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.

Optimal control for haptic rendering: Fast energy dissipation and minimum overshoot

“…In comparison, criteria that only consider the square error of the position (e.g. [11], [13]), i.e. only the potential energy stored in the springs, result in optimal curves with faster movements and slower dissipation of the total energy than the suggested criteria.…”

“…A common way of optimizing system behavior is placing the system poles inside certain regions in the plane of the complex variable [13]. More interesting than pole-based criteria for the practical use are criteria that consider the system response of haptic systems directly.…”

A Practically Linear Relation Between Time Delay and the Optimal Settling Time of a Haptic Device

“…This design criterion appears to be of particular relevance for haptic rendering, because even if the numerical value of contact stiffness is high, the appearance of long lasting oscillations may degrade the realistic impression of such stiff contacts with a virtual environment. The approach advances previous work [14], [15], [17], in which stability and optimal control design for haptic devices were investigated in the parameter (a) Experimental setup with the Light-Weight Robots of the bimanual haptic interaction device HUG [18]. The red round arrow indicates the direction of the movements in the experiments.…”

“…To this end, Salcudean and Vlaar [4] investigated the location of the system poles to determine optimal control parameters which settle quickly. Hulin et al [14] enhanced this approach and considered the pole damping in addition to the settling behavior. Later, the same research group introduced performance measures to investigate the actual transient performance of a haptic device [15].…”

Stability boundary for haptic rendering: Influence of human operator

“…This approach was enhanced by the authors of [8], considering also time delay as parameter. A more complex model of the haptic system including physical damping was investigated in [9].…”