A Geometric Task-Space Port-Hamiltonian Formulation for Redundant Manipulators
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914203995996160 |
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| author | Califano, Federico Rota, Camilla Zanella, Riccardo Franchi, Antonio |
| author_facet | Califano, Federico Rota, Camilla Zanella, Riccardo Franchi, Antonio |
| contents | We present a novel geometric port-Hamiltonian formulation of redundant manipulators performing a differential kinematic task $η=J(q)\dot{q}$, where $q$ is a point on the configuration manifold, $η$ is a velocity-like task space variable, and $J(q)$ is a linear map representing the task, for example the classical analytic or geometric manipulator Jacobian matrix. The proposed model emerges from a change of coordinates from canonical Hamiltonian dynamics, and splits the standard Hamiltonian momentum variable into a task-space momentum variable and a null-space momentum variable. Properties of this model and relation to Lagrangian formulations present in the literature are highlighted. Finally, we apply the proposed model in an \textit{Interconnection and Damping Assignment Passivity-Based Control} (IDA-PBC) design to stabilize and shape the impedance of a 7-DOF Emika Panda robot in simulation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Geometric Task-Space Port-Hamiltonian Formulation for Redundant Manipulators Califano, Federico Rota, Camilla Zanella, Riccardo Franchi, Antonio Systems and Control Robotics We present a novel geometric port-Hamiltonian formulation of redundant manipulators performing a differential kinematic task $η=J(q)\dot{q}$, where $q$ is a point on the configuration manifold, $η$ is a velocity-like task space variable, and $J(q)$ is a linear map representing the task, for example the classical analytic or geometric manipulator Jacobian matrix. The proposed model emerges from a change of coordinates from canonical Hamiltonian dynamics, and splits the standard Hamiltonian momentum variable into a task-space momentum variable and a null-space momentum variable. Properties of this model and relation to Lagrangian formulations present in the literature are highlighted. Finally, we apply the proposed model in an \textit{Interconnection and Damping Assignment Passivity-Based Control} (IDA-PBC) design to stabilize and shape the impedance of a 7-DOF Emika Panda robot in simulation. |
| title | A Geometric Task-Space Port-Hamiltonian Formulation for Redundant Manipulators |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2512.14349 |