Learning Neural Force Manifolds for Sim2Real Robotic Symmetrical Paper Folding

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.