A Physically Consistent Stiffness Formulation for Contact-Rich Manipulation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913727444418560 |
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| author | Lachner, Johannes Nah, Moses C. Hogan, Neville |
| author_facet | Lachner, Johannes Nah, Moses C. Hogan, Neville |
| contents | Ensuring symmetric stiffness in impedance-controlled robots is crucial for physically meaningful and stable interaction in contact-rich manipulation. Conventional approaches neglect the change of basis vectors in curved spaces, leading to an asymmetric joint-space stiffness matrix that violates passivity and conservation principles. In this work, we derive a physically consistent, symmetric joint-space stiffness formulation directly from the task-space stiffness matrix by explicitly incorporating Christoffel symbols. This correction resolves long-standing inconsistencies in stiffness modeling, ensuring energy conservation and stability. We validate our approach experimentally on a robotic system, demonstrating that omitting these correction terms results in significant asymmetric stiffness errors. Our findings bridge theoretical insights with practical control applications, offering a robust framework for stable and interpretable robotic interactions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Physically Consistent Stiffness Formulation for Contact-Rich Manipulation Lachner, Johannes Nah, Moses C. Hogan, Neville Robotics Ensuring symmetric stiffness in impedance-controlled robots is crucial for physically meaningful and stable interaction in contact-rich manipulation. Conventional approaches neglect the change of basis vectors in curved spaces, leading to an asymmetric joint-space stiffness matrix that violates passivity and conservation principles. In this work, we derive a physically consistent, symmetric joint-space stiffness formulation directly from the task-space stiffness matrix by explicitly incorporating Christoffel symbols. This correction resolves long-standing inconsistencies in stiffness modeling, ensuring energy conservation and stability. We validate our approach experimentally on a robotic system, demonstrating that omitting these correction terms results in significant asymmetric stiffness errors. Our findings bridge theoretical insights with practical control applications, offering a robust framework for stable and interpretable robotic interactions. |
| title | A Physically Consistent Stiffness Formulation for Contact-Rich Manipulation |
| topic | Robotics |
| url | https://arxiv.org/abs/2503.06802 |