Influence of human operator on stability of haptic rendering: a closed-form equation

In this paper an analytical stability criterion for linear haptic devices is determined, in the presence of the operator. The model of the haptic device and the virtual environment are assumed as mass-damper and spring-damper, respectively. Two different models for operator’s hand are assumed, and the stability boundaries are derived analytically. The main contribution of this paper is the analytical formulation of a closed-form stability equation in the presence of the operator; which can predict the stability boundary with small and even large values of virtual damping and time delay. This closed-form stability criterion can be useful in applications such as haptic rendering of deformable objects using finite element method, where the computational time delay is considerable. The influence of operator’s hand and effective mass on the stability is studied analytically and verified by simulations and experiments on a KUKA Light Weight Robot.