We introduce MPM Lite, a hybrid Lagrangian/Eulerian method that eliminates the need for particle-based quadrature at solve time. Standard Material Point Method (MPM) practices suffer from a performance bottleneck where expensive implicit solves are proportional to particle-per-cell (PPC) counts due to the the choices of particle-based quadrature and wide-stencil kernels. By contrast, MPM Lite treats particles primarily as carriers of kinematic state and material history. Conceptualizing the background Cartesian grid as a voxel hexahedral mesh, we resample particle states onto fixed-location quadrature points using efficient, compact linear kernels. This architectural shift allows force assembly and the entire time-integration process to proceed without accessing particles, thus making the solver's complexity independent of the particle count. At the core of our method is a novel stress transfer and stretch reconstruction strategy. To avoid non-physical averaging of deformation gradients, we resample the extensive Kirchhoff stress and derive a rotation-free deformation reference solution, which naturally supports an optimization-based incremental potential formulation. Consequently, MPM Lite can be implemented as modular resampling units coupled with an FEM-style integration module, enabling the direct use of off-the-shelf nonlinear solvers, preconditioners, and unambiguous boundary conditions. We demonstrate through extensive experiments that MPM Lite preserves the robustness and versatility of traditional MPM across diverse materials while delivering significant speedups in implicit settings while simultaneously improving explicit ones. Project page: https://mpmlite.github.io.

Physics-based simulation is essential for developing and evaluating robot manipulation policies, particularly in scenarios involving deformable objects and complex contact interactions. However, existing simulators often struggle to balance computational efficiency with numerical accuracy, especially when modeling deformable materials with frictional contact constraints. We introduce an efficient subspace representation for the Incremental Potential Contact (IPC) method, leveraging model reduction to decrease the number of degrees of freedom. Our approach decouples simulation complexity from the resolution of the input model by representing elasticity in a low-resolution subspace while maintaining collision constraints on an embedded high-resolution surface. Our barrier formulation ensures intersection-free trajectories and configurations regardless of material stiffness, time step size, or contact severity. We validate our simulator through quantitative experiments with a soft bubble gripper grasping and qualitative demonstrations of placing a plate on a dish rack. The results demonstrate our simulator's efficiency, physical accuracy, computational stability, and robust handling of frictional contact, making it well-suited for generating demonstration data and evaluating downstream robot training applications. More details and supplementary material are on the website: https://sites.google.com/view/embedded-ipc.

Visuotactile sensors are a popular tactile sensing strategy due to high-fidelity estimates of local object geometry. However, existing algorithms for processing raw sensor inputs to useful intermediate signals such as contact patches struggle in high-deformation regimes. This is due to physical constraints imposed by sensor hardware and small-deformation assumptions used by mechanics-based models. In this work, we propose a fusion algorithm for proximity and visuotactile point clouds for contact patch segmentation, entirely independent from membrane mechanics. This algorithm exploits the synchronous, high spatial resolution proximity and visuotactile modalities enabled by an extremely deformable, selectively transmissive soft membrane, which uses visible light for visuotactile sensing and infrared light for proximity depth. We evaluate our contact patch algorithm in low ($\mathbf{1 0 \%}$), medium ($\mathbf{6 0 \%}$), and high$(100 \%+)$strain states. We compare our method against three baselines: proximity-only, tactile-only, and a first principles mechanics model. Our approach outperforms all baselines with an average RMSE under 2.8 mm of the contact patch geometry across all strain ranges. We demonstrate our contact patch algorithm in four applications: varied stiffness membranes, torque and shear-induced wrinkling, closed loop control, and pose estimation.

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 500× 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.

We present Irrotational Contact Fields (ICF), a framework for generating convex approximations of complex contact models, incorporating experimentally validated models like Hunt & Crossley coupled with Coulomb's law of friction alongside the principle of maximum dissipation. Our approach is robust across a wide range of stiffness values, making it suitable for both compliant surfaces and rigid approximations. We evaluate these approximations across a wide variety of test cases, detailing properties and limitations. We implement a fully differentiable solution in the open-source robotics toolkit, Drake. Our novelhybridapproach enables efficient computation of gradients for complex geometric models by reusing factorizations from contact resolution. We demonstrate robust simulation of robotic tasks at interactive rates, with accurately resolved stiction and contact transitions, supporting effective sim-to-real transfer.

In this article, we present a convex formulation of compliant frictional contact and a robust performant method to solve it in practice. By analytically eliminating contact constraints, we obtain an unconstrained convex problem. Our solver has proven global convergence and warm-starts effectively, enabling simulation at interactive rates. We develop compact analytical expressions of contact forces allowing us to describe our model in clear physical terms and to rigorously characterize our approximations. Moreover, this enables us not only to model point contact but also to incorporate sophisticated models of compliant contact patches. Our time stepping scheme includes the midpoint rule, which we demonstrate achieves second order accuracy even with frictional contact. We introduce a number of accuracy metrics and show that our method outperforms the existing commercial and open-source alternatives without sacrificing accuracy. Finally, we demonstrate the robust simulation of robotic manipulation 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.