In this paper, we present a general approach to automatically visual-servo control the position and shape of a deformable object whose deformation parameters are unknown. The servo-control is achieved by online learning a model mapping between the robotic end-effector's movement and the object's deformation measurement. The model is learned using the Gaussian Process Regression (GPR) to deal with its highly nonlinear property, and once learned, the model is used for predicting the required control at each time step. To overcome GPR's high computational cost while dealing with long manipulation sequences, we implement a fast online GPR by selectively removing uninformative observation data from the regression process. We validate the performance of our controller on a set of deformable object manipulation tasks and demonstrate that our method can achieve effective and accurate servo-control for general deformable objects with a wide variety of goal settings. Experiment videos are available at https://sites.google.com/view/mso-fogpr
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