Robotic manipulation of slender objects is challenging, especially when the induced deformations are large and nonlinear. Traditionally, learning-based control approaches, such as imitation learning, have been used to address deformable material manipulation. These approaches lack generality and often suffer critical failure from a simple switch of material, geometric, and/or environmental (e.g., friction) properties. This article tackles a fundamental but difficult deformable manipulation task: forming a predefined fold in paper with only a single manipulator. A data-driven framework combining physically-accurate simulation and machine learning is used to train a deep neural network capable of predicting the external forces induced on the manipulated paper given a grasp position. We frame the problem using scaling analysis, resulting in a control framework robust against material and geometric changes. Path planning is then carried out over the generated "neural force manifold" to produce robot manipulation trajectories optimized to prevent sliding, with offline trajectory generation finishing 15$\times$ faster than previous physics-based folding methods. The inference speed of the trained model enables the incorporation of real-time visual feedback to achieve closed-loop sensorimotor control. Real-world experiments demonstrate that our framework can greatly improve robotic manipulation performance compared to state-of-the-art folding strategies, even when manipulating paper objects of various materials and shapes.

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