Controlling Deformable Objects With Nonnegligible Dynamics: A Shape-Regulation Approach to End-Point Positioning

Abstract

Model-based manipulation of deformable objects has traditionally dealt with objects while neglecting their dynamics, thus mostly focusing on very lightweight objects at steady state. At the same time, soft robotic research has made considerable strides toward general modeling and control, despite soft robots and deformable objects being very similar from a mechanical standpoint. In this work, we leverage these recent results to develop a control-oriented, fully dynamic framework of slender deformable objects grasped at one end 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 state. The nature of this work is intended to be markedly experimental. We provide an extensive experimental validation of the proposed ideas, tasking a robot arm with controlling the distal end of six different cables, in a given planar position and orientation in space.