Human Threshold Model for Perceiving Changes in System Dynamics

Limitations of a haptic device can cause distortions of the force feedback it presents. Just-noticeable difference (JND) in system dynamics is important for creating transparent haptic interaction. Based on the previous work, this article presents a unified model that extends the existing JND rule. Our approach projects the JNDs in the mechanical properties of a second-order mass-spring-damper system onto the real and imaginary components of the system's frequency response function (FRF). We discuss the results of two experiments and show that the JNDs obtained for both the real and imaginary components can be expressed as the same fraction of, and thus are proportional to, the magnitude of the total system's FRF. Furthermore, the findings are generalized to cases where the system's dynamics order is different than two. What results is a unified model that accurately describes the threshold for changes in human perception of any linear system dynamics with only two dimensions: the real and imaginary axes in the complex plane.