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.

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.