Perception of Delayed Stiffness

Abstract

Advanced technology has recently provided truly immersive virtual environments with teleoperated robotic devices. In order to control movements from a distance, the human sensorimotor system has to overcome the e fects of delay. Currently, little is known about the mechanisms that underlie haptic estimation in delayed environments. The aim of this research is to explore the e fect of a delay on perception of surfaces sti fness. A forced choice paradigm was used in which subjects were asked to identify the sti fer of two virtual spring-like surfaces based on manipulation without visual feedback. Virtual surfaces were obtained by generating an elastic force proportional to the penetration of the handle of a manipulandum inside a virtual boundary. The elastic force was either an instantaneous function of the displacement, delayed at 30 or 60 milliseconds after the displacement or led the displacement (by means of Kalman predictor) by 50 milliseconds. It was assumed that, to estimate sti fness, the brain relates the experienced interaction forces with the amount of penetration. The results of the experiment indicate a systematic dependence of the estimated sti fness upon the delay between position and force. When the force lagged the penetration, surfaces were perceived as sti fer. Conversely, when the force led the penetration, surfaces were perceived as softer. The perceptual findings were compared with different regression models. This allowed some candidate models to be discarded. To further refine the analysis, a second experiment was carried out in which the delay was introduced only during part of the hand/surface interaction, either while the hand was moving into the spring-like surface or when it was moving out of it. Findings are consistent with sti fness estimates based on dividing the maximum force by the perceived amount of penetration. Findings are not consistent with an estimate of compliance based on the maximum position or local sti fness on the way out nor with linear estimates of sti fness based on the entire force/motion history.