Dynamic Modeling of Linear Object Deformation based on Differential Geometry Coordinates

This paper describes the dynamic modeling of linear object deformation based on differential geometry coordinates. Deformable linear objects such as cables and strings are widely used in our daily life, electric industries, medical operations. Modeling, control, and manipulation of deformable linear objects are keys to many applications. We have proposed the differential geometry coordinates to describe the 2D/3D deformation of a linear object with the minimum number of parameters. Based on this description, we have formulated the static deformation of a linear object using the differential geometry coordinates but the dynamic deformation has not been investigated yet. In this paper, we apply differential geometry coordinates to the dynamic modeling of linear objects. First, we formulate the dynamic 2D deformation of an inextensible linear object based on a differential geometry coordinate system. Second, we show simulation results using the proposed modeling technique. Next, we apply the proposed dynamic modeling to the control of a flexible link.