Active Learning of Fractional-Order Viscoelastic Model Parameters for Realistic Haptic Rendering

TL;DR

This work addresses the challenge of realistically rendering viscoelastic tissues in haptic medical simulators by using fractional-order standard linear solid (FO-SLS) models. It introduces a human-in-the-loop Bayesian optimization framework that learns parameters from qualitative perceptual feedback and then aggregates individual perceptual maps into a population-level perceptual map via Bayesian Committee Machine (BCM). The approach yields population-level FO-SLS parameters that closely match real tissue behavior (low NRMSE against system-identified values) and demonstrates robust generalization across participants. The method has the potential to substantially improve sim-to-real realism in medical training simulators by enabling efficient, perceptually grounded parameterization of complex viscoelastic models.

Abstract

Effective medical simulators necessitate realistic haptic rendering of biological tissues that display viscoelastic material properties, such as creep and stress relaxation. Fractional-order models provide an effective means of describing intrinsically time-dependent viscoelastic dynamics with few parameters, as these models can naturally capture memory effects. However, due to the unintuitive frequency-dependent coupling between the order of the fractional element and the other parameters, determining appropriate parameters for fractional-order models that yield high perceived realism remains a significant challenge. In this study, we propose a systematic means of determining the parameters of fractional-order viscoelastic models that optimizes the perceived realism of haptic rendering across general populations. First, we demonstrate that the parameters of fractional-order models can be effectively optimized through active learning, via qualitative feedback-based human-in-the-loop~(HiL) optimizations, to ensure consistently high realism ratings for each individual. Second, we propose a rigorous method to combine HiL optimization results to form an aggregate perceptual map trained on the entire dataset and demonstrate the selection of population-level optimal parameters from this representation that are broadly perceived as realistic across general populations. Finally, we provide evidence of the effectiveness of the generalized fractional-order viscoelastic model parameters by characterizing their perceived realism through human-subject experiments. Overall, generalized fractional-order viscoelastic models established through the proposed HiL optimization and aggregation approach possess the potential to significantly improve the sim-to-real transition performance of medical training simulators.

Figures (9)

• Figure 1: Fractional-order standard linear solid model
• Figure 2: Experimental data from (a) stress relaxation experiment under a constant deformation, and (b) creep with recovery experiment under a step force. Best fits of the fractional-order SLS model for different memory lengths are also shown.
• Figure 3: (a) The experimental setup with a participant. (b) Two identical haptic interfaces: The reference device with the physical viscoelastic material is on the left, while the test device rendering a viscoelastic model is on the right.
• Figure 4: The progression of the posterior GP model of perceived realism depicted at various trials of the HiL optimization for a participant. The first row captures the mean, while the second row presents the standard deviation. For the presentation, the fractional order coefficient $\alpha$ is taken as a constant at $\alpha=0.19$, and two-dimensional slices in $K_1$ and $B_1$ axes are depicted. The white area represents a non-passive region that the optimization algorithm omits while sampling new parameter sets.
• Figure 5: NRMSE between each participant’s current best predicted parameter set versus their final best predicted parameter set. The solid blue line denotes the median across participants, and the shaded region indicates the IQR.