Model-Free 3-D Shape Control of Deformable Objects Using Novel Features Based on Modal Analysis

Shape control of deformable objects is a challenging and important robotic problem. This article proposes a model-free controller using novel 3-D global deformation features based on modal analysis. Unlike most existing controllers using geometric features, our controller employs physically based deformation features designed by decoupling global deformation into low-frequency modes. Although modal analysis is widely adopted in computer vision and simulation, its usage in robotic deformation control is still an open topic. We develop a new model-free framework for the modal-based deformation control. Physical interpretation of the modes enables us to formulate an analytical deformation Jacobian matrix mapping the robot manipulation onto changes of the modal features. In the Jacobian matrix, unknown geometric and physical models of the object are treated as low-dimensional modal parameters, which can be used to linearly parameterize the closed-loop system. Thus, an adaptive controller with proven stability can be designed to deform the object while online estimating the modal parameters. Simulations and experiments are conducted using linear, planar, and volumetric objects under different settings. The results not only confirm the superior performance of our controller, but also demonstrate its advantages over the baseline method.