Fundamental limits in the rendering of virtual haptic textures

We discuss the properties of force-feedback haptic simulation systems that fundamentally limit the re-creation of periodic gratings, and hence, of any texture. These include sampling rate, device resolution, and structural dynamics. Basic sampling limitations are analyzed in terms of the Nyquist and the Courant conditions. The analysis proposes that noise due to sampling and other sources injected in the system may prevent it to achieve acceptable performance in most operating conditions, unless special precautions such as the use of a reconstruction filter, make the closed-loop more robust to noise. The structural response of a PHANTOM 1.0 A device was such that no such filter could be found, and the system introduced heavy distortion in gratings as coarse as 10 mm. The Pantograph Mark-II device having more favorable structural properties could reliably create gratings between 1 and 10 mm.