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.

本文在操作员在场的情况下确定了线性触觉设备的分析稳定性标准。触觉设备的模型和虚拟环境分别假定为质量阻尼器和弹簧阻尼器。假设操作员的手有两种不同的模型，并通过分析得出稳定性边界。本文的主要贡献是在存在算子的情况下解析形式的稳定性方程。可以用较小甚至较大的虚拟阻尼和时延值预测稳定性边界。这种封闭形式的稳定性标准可用于诸如使用有限元方法对可变形对象进行触觉渲染的应用中，其中计算时间延迟相当大。