In order to overcome topological obstructions, this paper introduces a gradient-based hybrid observer that ensures global asymptotic convergence of estimation errors to zero. Moreover, integral action is augmented into the proposed observer to estimate unknown constant bias. Accordingly, a projection scheme is designed to cope with the integral action. Lyapunov stability theorem is used to prove the global asymptotic convergence of the proposed algorithm. Experimental and simulation results are provided to evaluate the performance and demonstrate the effectiveness and robustness of the proposed observer. |
| first_indexed | 2024-04-13T13:30:41Z |
| format | Article |
| id | doaj.art-9e751b4604fc4e57b5861e26375f7a19 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-13T13:30:41Z |
| publishDate | 2022-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-9e751b4604fc4e57b5861e26375f7a192022-12-22T02:44:59ZengIEEEIEEE Access2169-35362022-01-011012241412242210.1109/ACCESS.2022.32215249945956Global Asymptotic Convergent Observer for SLAMSeyed Hamed Hashemi0https://orcid.org/0000-0003-2780-5709Jouni Mattila1https://orcid.org/0000-0003-1799-4323Faculty of Engineering and Natural Sciences, Unit of Automation Technology and Mechanical Engineering, Tampere University, Tampere, FinlandFaculty of Engineering and Natural Sciences, Unit of Automation Technology and Mechanical Engineering, Tampere University, Tampere, FinlandThis paper investigates the global convergence problem of SLAM algorithms, a problem that has been subject to topological obstacles. This is due to the fact that state-space of attitude kinematics, <inline-formula> <tex-math notation="LaTeX">$SO(3)$ </tex-math></inline-formula>, is a non-contractible manifold. Hence, <inline-formula> <tex-math notation="LaTeX">$SO(3)$ </tex-math></inline-formula> is not diffeomorphic to Euclidean space. Therefore, existing SLAM algorithms can only guarantee almost global convergence. In order to overcome topological obstructions, this paper introduces a gradient-based hybrid observer that ensures global asymptotic convergence of estimation errors to zero. Moreover, integral action is augmented into the proposed observer to estimate unknown constant bias. Accordingly, a projection scheme is designed to cope with the integral action. Lyapunov stability theorem is used to prove the global asymptotic convergence of the proposed algorithm. Experimental and simulation results are provided to evaluate the performance and demonstrate the effectiveness and robustness of the proposed observer.https://ieeexplore.ieee.org/document/9945956/Geometric observersglobal convergencehybrid systemssimultaneous localization and mapping (SLAM) |
| spellingShingle | Seyed Hamed Hashemi Jouni Mattila Global Asymptotic Convergent Observer for SLAM IEEE Access Geometric observers global convergence hybrid systems simultaneous localization and mapping (SLAM) |
| title | Global Asymptotic Convergent Observer for SLAM |
| title_full | Global Asymptotic Convergent Observer for SLAM |
| title_fullStr | Global Asymptotic Convergent Observer for SLAM |
| title_full_unstemmed | Global Asymptotic Convergent Observer for SLAM |
| title_short | Global Asymptotic Convergent Observer for SLAM |
| title_sort | global asymptotic convergent observer for slam |
| topic | Geometric observers global convergence hybrid systems simultaneous localization and mapping (SLAM) |
| url | https://ieeexplore.ieee.org/document/9945956/ |
| work_keys_str_mv | AT seyedhamedhashemi globalasymptoticconvergentobserverforslam AT jounimattila globalasymptoticconvergentobserverforslam |