A Constrained Saddle Search Approach for Constructing Singular and Flexible Bar Frameworks
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866917049704382464 |
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| author | Li, Xuenan Leonte, Mihnea Santangelo, Christian D. Holmes-Cerfon, Miranda |
| author_facet | Li, Xuenan Leonte, Mihnea Santangelo, Christian D. Holmes-Cerfon, Miranda |
| contents | Singularity analysis is essential in robot kinematics, as singular configurations cause loss of control and kinematic indeterminacy. This paper models singularities in bar frameworks as saddle points on constrained manifolds. Given an under-constrained, non-singular bar framework, by allowing one edge to vary its length while fixing lengths of others, we define the squared length of the free edge as an energy functional and show that its local saddle points correspond to singular and flexible frameworks. Using our constrained saddle search approach, we identify previously unknown singular and flexible bar frameworks, providing new insights into singular robotics design and analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_14807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Constrained Saddle Search Approach for Constructing Singular and Flexible Bar Frameworks Li, Xuenan Leonte, Mihnea Santangelo, Christian D. Holmes-Cerfon, Miranda Robotics Mathematical Physics Optimization and Control Singularity analysis is essential in robot kinematics, as singular configurations cause loss of control and kinematic indeterminacy. This paper models singularities in bar frameworks as saddle points on constrained manifolds. Given an under-constrained, non-singular bar framework, by allowing one edge to vary its length while fixing lengths of others, we define the squared length of the free edge as an energy functional and show that its local saddle points correspond to singular and flexible frameworks. Using our constrained saddle search approach, we identify previously unknown singular and flexible bar frameworks, providing new insights into singular robotics design and analysis. |
| title | A Constrained Saddle Search Approach for Constructing Singular and Flexible Bar Frameworks |
| topic | Robotics Mathematical Physics Optimization and Control |
| url | https://arxiv.org/abs/2503.14807 |