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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.16242 |
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| _version_ | 1866914450071617536 |
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| author | Yaqubi, S. Mattila, J. |
| author_facet | Yaqubi, S. Mattila, J. |
| contents | This paper presents a novel and scalable screw-theoretic multibody synthesis framework for PDE-based dynamic modeling of serial robotic manipulators with an arbitrary number of flexible links in three-dimensional space. The proposed approach systematically constructs screw-theoretic PDE models for individual flexible links and rigorously enforces holonomic joint constraints through interaction forces. The dynamics of each link are formulated using a set of dual screws expressed in body-fixed coordinates: one describing the motion of the body-fixed frame relative to the inertial frame, a second relating the body-fixed frame to the undeformed configuration, and a third capturing elastic deformations. By expressing the system energy and applying variational principles, the governing dynamics of each link had been previously derived in a unified manner. Synthesizing the individual link models yields an infinitely scalable multibody representation capable of capturing both local (subsystem-level) and global (system-level) dynamics. The framework explicitly recovers all dynamic states, including the motion of each body-fixed frame and the distributed deformation fields of the flexible links. For computational tractability and mathematical rigor, the resulting governing equations are formulated as a semi-explicit index-1 differential-algebraic system. Furthermore, by applying separation of variables, the PDE model is recast as an abstract Cauchy problem, and well-posedness of the resulting system is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16242 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scalable Screw-Theoretic Synthesis for PDE-Based Dynamic Modeling of Multibody Flexible Manipulators Yaqubi, S. Mattila, J. Robotics This paper presents a novel and scalable screw-theoretic multibody synthesis framework for PDE-based dynamic modeling of serial robotic manipulators with an arbitrary number of flexible links in three-dimensional space. The proposed approach systematically constructs screw-theoretic PDE models for individual flexible links and rigorously enforces holonomic joint constraints through interaction forces. The dynamics of each link are formulated using a set of dual screws expressed in body-fixed coordinates: one describing the motion of the body-fixed frame relative to the inertial frame, a second relating the body-fixed frame to the undeformed configuration, and a third capturing elastic deformations. By expressing the system energy and applying variational principles, the governing dynamics of each link had been previously derived in a unified manner. Synthesizing the individual link models yields an infinitely scalable multibody representation capable of capturing both local (subsystem-level) and global (system-level) dynamics. The framework explicitly recovers all dynamic states, including the motion of each body-fixed frame and the distributed deformation fields of the flexible links. For computational tractability and mathematical rigor, the resulting governing equations are formulated as a semi-explicit index-1 differential-algebraic system. Furthermore, by applying separation of variables, the PDE model is recast as an abstract Cauchy problem, and well-posedness of the resulting system is established. |
| title | Scalable Screw-Theoretic Synthesis for PDE-Based Dynamic Modeling of Multibody Flexible Manipulators |
| topic | Robotics |
| url | https://arxiv.org/abs/2601.16242 |