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.

翻译：基于学习的多刚体动力学模拟仍面临挑战，原因在于接触不连续性及误差随长时间尺度的累积。现有方法大多受限于网格拓扑与顶点级信息传递，难以适用于点云等无网格输入，且计算成本高昂。因此，如何从无网格表示高效建模高保真刚体动力学仍是一大难题。我们提出RigidFormer——一种以物体为中心的Transformer模型，通过学习可控积分步长实现无网格刚体动力学建模。RigidFormer在物体层级进行推理，并通过紧凑锚点推动每个物体运动；锚点-顶点池化机制利用局部顶点特征丰富锚点信息，在不依赖密集顶点交互的前提下保留与接触相关的几何特征。我们提出基于锚点的RoPE机制，将锚点几何信息融入注意力计算，同时保持物体与锚点的无序性：物体令牌的处理过程具有置换等变性，均值池化后的锚点描述子对锚点重索引具有不变性，且能保留物体形状的尺度信息。RigidFormer进一步通过可微卡布施对齐将更新投影至刚体流形，以此强制约束刚体特性。在标准基准测试中，RigidFormer基于点云输入的表现优于或持平于网格基线方法，运行速度更快，能泛化至未见过的点云分辨率及跨数据集场景，并可扩展至200个以上物体；我们还初步展示了其在命令驱动铰链体上的扩展能力，即将部件视为交互的物体级组件。