Model-Free 3D 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 paper proposes a model-free controller using novel 3D global deformation features based on modal analysis. Unlike most existing controllers using geometric features, our controller employs a physically-based deformation feature by decoupling 3D global deformation into low-frequency mode shapes. Although modal analysis is widely adopted in computer vision and simulation, it has not been used in robotic deformation control. We develop a new model-free framework for modal-based deformation control under robot manipulation. Physical interpretation of mode shapes enables us to formulate an analytical deformation Jacobian matrix mapping the robot manipulation onto changes of the modal features. In the Jacobian matrix, unknown geometry and physical properties 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 solid objects under different settings. The results not only confirm the superior performance of our controller but also demonstrate its advantages over the baseline method.