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Shape control of deformable objects is a challenging and important roboticproblem. This paper proposes a model-free controller using novel 3D globaldeformation features based on modal analysis. Unlike most existing controllersusing geometric features, our controller employs a physically-based deformationfeature by decoupling 3D global deformation into low-frequency mode shapes.Although modal analysis is widely adopted in computer vision and simulation, ithas not been used in robotic deformation control. We develop a new model-freeframework for modal-based deformation control under robot manipulation.Physical interpretation of mode shapes enables us to formulate an analyticaldeformation Jacobian matrix mapping the robot manipulation onto changes of themodal features. In the Jacobian matrix, unknown geometry and physicalproperties of the object are treated as low-dimensional modal parameters whichcan be used to linearly parameterize the closed-loop system. Thus, an adaptivecontroller with proven stability can be designed to deform the object whileonline estimating the modal parameters. Simulations and experiments areconducted using linear, planar, and solid objects under different settings. Theresults not only confirm the superior performance of our controller but alsodemonstrate its advantages over the baseline method.

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