Stability Boundary for Haptic Rendering: Influence of Physical Damping

Physical damping is increasing the z-width of haptic simulations. This paper derives the normalized stability boundaries for physically damped one degree of freedom haptic devices colliding with a virtual wall represented as spring-damper system. These boundaries are independent of the haptic device's mass and the sampling time. Furthermore, the dependency of the maximum stable virtual stiffness is discussed. Moreover, this paper illustrates that the passive region which is defined by Colgate's passivity condition is a subset inside the stable region for undelayed systems, but not for delayed systems