Simulating large-scale articulated assemblies poses a significant challenge due to the numerical stiffness and geometric complexity of jointed structures. Conventional rigid body solvers struggle with the high nonlinearity induced by rotation parameterization. This difficulty becomes more pronounced for multiple two-way-coupled bodies. This paper introduces a novel framework that leverages the linear kinematic mapping of Affine Body Dynamics (ABD). As ABD targets near-rigid objects, the constitutive variations of different materials become negligible, which justifies a co-rotational approach to isolate geometric nonlinearities of the system. This insight enables the use of constant system matrices that can be pre-factorized throughout the simulation, even with fully implicit integration schemes. To manage the high DOF counts of large-scale systems, we map primal body coordinates onto a compact dual space defined by minimal joint degrees of freedom. By solving the resulting KKT systems, our method ensures exact constraint enforcement and physically accurate motion propagation. We provide a suite of specialized solvers tailored for diverse joint topologies, including chains, trees, closed loops, and irregular networks. Experimental results show that our approach achieves interactive rates for systems with hundreds of thousands of bodies on a single CPU core, while maintaining excellent stability at large time steps.

翻译：模拟大规模铰接装配体因关节结构的数值刚性与几何复杂性而面临重大挑战。传统刚体求解器难以处理由旋转参数化引起的高度非线性问题，对于多个双向耦合体而言该困难尤为显著。本文提出一种新颖框架，该框架利用仿射体动力学（ABD）的线性运动学映射。由于ABD针对近刚体对象，不同材料的本构变化可忽略不计，这为采用共旋方法分离系统几何非线性提供了理论依据。该洞见使得系统可采用恒定系统矩阵，即使采用完全隐式积分方案，这些矩阵也能在全程仿真中预分解。为处理大规模系统的高自由度数量，我们将原始体坐标映射到由最小关节自由度定义的紧凑对偶空间。通过求解所得KKT系统，本方法确保约束的精确执行与物理精确的运动传播。我们提供一套专为多样化关节拓扑定制的求解器，涵盖链式、树状、闭环及不规则网络结构。实验结果表明，本方法在单CPU核心上对包含数十万体的系统实现了交互级计算速率，同时在大时间步长下保持卓越的稳定性。