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

TL;DR

This paper develops a unified theoretical framework for passivity and fidelity in haptic rendering of fractional-order viscoelastic models, validated through experiments and human perception studies.

Contribution

It derives closed-form passivity conditions for fractional-order models and generalizes previous integer-order results, enhancing realistic haptic simulations.

Findings

Passivity bounds are validated experimentally.

Human perception experiments confirm realism of FO-SLS models.

Unified framework encompasses integer-order viscoelastic models.

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.