Uncoupled stability analysis of haptic simulation systems for various kinematic sampled data and discretization methods

Previous research has shown that the stability of haptic simulation systems is largely affected by the type of signals sampled and the discretization method used for implementing the virtual environment. In this paper, we analytically derive and experimentally evaluate the uncoupled stability of haptic simulation systems, that is when these systems are not being held by any operator, for various conditions. These stability conditions are expected to be the most stringent ones, as operators´ grasp tend to stabilize the coupled system. Our evaluation includes cases in which position, velocity or both signals are sampled, the backward difference or Tustin methods are used to implement a linear-time-invariant damper-spring environment. Our results show that sampling the velocity signal will significantly increase the range of environment dynamics that can be stably implemented, particularly when the backward difference method is applied as the discretization method.