Analytical Stability Criterion in Haptic Rendering: the Role of Damping

A new closed-form equation for stability analysis of a haptic device is presented using frequency response function analysis via continuous time model of the system. Desired impedance of the virtual environment (VE), time delay, and zero-order hold are considered, beside the continuous model of the haptic device. The developed equations provide critical virtual damping and stiffness of the VE versus the mass and viscous friction of the haptic device, sampling time, and time delay. Unlike prior work in this field, the developed equations are valid without any limitation on the values of the time delay and virtual damping. It is shown that they cover available well-known equations in literature for special cases of small values of virtual damping and time delay. The resulting equations are of practical usefulness in many fields, such as surgery simulation for avoiding instability during virtual tool interaction with high-stiffness VEs. The proposed analytical derivation can also be used for studying the effect of operator, sensors, actuator dynamics, and velocity filtering. Simulation and experimental results on the KUKA light weight robot show that the proposed criterion can accurately predict the stability boundaries.