An Intuitive Formulation of the Human Arm Active Endpoint Stiffness
In this work, we propose an intuitive and real-time model of the human arm active endpoint stiffness. In our model, the symmetric and positive-definite stiffness matrix is constructed through the eigendecomposition <inline-formula><math display="inline"><semantics><mro...
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MDPI AG
2020-09-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/20/18/5357 |
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| author | Yuqiang Wu Fei Zhao Wansoo Kim Arash Ajoudani |
| author_facet | Yuqiang Wu Fei Zhao Wansoo Kim Arash Ajoudani |
| author_sort | Yuqiang Wu |
| collection | DOAJ |
| description | In this work, we propose an intuitive and real-time model of the human arm active endpoint stiffness. In our model, the symmetric and positive-definite stiffness matrix is constructed through the eigendecomposition <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-italic">K</mi><mi>c</mi></msub><mo>=</mo><mi mathvariant="bold-italic">V</mi><mi mathvariant="bold-italic">D</mi><msup><mi mathvariant="bold-italic">V</mi><mi>T</mi></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math display="inline"><semantics><mi mathvariant="bold-italic">V</mi></semantics></math></inline-formula> is an orthonormal matrix whose columns are the normalized eigenvectors of <inline-formula><math display="inline"><semantics><msub><mi mathvariant="bold-italic">K</mi><mi>c</mi></msub></semantics></math></inline-formula>, and <inline-formula><math display="inline"><semantics><mi mathvariant="bold-italic">D</mi></semantics></math></inline-formula> is a diagonal matrix whose entries are the eigenvalues of <inline-formula><math display="inline"><semantics><msub><mi mathvariant="bold-italic">K</mi><mi>c</mi></msub></semantics></math></inline-formula>. In this formulation, we propose to construct <inline-formula><math display="inline"><semantics><mi mathvariant="bold-italic">V</mi></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi mathvariant="bold-italic">D</mi></semantics></math></inline-formula> directly by exploiting the geometric information from a reduced human arm skeleton structure in 3D and from the assumption that human arm muscles work synergistically when co-contracted. Through the perturbation experiments across multiple subjects under different arm configurations and muscle activation states, we identified the model parameters and examined the modeling accuracy. In comparison to our previous models for predicting human active arm endpoint stiffness, the new model offers significant advantages such as fast identification and personalization due to its principled simplicity. The proposed model is suitable for applications such as teleoperation, human–robot interaction and collaboration, and human ergonomic assessments, where a personalizable and real-time human kinodynamic model is a crucial requirement. |
| first_indexed | 2024-03-10T16:13:49Z |
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| id | doaj.art-a600beb2708e4a25a1d44d770828da7d |
| institution | Directory Open Access Journal |
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| language | English |
| last_indexed | 2024-03-10T16:13:49Z |
| publishDate | 2020-09-01 |
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| spelling | doaj.art-a600beb2708e4a25a1d44d770828da7d2023-11-20T14:16:14ZengMDPI AGSensors1424-82202020-09-012018535710.3390/s20185357An Intuitive Formulation of the Human Arm Active Endpoint StiffnessYuqiang Wu0Fei Zhao1Wansoo Kim2Arash Ajoudani3State Key Laboratory for Manufacturing System Engineering, Xi’an Jiaotong University, Xi’an 710049, ChinaState Key Laboratory for Manufacturing System Engineering, Xi’an Jiaotong University, Xi’an 710049, ChinaHuman Robot Interfaces and physical Interaction lab (HRI<sup>2</sup>), Istituto Italiano di Tecnologia (IIT), 16163 Genova, ItalyHuman Robot Interfaces and physical Interaction lab (HRI<sup>2</sup>), Istituto Italiano di Tecnologia (IIT), 16163 Genova, ItalyIn this work, we propose an intuitive and real-time model of the human arm active endpoint stiffness. In our model, the symmetric and positive-definite stiffness matrix is constructed through the eigendecomposition <inline-formula><math display="inline"><semantics><mrow><msub><mi mathvariant="bold-italic">K</mi><mi>c</mi></msub><mo>=</mo><mi mathvariant="bold-italic">V</mi><mi mathvariant="bold-italic">D</mi><msup><mi mathvariant="bold-italic">V</mi><mi>T</mi></msup></mrow></semantics></math></inline-formula>, where <inline-formula><math display="inline"><semantics><mi mathvariant="bold-italic">V</mi></semantics></math></inline-formula> is an orthonormal matrix whose columns are the normalized eigenvectors of <inline-formula><math display="inline"><semantics><msub><mi mathvariant="bold-italic">K</mi><mi>c</mi></msub></semantics></math></inline-formula>, and <inline-formula><math display="inline"><semantics><mi mathvariant="bold-italic">D</mi></semantics></math></inline-formula> is a diagonal matrix whose entries are the eigenvalues of <inline-formula><math display="inline"><semantics><msub><mi mathvariant="bold-italic">K</mi><mi>c</mi></msub></semantics></math></inline-formula>. In this formulation, we propose to construct <inline-formula><math display="inline"><semantics><mi mathvariant="bold-italic">V</mi></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mi mathvariant="bold-italic">D</mi></semantics></math></inline-formula> directly by exploiting the geometric information from a reduced human arm skeleton structure in 3D and from the assumption that human arm muscles work synergistically when co-contracted. Through the perturbation experiments across multiple subjects under different arm configurations and muscle activation states, we identified the model parameters and examined the modeling accuracy. In comparison to our previous models for predicting human active arm endpoint stiffness, the new model offers significant advantages such as fast identification and personalization due to its principled simplicity. The proposed model is suitable for applications such as teleoperation, human–robot interaction and collaboration, and human ergonomic assessments, where a personalizable and real-time human kinodynamic model is a crucial requirement.https://www.mdpi.com/1424-8220/20/18/5357human factorsphysical human–robot collaborationrobot adaptation and learning |
| spellingShingle | Yuqiang Wu Fei Zhao Wansoo Kim Arash Ajoudani An Intuitive Formulation of the Human Arm Active Endpoint Stiffness Sensors human factors physical human–robot collaboration robot adaptation and learning |
| title | An Intuitive Formulation of the Human Arm Active Endpoint Stiffness |
| title_full | An Intuitive Formulation of the Human Arm Active Endpoint Stiffness |
| title_fullStr | An Intuitive Formulation of the Human Arm Active Endpoint Stiffness |
| title_full_unstemmed | An Intuitive Formulation of the Human Arm Active Endpoint Stiffness |
| title_short | An Intuitive Formulation of the Human Arm Active Endpoint Stiffness |
| title_sort | intuitive formulation of the human arm active endpoint stiffness |
| topic | human factors physical human–robot collaboration robot adaptation and learning |
| url | https://www.mdpi.com/1424-8220/20/18/5357 |
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