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.