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

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.

A Theory of Irrotational Contact Fields

We present a framework that enables to write a family of convex approximations of complex contact models. Within this framework, we show that we can incorporate well established and experimentally validated contact models such as the Hunt & Crossley model. Moreover, we show how to incorporate Coulomb's law and the principle of maximum dissipation using a regularized model of friction. Contrary to common wisdom that favors the use of rigid contact models, our convex formulation is robust and performant even at high stiffness values far beyond that of materials such as steel. Therefore, the same formulation enables the modeling of compliant surfaces such as rubber gripper pads or robot feet as well as hard objects. We characterize and evaluate our approximations in a number of tests cases. We report their properties and highlight limitations. Finally, we demonstrate robust simulation of robotic tasks at interactive rates, with accurately resolved stiction and contact transitions, as required for meaningful sim-to-real transfer. Our method is implemented in the open source robotics toolkit Drake.