Guaranteed stability of haptic systems with nonlinear virtual environments

Design of haptic systems that guarantee stable interaction is a challenging task. Virtual environments are typically highly nonlinear—resulting in a nonpassive discrete-time model. This paper will investigate how nonlinear mass/spring/damper virtual environments can be designed to guarantee the absence of oscillations and other chaotic behavior in the signal presented to the human operator. In particular, delayed and nondelayed implementation of the mass/spring/damper virtual environment is considered, revealing a nonintuitive result with regard to the allowable local stiffness.