Learning Equivariant Neural-Augmented Object Dynamics From Few Interactions

Simulating deformable objects is essential for a wide range of robotic manipulation applications, yet accurately predicting their dynamics remains challenging. We propose Physics-Guided Residual Dynamics (PGRD), a hybrid simulation framework that combines the advantages of physics-based and learning-based approaches. Specifically, PGRD combines an optimizable spring-mass simulator as a backbone with a learned neural network that predicts residual corrections to the physics-based predictions. We adopt a velocity-based formulation to ensure stable simulation and a sliding-window transformer architecture to capture temporal dependencies. We show that PGRD produces more accurate results than both purely physics-based and learning-based methods on a set of diverse real-world deformable objects. We further demonstrate the utility of PGRD in two applications: manipulation planning via Model Predictive Control, including a language-conditioned setting with a generated goal image; and interactive simulation via action-conditioned video prediction by 3D Gaussian Splatting.

Predicting how deformable objects evolve under robotic manipulation is a longstanding challenge. Existing approaches typically rely on per-object optimization to fit material parameters, which can be slow and cannot generalize, while end-to-end learned alternatives extrapolate poorly and often violate basic physical structure. We present PhysCoRe, a physics-corrected residual world model that couples a differentiable Material Point Method (MPM) simulator with two feed-forward neural networks. A material refinement module, Material from Motion (MfM), infers per-particle elasticity from visual observations, grounding the simulator in object-specific physics. A residual correction module, Residual from Dynamics (RfD), learns the discrepancy and predicts corrections to the simulator's internal dynamics, absorbing systematic biases that the analytical model cannot capture. This design also supports online material identification on novel objects. MfM adapts from limited interactions, and its predictive uncertainty steers further exploration toward the regions where its estimate is least confident. Experiments on real deformable-object manipulation sequences show that PhysCoRe outperforms state-of-the-art baselines in prediction accuracy, and that its predicted confidence forms a reliable distribution across the object's geometry, providing a natural signal for future confidence-guided exploration.

Bridging abstract semantics and precise physical control remains a fundamental challenge in open-world robotic manipulation. While recent data-driven policies show promise, their reliance on isolated contact points or latent affordance embeddings lacks the rigorous kinematic constraints necessary for complex articulated objects.To overcome the limitation, we introduce RelAfford6D, a novel training-free framework centered on a Relational 6D Affordance Graph. Given a free-form instruction, our system deduces a semantic topology linking a primary interacting part to its physical anchor. By elevating these topological nodes into precise metric $SE(3)$ poses via vision foundation models, we analytically formulate downstream execution as a kinematic constraint satisfaction problem. The robot synthesizes continuous trajectories by tracking strictly defined physical manifolds (e.g., revolute or prismatic orbits). Coupled with a closed-loop tracking mechanism for dynamic replanning against disturbances, our physically grounded approach achieves superior zero-shot success rates, cross-category generalization and execution robustness in both simulation and the real world environments, outperforming existing data-driven baselines.