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

TL;DR

The paper addresses the bottleneck of balancing accuracy and speed in physics-based robot manipulation simulators, particularly for deformable objects with frictional contact. It introduces Embedded IPC, a subspace-reduced version of Incremental Potential Contact that decouples simulation cost from input resolution by representing elasticity in a reduced subspace while enforcing collision constraints on a high-resolution embedded collision surface. The method uses a linear embedding x = J q, constructs the reduced energy E_IPC = E_IP + h^2 B(x) + h^2 D(x, x^n), and solves via a Projected Newton method with CCD safeguards, ensuring intersection-free trajectories. Experiments demonstrate interactive, real-time performance with robust contact handling and non-penetration guarantees, making the approach suitable for generating data and evaluating downstream robot training pipelines.

Abstract

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.

Figures (11)

• Figure 1: Our method can simulate grasping a deformable teddy bear with a bubble gripper and manipulating stiff plates with a FinRay gripper, all while ensuring a non-penetration guarantee at interactive rates.
• Figure 2: A simple 2-dimensional case illustration. The blue mesh is the embedding for the orange collision mesh. We denote the red vertex of the collision mesh by ${\bm{x}}_k$, the associated embedding triangle of ${\bm{x}}_k$ is $T_{i(k)}$ which is highlighted by the green area. In a 3-dimensional space it should be an embedding tetrahedron as we stated in Sec. \ref{['sec:embedding_impl']}. The vertex positions of $T_{i(k)}$ are ${\bm{q}}_{i^j(k)}, j \in \mathbb{N}, 1 \leq j \leq d + 1$, where $d$ is the world-space dimension.
• Figure 3: We simulate grasping a soft teddy bear with a soft bubble gripper. The process contains 3 steps: (i). Grasping: Moving the bubbles toward the teddy bear to grasp it, moving from (a) to (b)). (ii). Lifting: Lifting the teddy bear vertically off the ground, moving from (b) to (c). (iii). Holding: The bubble gripper remains stationary, holding the teddy bear as in (c).
• Figure 4: Contact forces between the left deformable bubble and the teddy bear. The simulation has a time step size of $h = 0.005\text{s}$.
• Figure 5: Number of contacts as a function of time. The simulation has a time-step of $h = 0.005s$ as in Fig. \ref{['fig:bubble_gripper_forces']}.