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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.13367 |
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| _version_ | 1866909114643251200 |
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| author | Bousclet, Anis Boyer, Frederic Chitour, Yacine Marx, Swann |
| author_facet | Bousclet, Anis Boyer, Frederic Chitour, Yacine Marx, Swann |
| contents | In this paper, we present an intrinsic derivation of the equations ruling the dynamics motion of a snake robot dynamics. Based on a Cosserat beam model, we first show that the extended configuration space is a Lie group. Endowing it with an appropriate left invariant metric, the corresponding Euler-Poincaré equations can be reduced to a system of hyperbolic PDEs in the Lie algebra $\mathfrak{se}(3)$. We also provide the constitutive law describing the actuation in this system of PDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intrinsic Derivation of the Equations of a Snake Robot based on a Cosserat Beam Model Bousclet, Anis Boyer, Frederic Chitour, Yacine Marx, Swann Optimization and Control 93C20 In this paper, we present an intrinsic derivation of the equations ruling the dynamics motion of a snake robot dynamics. Based on a Cosserat beam model, we first show that the extended configuration space is a Lie group. Endowing it with an appropriate left invariant metric, the corresponding Euler-Poincaré equations can be reduced to a system of hyperbolic PDEs in the Lie algebra $\mathfrak{se}(3)$. We also provide the constitutive law describing the actuation in this system of PDEs. |
| title | Intrinsic Derivation of the Equations of a Snake Robot based on a Cosserat Beam Model |
| topic | Optimization and Control 93C20 |
| url | https://arxiv.org/abs/2402.13367 |