Robust Shape Control of Deformable Objects Using Model-Based Techniques

Shape control of a deformable object by a robotic system is a challenging problem because of the difficulty of imposing shape change by a finite number of actuation points to an essentially infinite-dimensional object. In this paper, a new approach to shape changing of deformable objects by a system of manipulators is presented. First, an integrated dynamic equation of motion for a system of multiple manipulators handling a deformable object is developed. A shape correspondence between the initial contact points of the multiple manipulators on a deformable object and a two-dimensional curve that represents the final desired shape is determined. A shape Jacobian that contains the local shape information of the desired shape of the object is formulated and is introduced into the control law. We develop a shape estimator with a second-order dynamics that is used to estimate the curve parameters corresponding to the end-effector position in each time step as the initial object is deformed to its desired final shape. Finally, we design a robust controller for the shape changing task that can work in the presence of modeling uncertainty. The simulation results demonstrate the efficacy of the proposed method. (C) Koninklijke Brill NV, Leiden, 2011