Haptic Rendering of Fractional-Order Viscoelasticity: Passivity and Rendering Fidelity

• URL: http://arxiv.org/abs/2605.16389v1
• Date: Mon, 11 May 2026 18:16:45 GMT
• Title: Haptic Rendering of Fractional-Order Viscoelasticity: Passivity and Rendering Fidelity
• Abstract summary: Haptic rendering of viscoelastic materials that exhibit creep and stress relaxation is crucial for many applications.<n>We present analyses of passivity and rendering performance for fractional-order viscoelastic models under finite-memory discretization.
• Score: 1.9307952728103128
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Haptic rendering of viscoelastic materials that exhibit creep and stress relaxation is crucial for many applications, such as medical training with realistic biological tissue models. Fractional-order viscoelastic models provide an effective means of describing intrinsically time-dependent dynamics with few parameters, as these models can naturally capture memory effects. In this study, we present analyses of passivity and rendering performance for fractional-order viscoelastic models under finite-memory discretization. We derive closed-form expressions to ensure the passivity of haptic rendering with a fractional-order (FO) standard linear solid (SLS) model based on Grunwald-Letnikov derivative under short-memory discretization. We also provide symbolic expressions for the effective stiffness and damping of such FO-SLS models. The resulting passivity conditions constitute a unified framework that generalizes previously reported results for integer-order Kelvin-Voigt, Maxwell, and SLS models, since these results are special cases of the newly derived condition. Furthermore, we provide experimental validations of the theoretical passivity bounds and human-subject evaluations of perceived realism of FO-SLS models. Overall, this study establishes a unified theoretical framework and experimental evaluations for FO viscoelastic rendering under short-memory discretization.

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