A Convex Formulation of Frictional Contact for the Material Point Method and Rigid Bodies

In this paper, we introduce a novel convex formu- lation 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 ef- fective 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 com- promising 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 simula- tors, 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. The supplemental video is available here.