S4R: Scaling for Rigid-Body Interpenetration Resolution

Learning-based simulation of multi-object rigid-body dynamics remains difficult because contact is discontinuous and errors compound over long horizons. Most existing methods remain tied to mesh connectivity and vertex-level message passing, which limits their applicability to mesh-free inputs such as point clouds and leads to high computational cost. Efficiently modeling high-fidelity rigid-body dynamics from mesh-free representations, therefore, remains challenging. We introduce RigidFormer, an object-centric Transformer-based model that learns mesh-free rigid-body dynamics with controllable integration step sizes. RigidFormer reasons at the object level and advances each object through compact anchors; Anchor-Vertex Pooling enriches these anchors with local vertex features, retaining contact-relevant geometry without dense vertex-level interaction. We propose Anchor-based RoPE to inject anchor geometry into attention while respecting the unordered nature of objects and anchors: object-token processing is permutation-equivariant, and the mean-pooled anchor descriptor is invariant to anchor reindexing while preserving shape extent. RigidFormer further enforces rigidity by projecting updates onto the rigid-body manifold using differentiable Kabsch alignment. On standard benchmarks, RigidFormer outperforms or matches mesh-based baselines using point inputs, runs faster, generalizes to unseen point resolutions and across datasets, and scales to 200+ objects; we also show a preliminary extension to command-conditioned articulated bodies by treating body parts as interacting object-level components.

Despite substantial progress in text-driven 3D human motion synthesis, generating realistic multi-person interaction sequences remains challenging. Notably, body inter-penetration is a pervasive issue from both data acquisition to the generated results, which significantly undermines the realism and usability. Previous generative models either ignored this issue or introduced computationally expensive mesh-level loss functions to alleviate inter-body collisions. In this paper, we propose a general-purpose and computationally efficient optimization strategy named PhysiGen to explicitly integrate collision-aware physical constraints for human-human interaction generation. Specifically, we simplify the high-resolution human body mesh into geometric primitives to greatly reduce the cost of inter-person collision detection. Moreover, we identify the collision regions as the guidance of the optimization directions. PhysiGen is plug-and-play and can be readily integrated into existing human interaction generation models. Extensive cross-dataset and cross-model experiments show that our method can effectively reduce interpenetration and significantly improve visual coherence and physical plausibility compared to the state-of-the-art methods.

Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. Developing methods that make use of first/second order information about rigid-body dynamics in the presence of contact holds great promise in terms of increasing the solution speed and computational efficiency. The main bottleneck in this research direction is the difficulty in obtaining gradients and Hessians that are actually useful for numerical optimization, due to pathologies in all three steps of a common simulation pipeline: i) collision detection, ii) contact dynamics, iii) time integration. This abstract proposes a method that aims to address the collision detection part of the puzzle, via a novel pipeline designed from scratch with smooth (i.e. twice) differentiability and massive vectorizability on GPUs as the main priorities. This is in contrast to standard collision detection routines that are instead optimized for runtime on CPUs and minimal memory footprint, but do employ logic and control flow that hinder differentiability and vectorization. The proposed pipeline consists of the following contributions: i) highly expressive and compute efficient SDF representations, ii) differentiable broad-phase and narrow-phase routines that use these representations to generate vertex-SDF and edge-SDF contacts, iii) a differentiable routine for convex decomposition based contact blending.