Static Modeling of Linear Object Deformation Based on Differential Geometry

We describe the modeling of linear object deformation based on differential geometry and its applications to manipulative operations. A particle-based approach, the finite element method, and the Cosserat theory have been applied to the modeling of linear object deformation. In this paper, we establish an alternative modeling approach based on an extension of differential geometry. First, we extend differential geometry to describe linear object deformation including flexure, torsion, and extension. Secondly, we show computational results to demonstrate the feasibility of the proposed modeling technique, and we compare computational and experimental results to demonstrate the accuracy of the model. Next, we apply the proposed approach to the grasping of a deformable linear object. We propose a disturbance force margin to indicate the stability of the grasping and we describe the computation of the margin using the proposed approach. Finally, we apply the proposed approach to the deformation path planning of a linear object. We formulate the minimization of potential energy during a deformation path. We compute the optimal deformation path and a feasible deformation path, which are compared with an experimental result.