Overlapping Schwarz Preconditioners for Pose-Graph SLAM in Robotics
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918380723765248 |
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| author | Köhler, Stephan Rheinbach, Oliver Tee, Yue Xiang Zug, Sebastian |
| author_facet | Köhler, Stephan Rheinbach, Oliver Tee, Yue Xiang Zug, Sebastian |
| contents | We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph optimization back-end in Simultaneous Localization and Mapping (SLAM) in robotics. A brief introduction to both SLAM and domain decomposition preconditioners is given, followed by a description of the nonlinear least-squares formulation, its linearization, and the resulting matrix structure, making the paper accessible to readers without prior knowledge of either field. Numerical experiments for a simple model problem demonstrate the numerical scalability of the preconditioned conjugate gradient method to solve the linear systems resulting from Gauss--Newton linearization: Using the additive overlapping Schwarz preconditioner, the number of conjugate gradient iterations remains bounded independently of the problem size. We also show that a simplified SLAM problem can be interpreted as a finite element problem using linear elastic bars, highlighting the structural analogy to PDE discretizations and motivating the use of PDE-based preconditioners such as scalable domain decomposition preconditioners. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08975 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Overlapping Schwarz Preconditioners for Pose-Graph SLAM in Robotics Köhler, Stephan Rheinbach, Oliver Tee, Yue Xiang Zug, Sebastian Numerical Analysis We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph optimization back-end in Simultaneous Localization and Mapping (SLAM) in robotics. A brief introduction to both SLAM and domain decomposition preconditioners is given, followed by a description of the nonlinear least-squares formulation, its linearization, and the resulting matrix structure, making the paper accessible to readers without prior knowledge of either field. Numerical experiments for a simple model problem demonstrate the numerical scalability of the preconditioned conjugate gradient method to solve the linear systems resulting from Gauss--Newton linearization: Using the additive overlapping Schwarz preconditioner, the number of conjugate gradient iterations remains bounded independently of the problem size. We also show that a simplified SLAM problem can be interpreted as a finite element problem using linear elastic bars, highlighting the structural analogy to PDE discretizations and motivating the use of PDE-based preconditioners such as scalable domain decomposition preconditioners. |
| title | Overlapping Schwarz Preconditioners for Pose-Graph SLAM in Robotics |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2603.08975 |