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

2026-03-09

AI Summary

Simulating large-scale articulated rigid-body systems remains challenging for conventional rigid-body solvers due to geometric nonlinearities and numerical stiffness. This work proposes a co-rotational framework based on Affine Body Dynamics (ABD) that decouples geometric nonlinearities through a linear kinematic mapping and projects high-dimensional body coordinates onto a dual space spanned by the minimal joint degrees of freedom. By combining implicit integration with KKT system solves, the method enforces exact constraint satisfaction and ensures physically accurate motion propagation. It supports diverse topologies—including chains, trees, closed loops, and irregular networks—and leverages pre-factorization of constant-coefficient matrices to achieve significant computational efficiency. The approach enables interactive simulation of systems comprising hundreds of thousands of rigid bodies on a single CPU core, maintaining high stability and accuracy even with large time steps.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• articulated assemblies
• numerical stiffness
• geometric complexity
• rotation parameterization
• multi-body dynamics

Innovation

• Affine Body Dynamics
• co-rotational formulation
• dual-space reduction
• KKT solver
• scalable multi-body simulation