In this paper, we introduce a novel convex formulation that seamlessly integrates the Material Point Method (MPM) with articulated rigid body dynamics in frictional contact scenarios. We extend the linear corotational hyperelastic model into the realm of elastoplasticity and include an efficient return mapping algorithm. This approach is particularly effective for MPM simulations involving significant deformation and topology changes, while preserving the convexity of the optimization problem. Our method ensures global convergence, enabling the use of large simulation time steps without compromising robustness. We have validated our approach through rigorous testing and performance evaluations, highlighting its superior capabilities in managing complex simulations relevant to robotics. Compared to previous MPM based robotic simulators, our method significantly improves the stability of contact resolution -- a critical factor in robot manipulation tasks. We make our method available in the open-source robotics toolkit, Drake.

翻译：本文提出了一种新颖的凸优化公式，能够无缝集成材料点法（MPM）与关节刚体动力学在摩擦接触场景中的应用。我们将线性共旋超弹性模型扩展至弹塑性领域，并引入高效的返回映射算法。该方法对涉及大变形和拓扑变化的MPM模拟尤为有效，同时保持优化问题的凸性。我们的方法保证了全局收敛性，使得在不牺牲鲁棒性的前提下能够采用较大的模拟时间步长。通过严格的测试和性能评估，我们验证了该方法在管理机器人相关复杂模拟方面的卓越能力。与以往基于MPM的机器人模拟器相比，我们的方法显著提升了接触求解的稳定性——这是机器人操作任务中的关键因素。我们将该方法开源集成于机器人工具包Drake中。