| Summary: | 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.
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