Model-based Manipulation of Deformable Objects with Non-negligible Dynamics as Shape Regulation

Model-based manipulation of deformable objects has traditionally dealt with objects in the quasi-static regimes, either because they are extremely lightweight/small or constrained to move very slowly. On the contrary, soft robotic research has made considerable strides toward general modeling and control - despite soft robots and deformable linear objects being very similar from a mechanical standpoint. In this work, we leverage these recent results to develop a fully dynamic framework of slender deformable objects grasped at one of their ends by a robotic manipulator. We introduce a dynamic model of this system using functional strain parameterizations and describe the manipulation challenge as a regulation control problem. This enables us to define a fully model-based control architecture, for which we can prove analytically closed-loop stability and provide sufficient conditions for steady state convergence to the desired manipulation state. The nature of this work is intended to be markedly experimental. We propose an extensive experimental validation of the proposed ideas. For that, we use a 7-DoF robot tasked with the goal of positioning the distal end of six different electric cables, moving on a plane, in a given position and orientation in space.