ComFree-Sim: A GPU-Parallelized Analytical Contact Physics Engine for Scalable Contact-Rich Robotics Simulation and Control

Abstract

Physics simulation for contact-rich robotics is often bottlenecked by contact resolution: mainstream engines enforce non-penetration and Coulomb friction via complementarity constraints or constrained optimization, requiring per-step iterative solves whose cost grows superlinearly with contact density. We present ComFree-Sim, a GPU-parallelized analytical contact physics engine built on complementarity-free contact modeling. ComFree-Sim computes contact impulses in closed form via an impedance-style prediction--correction update in the dual cone of Coulomb friction. Contact computation decouples across contact pairs and becomes separable across cone facets, mapping naturally to GPU kernels and yielding near-linear runtime scaling with the number of contacts. We further extend the formulation to a unified 6D contact model capturing tangential, torsional, and rolling friction, and introduce a practical dual-cone impedance heuristic. ComFree-Sim is implemented in Warp and exposed through a MuJoCo-compatible interface as a drop-in backend alternative to MuJoCo Warp (MJWarp). Experiments benchmark penetration, friction behaviors, stability, and simulation runtime scaling against MJWarp, demonstrating near-linear scaling and 2--3 times higher throughput in dense contact scenes with comparable physical fidelity. We deploy ComFree-Sim in real-time MPC for in-hand dexterous manipulation on a real-world multi-fingered LEAP hand and in dynamics-aware motion retargeting, demonstrating that low-latency simulation yields higher closed-loop success rates and enables practical high-frequency control in contact-rich tasks.

Figures (9)

• Figure 1: Different contact modes captured by ComFree-Sim.
• Figure 2: Penetration-depth benchmark in a collision-rich drop test: (a) stacked arrays of primitives released to free-fall onto a flat box; (b) mean$\pm$std penetration depth over all detected contacts. In all tests, simulation timestep $dt=0.002$.
• Figure 3: Isolated benchmark environments.
• Figure 4: Results of torsional and rolling friction test.
• Figure 5: Numerical stability test: horizontal speed and vertical position $z$ of free-fall-and-sliding cube over time. Left: ComFree-Sim with varying $(k_{\text{user}},d_{\text{user}})$ at $d t{=}0.002$s. Right: ComFree-Sim under varying timestep $dt$.