Embedded IPC: Fast and Intersection-free Simulation in Reduced Subspace for Robot Manipulation

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.