用凸优化方法高效模拟软体与刚体交互，支持实时机器人操作仿真。
A Convex Formulation of Material Points and Rigid Bodies with GPU-Accelerated Async-Coupling for Interactive Simulation
- 通过凸优化弱耦合粒子法与刚体动力学，实现摩擦接触建模。
- 采用异步时间分裂方案，支持不同步长并行计算，比以往快500倍。
- 适用于机器人抓取、布料和颗粒物等复杂场景，适合高并发仿真需求。
我们提出一种新型凸优化方法，通过摩擦接触将材料点法（MPM）与刚体动力学弱耦合，专为高效的GPU并行化设计。采用异步时间分裂方案，在不同时间步长下集成MPM与刚体动力学。开发了全局收敛的拟牛顿求解器，可大规模并行，相比以往凸形式实现高达500倍加速，同时保持稳定性。该方法支持以交互速率模拟机器人操作任务，涵盖多种可变形物体，包括颗粒材料和布料，并具备强收敛保证。我们详述关键实现策略以最大化性能，通过严格实验验证，相较于现有先进MPM模拟器在速度、精度和稳定性上均表现更优。本方法已开源集成至机器人工具包Drake。
原文摘要 · Abstract (English)
We present a novel convex formulation that weakly couples the Material Point Method (MPM) with rigid body dynamics through frictional contact, optimized for efficient GPU parallelization. Our approach features an asynchronous time-splitting scheme to integrate MPM and rigid body dynamics under different time step sizes. We develop a globally convergent quasi-Newton solver tailored for massive parallelization, achieving up to 500x speedup over previous convex formulations without sacrificing stability. Our method enables interactive-rate simulations of robotic manipulation tasks with diverse deformable objects including granular materials and cloth, with strong convergence guarantees. We detail key implementation strategies to maximize performance and validate our approach through rigorous experiments, demonstrating superior speed, accuracy, and stability compared to state-of-the-art MPM simulators for robotics. We make our method available in the open-source robotics toolkit, Drake.
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