AI 中文总结
本文针对多体系统动力学的复杂问题，提出一种基于仿射体动力学的稳定并行GPU算法，实现刚柔体复杂相互作用的实时模拟。
AI 中文摘要
多体系统在机器人学、娱乐、动画等诸多领域有广泛应用，其建模与模拟互联体间复杂相互作用的能力使其在各领域极具价值。但非光滑接触处理、柔性关节非线性、并行化挑战等因素带来了复杂性。我们在仿射体动力学中提出一种稳定且高度并行的GPU算法，用于求解带非线性约束的多体动力学。该创新将带约束的多体动力学重新表述为变分形式，把系统视为通过近场动力学键连接的一组仿射体，此表述为仿射体动力学、约束与接触提供了统一模型，还便于整合半隐式逐次替换方法，以全局-局部迭代方式求解非线性优化。所提方法无需组装全局海森矩阵，非常适合在GPU上高效实现，可对包含接触、关节约束和摩擦的刚柔体复杂相互作用进行实时模拟。
英文摘要
Multibody systems have widespread applications in diverse fields such as robotics, entertainment, and animation. Their capability to model and simulate intricate interactions among interconnected bodies makes them invaluable in various domains. However, complexity arises with factors like non-smooth contact handling, nonlinearity in flexible joints, and parallelization challenges. We introduce a stable and highly parallel GPU algorithm within affine body dynamics for solving constrained multibody dynamics with nonlinear constraints.Our innovation involves reformulating constrained multibody dynamics into a variational form, treating the system as a set of affine bodies connected with peridynamic bonds. This formulation provides a unified model for affine body dynamics, constraints, and contact within the peridynamics framework.It also facilitates the integration of the semi-implicit successive substitution method to solve nonlinear optimization in a global-local iterative manner. The proposed method obviates the necessity of assembling a global Hessian, rendering it highly suitable for efficient implementation on GPUs.This allows real-time simulation of intricate interactions involving both rigid and flexible bodies, encompassing contact, joint constraints, and friction.
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