Improved passivity criterion in haptic rendering: influence of Coulomb and viscous friction

In this paper, a new criterion for passivity of haptic devices is obtained. This criterion creates a relationship between Coulomb friction coefficient, viscous friction coefficient, sampling rate, and the maximum simulated stiffness. The process of derivation of the passivity criterion is described in detail. This criterion is improved compared with other existing criteria and predicts passivity in haptic rendering more accurately. In particular, for speeds of less than 5 cm/s, the new passivity criterion should replace the previous criteria to avoid unwanted vibrations of stiff virtual walls. Analytical and numerical investigations are presented to validate the new criterion. A specific trajectory is designed and the movement of the haptic robot is investigated on this trajectory to validate and compare this passivity criterion with the previous criteria.