Stable Discrete-Time Impedances for Haptic Systems With Vibration Modes and Delay

The stability of haptic rendering is affected by many factors that limit the range of impedances that can be applied to virtual objects. This paper addresses the effect of the vibration modes of the haptic interface on the stability of the impedance control loop. It is well known that experimental stability boundaries present complex shapes, making it difficult to predict the final Z-width of the haptic system. This paper shows how the vibration modes of the mechanical interface highly affect the size of the Z-width, causing a sudden reduction in the critical virtual stiffness K if the virtual damping B is increased beyond a certain value. The inclusion of the most significant vibration modes in the theoretical model of the haptic system-together with the viscous damping, time delay and sampling rate-makes it possible to obtain the stable impedances associated with the haptic device. A PHANToM Premium 1.0 haptic interface was used as a test bed to validate this paper. Although results have been tested only on this device, this paper proposes a methodology for obtaining the Z-width that can be generalized for any other haptic system.