# A Convex Formulation of Material Points and Rigid Bodies with GPU-Accelerated Async-Coupling for Interactive Simulation

arXiv: https://arxiv.org/abs/2503.05046 · HTML: https://mlsanity.com/paper/2503.05046/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2025.

## Built on by (most cited first, 1 of 1)

- [Size Doesn't Matter: Material-State Reinforcement Learning for Excavator Transferable Soil Manipulation](https://mlsanity.com/paper/2609.12677/) (2026)

## Abstract (arXiv)

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.