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

arXiv: https://arxiv.org/abs/2605.16389 · HTML: https://mlsanity.com/paper/2605.16389/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 47 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 2 of 2)

- [A Computational Multi-Criteria Optimization Approach to Controller Design for Physical Human-Robot Interaction](https://mlsanity.com/paper/2006.11218/) (2020)
- [Active Learning of Fractional-Order Viscoelastic Model Parameters for Realistic Haptic Rendering](https://mlsanity.com/paper/2512.00667/) (2025)

## Abstract (arXiv)

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.