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Deformable object manipulation (DOM) with point clouds has great potential asnon-rigid 3D shapes can be measured without detecting and tracking imagefeatures. However, robotic shape control of deformable objects with pointclouds is challenging due to: the unknown point-wise correspondences and thenoisy partial observability of raw point clouds; the modeling difficulties ofthe relationship between point clouds and robot motions. To tackle thesechallenges, this paper introduces a novel modal-graph framework for themodel-free shape servoing of deformable objects with raw point clouds. Unlikethe existing works studying the object's geometry structure, our method buildsa low-frequency deformation structure for the DOM system, which is robust tothe measurement irregularities. The built modal representation and graphstructure enable us to directly extract low-dimensional deformation featuresfrom raw point clouds. Such extraction requires no extra point processing ofregistrations, refinements, and occlusion removal. Moreover, to shape theobject using the extracted features, we design an adaptive robust controllerwhich is proved to be input-to-state stable (ISS) without offline learning oridentifying both the physical and geometric object models. Extensivesimulations and experiments are conducted to validate the effectiveness of ourmethod for linear, planar, tubular, and solid objects under different settings.

Modal-graph 3D shape servoing of deformable objects with raw point clouds