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

Abstract

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. The supplemental video is available at https://youtu.be/5jrQtF5D0DA

Figures (7)

• Figure 1: Rolling out dough with a rolling pin (see supplemental video). Our two-way coupled solver captures the dough's deformation as well as the rolling pin's rotation driven by frictional contact with the dough.
• Figure 2: A rigid ball rolling down a rigid slope. The analytical solution in \ref{['eq:roll-sphere-analytical']} is the displacement in $x$ direction.
• Figure 3: Displacement of the center of mass of a rigid ball along a rigid slope: analytical and numerical solutions. Our results match well with the analytical solution in both the slip mode ($\mu \leq \frac{2}{7}\tan\theta$) and the stick mode ($\mu > \frac{2}{7}\tan\theta$).
• Figure 4: A cookie dough is teared apart into two pieces by robot arms.
• Figure 5: A robot transferring liquid from a mug into a bin.