Shape Servoing of a Soft Object Using Fourier Series and a Physics-based Model

In this paper, we propose a physics-based robot controller to deform a soft object toward a desired 3D shape using a limited number of handling points. For this purpose, the shape of the deformable object is represented using Fourier descriptors. We derive the analytical relation that provides the variation of the Fourier coefficients as a function of the movements of the handling points by considering a mass-spring model (MSM). A control law is then designed from this relation. Since the MSM provides an approximation of the object behavior, which in practice can lead to a drift between the object and its model, an online realignment of the model with the real object is performed by tracking its surface from data provided by a remote RGB-D camera. Simulation results validate the approach for the case where many points interact on a 2D soft object while experimental results obtained with two robotic arms demonstrate the autonomous shaping of a 3D soft object.