Haptic Rendering of Fractional-Order Viscoelasticity: Passivity and Rendering Fidelity
Provides a unified theoretical framework for passivity in haptic rendering of viscoelastic materials, benefiting developers of haptic interfaces for medical training and other applications requiring realistic tissue simulation.
This work derives closed-form passivity conditions for haptic rendering of fractional-order viscoelastic models under finite-memory discretization, generalizing previous integer-order results. Human-subject evaluations confirm the perceived realism of the fractional-order models.
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.