Second order approximation of possible local displacement for curve objects

Most methods for assembly tasks calculate possible local displacement of objects by the screw theory or its equivalent. The calculation is first-order displacement approximation. Curvature information is not considered, so they can be applied only to polyhedral objects. In this paper, we propose a method to formulate and calculate the second-order approximation of possible local displacement. From our experiment, our method correctly calculated the displacement of curve objects, while most conventional methods failed.