Stability Boundary and Design Criteria for Haptic Rendering of Virtual Walls

Abstract This paper is about haptic simulations of virtual walls, which are represented by a discrete PD-control. A normalized discrete-time transfer function is used to derive the fundamental stability boundaries for this problem. Hereby, the case of direct action and the more often case of an one sampling step delayed action are addressed. Inside the stable region the set of all parameters was determined that result in real system poles. Furthermore, three different design criteria are compared to find optimum control parameters for the virtual wall. Finally, important conclusions for haptic simulations are derived.