Modeling of geometrical uncertainty in robotic assembly

In robotic assembly, the actual location of the workpieces and the environment vary in some regions due to geometrical uncertainty. So, modeling of geometrical uncertainty is to determine those uncertainty regions. The geometrical uncertainty is decomposed into position uncertainty (PU) and orientation uncertainty (OU). The PU and OU of every point is represented by uncertainty sphere (US) and uncertainty spherical surface (USS) respectively. The geometrical uncertainty region is obtained with the union of the USs and USSs of all the points in one object. Since the geometrical uncertainty region is fairly complex, some approximate methods are discussed to simplify the analysis.