Log-linear Backstepping control on $SE_2(3)$
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908638180802560 |
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| author | Lin, Li-Yu Perseghetti, Benjamin Goppert, James |
| author_facet | Lin, Li-Yu Perseghetti, Benjamin Goppert, James |
| contents | Most of the rigid-body systems which evolve on nonlinear Lie groups where Euclidean control designs lose geometric meaning. In this paper, we introduce a log-linear backstepping control law on SE2(3) that preserves full rotational-translational coupling. Leveraging a class of mixed-invariant system, which is a group-affine dynamic model, we derive exact logarithmic error dynamics that are linear in the Lie algebra. The closed-form expressions for the left- and right-Jacobian inverses of SE2(3) are expressed in the paper, which provides us the exact error dynamics without local approximations. A log-linear backstepping control design ensures exponential stability for our error dynamics; since our error dynamics is a block-triangular structure, this allows us to use Linear Matrix Inequality (LMI) formulation or $H_\infty$ gain performance design. This work establishes the exact backstepping framework for a class of mixed-invariant system, providing a geometrically consistent foundation for future Unmanned Aerial Vehicle (UAV) and spacecraft control design. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Log-linear Backstepping control on $SE_2(3)$ Lin, Li-Yu Perseghetti, Benjamin Goppert, James Systems and Control Most of the rigid-body systems which evolve on nonlinear Lie groups where Euclidean control designs lose geometric meaning. In this paper, we introduce a log-linear backstepping control law on SE2(3) that preserves full rotational-translational coupling. Leveraging a class of mixed-invariant system, which is a group-affine dynamic model, we derive exact logarithmic error dynamics that are linear in the Lie algebra. The closed-form expressions for the left- and right-Jacobian inverses of SE2(3) are expressed in the paper, which provides us the exact error dynamics without local approximations. A log-linear backstepping control design ensures exponential stability for our error dynamics; since our error dynamics is a block-triangular structure, this allows us to use Linear Matrix Inequality (LMI) formulation or $H_\infty$ gain performance design. This work establishes the exact backstepping framework for a class of mixed-invariant system, providing a geometrically consistent foundation for future Unmanned Aerial Vehicle (UAV) and spacecraft control design. |
| title | Log-linear Backstepping control on $SE_2(3)$ |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2511.05775 |