High-fidelity passive force-reflecting virtual environments

Passivity theory is applied to the creation of synthetic, complex multidimensional haptic environments. It can be shown that under appropriate conditions, sufficiently high rendering rates can guarantee the passivity of a simulation produced by a haptic device coupled to a discrete-time realization of a nominally passive environment. The creation of a passive, globally defined, virtual environment is either analytically complex or computationally costly. A method is described whereby a passive environment is created from transitions between locally defined force models that encode static conservative force fields. This is applied to the haptic rendering of tool contact with deformable bodies, in which sparse force-deflection responses are used to define local models. Passivity, continuity, and fidelity are provided by response-function interpolation rather than by interpolation of forces, as in previous methods. The work also includes an illustrative example.