Stability analysis of haptic interfaces for different types of sampled signals and virtual environment implementations

Robust stability of haptic simulation systems against any passive operator dynamics not only depends on the dynamic parameters of the haptic device, haptic controller and virtual environment but also on the type of signals sampled and the digital implementation of the virtual environment. In this paper, we analytically investigate the robust stability of the systems in which the device position or velocity is sampled, backward difference or Tustin differentiation method is employed for the implementation of damper-spring virtual environments, and accurate or approximate model is used to represent the sampling process. The analytical study reveals potential issues in the use of sampling approximation and more importantly introduces less conservative stability conditions on system dynamic parameters when velocity is sampled.