Dynamic modeling and control of flexible cables for shape forming

This paper investigates the dynamic modeling and control of flexible cables in order to form them into specific shapes while deploying them onto a surface. Because of the deformation and high degrees of freedom of such cables, the dynamic modeling and control are challenging. In this paper, we first adopt the discrete elastic rod model to dynamically model the stretching and bending deformation of the flexible cables. We also study the implementable solution of the cable model while considering the kinematic constraints of the cable and the physical contact between the cable and surface using a ‘time rollback and time step reduction’ method. Then we propose four control schemes to dynamically control one end of a cable to deploy it onto a surface and simultaneously form it to a desired shape. Finally, we perform simulation studies to illustrate the effectiveness of the dynamic model and also verify and compare our proposed control schemes. The results show that the proposed model can express the deformation of the flexible cables successfully and incorporating the shape errors of the deployed point and future deploying point in addition to the currently deploying point of a cable in control can significantly reduce the final shape errors.