Passive implementation for a class of static nonlinear environments in haptic display

This paper derives conditions for the absence of oscillations for a parametrized class of nonlinear environments. This class includes discrete-time environments that can exhibit non-passive behavior. The motivation for considering non-passive discrete-time environments is based on the fact that an interesting class of passive continuous-time environments have non-passive discrete-time counterparts. A design methodology is introduced that provides relationships between the haptic device, virtual coupling and maximum negative stiffness exhibited by the environment