A Lagrange-Newton Approach to Smoothing-and-Mapping
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910306596290560 |
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| author | Möller, Ralf |
| author_facet | Möller, Ralf |
| contents | In this report we explore the application of the Lagrange-Newton method to the SAM (smoothing-and-mapping) problem in mobile robotics. In Lagrange-Newton SAM, the angular component of each pose vector is expressed by orientation vectors and treated through Lagrange constraints. This is different from the typical Gauss-Newton approach where variations need to be mapped back and forth between Euclidean space and a manifold suitable for rotational components. We derive equations for five different types of measurements between robot poses: translation, distance, and rotation from odometry in the plane, as well as home-vector angle and compass angle from visual homing. We demonstrate the feasibility of the Lagrange-Newton approach for a simple example related to a cleaning robot scenario. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Lagrange-Newton Approach to Smoothing-and-Mapping Möller, Ralf Robotics In this report we explore the application of the Lagrange-Newton method to the SAM (smoothing-and-mapping) problem in mobile robotics. In Lagrange-Newton SAM, the angular component of each pose vector is expressed by orientation vectors and treated through Lagrange constraints. This is different from the typical Gauss-Newton approach where variations need to be mapped back and forth between Euclidean space and a manifold suitable for rotational components. We derive equations for five different types of measurements between robot poses: translation, distance, and rotation from odometry in the plane, as well as home-vector angle and compass angle from visual homing. We demonstrate the feasibility of the Lagrange-Newton approach for a simple example related to a cleaning robot scenario. |
| title | A Lagrange-Newton Approach to Smoothing-and-Mapping |
| topic | Robotics |
| url | https://arxiv.org/abs/2401.13302 |