M-ABD: Scalable, Efficient, and Robust Multi-Affine-Body Dynamics

TL;DR

This paper presents M-ABD, a scalable and efficient framework for simulating large-scale multi-body systems with complex joints, achieving real-time performance and stability on standard hardware.

Contribution

It introduces a novel affine body dynamics approach that simplifies nonlinearities, enabling pre-factorization and efficient constraint enforcement for large, complex articulated systems.

Findings

Achieves interactive simulation rates for hundreds of thousands of bodies.

Maintains stability with large time steps in complex multi-body systems.

Provides specialized solvers for various joint topologies.

Abstract

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.