Physics-Constrained Neural Operator Enables Differentiable Simulation of Soft Object Manipulation

Abstract

Accurate modeling of deformable object dynamics is critical for robotic manipulation but remains challenging due to complex physics and strict physical constraints. In this paper, PhysCon-Deform is introduced, which is a mixed framework for specific tasks, combining residual neurodynamics learning and a differential augmented Lagrangian projection layer. Using a grid-based graph representation, PhysCon-Deform integrates a physics-based neurodynamics operator (PINDO) and a differentiable constraint projection module to achieve the deployment of residual correction, grid-based neurodynamics and model predictive control (MPC). Based on standard simulation benchmarks (Cloth3D, SoftGym and SoftMAC), our framework is always superior to the existing baselines in clean and disturbed environments. Specifically, it reduces long-term constraint violations by over 50%, demonstrates high robustness to end-effector trajectory noise, and enables efficient real-time trajectory optimization within an MPC pipeline. Extensive ablation and bias studies reveal that removing PINDO increases the prediction mean squared error (MSE) from 0.28 cm2 to 0.68 cm2 (a 143% increase), while omitting the constraint projection layer leads to a fourfold increase in violation rates. Furthermore, the robustness analysis of a colored noise and random walk drift model verifies its elasticity to non-ideal sensing. Although the deformation mechanism with a moderate rate-dependent effect in the simulation environment is optimized at present, PhysCon-Deform provides a very practical method to balance the precision-constraint trade-off in the control of deformable objects with physical constraints.