Rendered and Characterized Closed-Loop Accuracy of Impedance-Type Haptic Displays

Abstract

Impedance-type kinesthetic haptic displays aim to render arbitrary desired dynamics to a human operator using force feedback. To render realistic virtual environments, the difference between desired and rendered dynamics must be small. In this paper, we analyze the closed-loop dynamics of haptic displays for three common virtual environments: a spring, a damper, and a spring-damper, including the effects of time delay and low-pass filtering. Using a linear model, we identify important parameters for the rendered dynamics in terms of effective impedances, a conceptual tool that decomposes the displays closed-loop impedance into components with physical analogs. Our results establish bandwidth limits for rendering effective stiffness and damping. The effective stiffness bandwidth is limited by the virtual stiffness and device mass, and the effective damping bandwidth is limited by the cut-off frequency of the low-pass filter which filters the device velocity estimate. We show that a general system impedance can be characterized by a mass, damper, and spring optimally by the solution to a convex optimization problem, and we present a quantitative metric, the Average Distortion Error (ADE), to describe the fidelity of this model. Time delay has no significant effect on characterized stiffness, and reduces characterized damping by the product of virtual stiffness and total time delay. Reducing the low-pass filter cut-off frequency reduces the characterized damping. Experimental data gathered with a Phantom Premium 1.5 validates the theoretical analysis. We also conducted human user experiments to investigate the effects of time delay and low-pass filtering on perceived stiffness and damping. Similar to the characterized dynamics results, we observed no significant effect of time delay on perceived stiffness, and increasing time delay resulted in reduced perceived damping. Lower filter cut-off frequencies resulted in lower perceived damping. This work informs haptic display design by presenting how closed-loop behavior changes with key parameters.

Framework for Human Haptic Perception With Delayed Force Feedback

“…Instead, the dynamics of the time delay and the mechanical properties are lumped together and perceived as a single mechanical system. This is consistent with the findings of previous research [7], [8], [10], [12]. A similar phenomenon also exists in the motor control in tracking tasks [22].…”

“…For a noticeable change in the stiffness, a minimum delay of 36ms is reported [24]. Delays below this noticeable level, as tested in [10], are therefore unlikely to cause significant effects.…”

“…If the reference signal possesses considerable energy over a relatively wide frequency range, the accuracy of the approximation depends on the magnitude of the time delay. The approximation can still be accurate when the delay is small, as demonstrated in [10]. However, when time delay increases, quantifying its effect using a model with a limited order is not possible any more.…”

“…During continuous contact with an elastic force field, humans underestimate the spring stiffness when the delay exists [8], [11], [13]. However, such an underestimation disappears in the case of small delays (up to 30 ms) [10]. Apparently, the reported effects related to different timedelay magnitudes on the haptic perception of spring stiffness are inconsistent.…”

Evaluation of Velocity Estimation Methods Based on Their Effect on Haptic Device Performance

“…Our fidelity of rendering measure builds upon the frequency response-based Zwidth plotting method proposed in [7]. Colonnese et al define the Average Distortion Error (ADE) as a metric for describing haptic accuracy and form an objective function to optimally compute linear system model parameters in [32]. ADE quantifies frequency dependent difference between actual and desired dynamics, normalized by desired dynamics and multiplied by a weighting function.…”