  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 sim2real 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 model-predictive 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.
