On the relationship between the force JND and the stiffness JND in haptic perception

A large variation of the haptic Just Noticeable difference (JND) in stiffness is found in literature. But no underlying model that explains this variation was found, limiting the practical use of the stiffness JND in the evaluation work of control loading system (CLS). To this end, we investigated the cause of this variation from humans' strategy for stiffness discrimination, by two experiments in which a configurable manipulator was used to generate an elastic force proportional to its angular displacement (deflection). In a first experiment, the stiffness JND was measured for three stiffness levels, and an invariant Weber fraction was obtained. We found that for stiffness discrimination, subjects reproduced the same amount of the manipulator deflection and used the difference in the terminal forces as the indication of the stiffness difference. We demonstrated that the stiffness Weber fraction and the force Weber fraction could be related by a systematic bias in the deflection reproduction, which was caused by the difference in the manipulator stiffness. A second experiment with two conditions was done to verify this model. In one condition, we measured the stiffness JND while asking subjects to move the manipulator to a target angular displacement. Thus the bias in the deflection reproduction was eliminated, and this resulted a stiffness Weber fraction that equaled the force Weber fraction. In the other condition, the stiffness JND was measured without the deflection target, and a bias in deflection reproduction was again observed. This bias related the measurements for the two conditions by the formulation obtained from the first experiment. This suggests that the accuracy of reproducing the manipulator position for stiffness discrimination, which may be susceptible to experimental setting, can be used to explain the variation of stiffness JND in literature. Suggestions are given for CLS evaluation and applications requiring precise manipulator motion control.