Modeling the Coupled Difference Threshold of Perceiving Mass and Stiffness from Force

Abstract

Abstract—Just notable difference (JND) thresholds for the perception of manipulator dynamic properties are relevant for tele-operation and simulation of vehicles. Manipulator dynamic properties are characterized by multiple variables (describing mass, spring and damping for a linear manipulator) and the JND threshold for any of these variables is affected by variation in the remaining variables. In previous work, we demonstrated and modeled the coupling of the stiffness JND and the mass JND, and investigated the effects of stiffness and mass properties on the damping JND. In this work we investigate how changes in the damping parameter affect the JND in perceiving stiffness and mass. In an experiment our subjects were instructed to discriminate between different levels of manipulator’s stiffness or mass, while tracking a prescribed sinusoidal manipulator movement. Results show that the JND in spring force and the JND in inertia force are identical, and increase for higher damping levels. The JND model developed in our previous work can successfully describe the experimental observations, thereby providing an extension of Weber’s law. The impedance of the manipulator is considered as the reference stimulus in the frequency domain, so that a single ratio describes the JND thresholds for all three properties. Index Terms—Just noticeable difference, Mass-spring-damper systems, Frequency response function, Weber’s law, haptics