Robust and Efficient Penetration-Free Elastodynamics without Barriers

TL;DR

<3-5 sentence high-level summary> The paper tackles the inefficiency of barrier-based penetration-free elastodynamics by introducing a barrier-free, second-order constrained optimization framework that uses a primal-dual augmented Lagrangian solver and immediate CCD-informed contact incorporation to avoid TOI locking. It replaces logarithmic barrier functions with adaptive Lagrange multipliers, supplemented by a constraint filtering and decay mechanism to maintain a compact active set, and employs a TOI-based finite-step termination with provable first-order accuracy. The authors demonstrate up to three orders of magnitude speedups over GIPC and substantial gains over barrier-based baselines across challenging, contact-rich benchmarks, supported by a GPU-optimized implementation and extensive evaluations. This approach significantly improves robustness, efficiency, and practicality of penetration-free elastodynamic simulation for robotics and virtual reality applications, with open-source code and data forthcoming.

Abstract

We introduce a barrier-free optimization framework for non-penetration elastodynamic simulation that matches the robustness of Incremental Potential Contact (IPC) while overcoming its two primary efficiency bottlenecks: (1) reliance on logarithmic barrier functions to enforce non-penetration constraints, which leads to ill-conditioned systems and significantly slows down the convergence of iterative linear solvers; and (2) the time-of-impact (TOI) locking issue, which restricts active-set exploration in collision-intensive scenes and requires a large number of Newton iterations. We propose a novel second-order constrained optimization framework featuring a custom augmented Lagrangian solver that avoids TOI locking by immediately incorporating all requisite contact pairs detected via CCD, enabling more efficient active-set exploration and leading to significantly fewer Newton iterations. By adaptively updating Lagrange multipliers rather than increasing penalty stiffness, our method prevents stagnation at zero TOI while maintaining a well-conditioned system. We further introduce a constraint filtering and decay mechanism to keep the active set compact and stable, along with a theoretical justification of our method's finite-step termination and first-order time integration accuracy under a cumulative TOI-based termination criterion. A comprehensive set of experiments demonstrates the efficiency, robustness, and accuracy of our method. With a GPU-optimized simulator design, our method achieves an up to 103x speedup over GIPC on challenging, contact-rich benchmarks - scenarios that were previously tractable only with barrier-based methods. Our code and data will be open-sourced.

Figures (23)

• Figure 1: Tackling the TOI locking issue. (a) The advancement in each Newton iteration is stalled at the contact pair with the minimum TOI (marked in red), thus incorporating only the earliest contacts into the constraint set (assuming small contact radius). All other contacts (marked in green) can continue to block the CCD in subsequent iterations. (b) IPC's Newton iterations, discarding the intermediate states $\hat{{\mathbf x}}$. (c) Our modified framework with explicitly maintained intermediate state $\hat{{\mathbf x}}$ and constraint set $\mathcal{C}$ carrying Lagrange multipliers, updated by a primal–dual augmented Lagrangian solver.
• Figure 2: Compressing chain rings. Three nested elastic rings are compressed within a shrinking boundary and then released to rebound, reaching a density increase of up to $185.2\times$ during compression. The simulation remains stable and preserves topology under extreme deformation and complex contacts.
• Figure 3: Animal well. A challenging test case featuring a large collection of objects (1.34M tetrahedra) and high velocity induced by gravity. The topmost objects are accelerated to $19.7\,\text{m/s}$ when colliding with the lower ones, traveling farther than their average size within a single time step.
• Figure 4: Ramen. An array of long noodles is dropped into a fixed bowl, stably picked up using chopsticks with static friction ($\mu_f=0.1$), and then released.
• Figure 5: Twisting rods. A bundle of elastic rods with boundaries rotated by $5400^\circ$ in opposite directions at both ends. The contact stiffness $\mu$ is adaptively adjusted to match the conditioning of the Neo-Hookean elasticity.