Passivity and stability boundaries for haptic systems with time delay

This paper presents a passivity and a stability analysis of a one degree of freedom haptic device that is interacting with a virtual wall. These two analyses take into account the influence of a human operator and time delay. A peculiarity of the presented approach is the exact combination of discrete- and continuous-time elements, which reveals fundamental parameter dependencies for passivity and stability. These dependencies do not only differ in scale for passivity and stability, but consist in substantially different relations. By using realistic parameter ranges for human arms, this paper clearly illustrates that the maximum stable stiffness of virtual walls is far higher than admitted by passivity. Responsible for this great disparity is the limited stiffness of real human arms, as passivity covers a stiffness range that is orders of magnitudes larger than feasible. Finally, useful guidelines for designing stable haptic systems are concluded.