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