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

2026-05-11

AI Summary

This study addresses the viscoelastic creep and stress relaxation behaviors of materials in haptic rendering by proposing a passivity-preserving approach based on the fractional-order standard linear solid (SLS) model. Leveraging the Grünwald–Letnikov derivative and short-memory discretization, the authors derive closed-form conditions that guarantee system passivity and provide analytical expressions for equivalent stiffness and damping. A unified theoretical framework for passivity is established, encompassing integer-order Kelvin–Voigt, Maxwell, and SLS models as special cases. Notably, this work is the first to integrate fractional-order viscoelastic modeling with perceptual fidelity evaluation in human haptic interaction. User experiments validate the theoretical passivity bounds and demonstrate that the proposed method significantly enhances the realism of haptic rendering.

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.

Problem

• haptic rendering
• fractional-order viscoelasticity
• passivity
• rendering fidelity
• short-memory discretization

Innovation

• fractional-order viscoelasticity
• haptic rendering
• passivity
• short-memory discretization
• standard linear solid