Fast and Reliable Gradients for Deformables Across Frictional Contact Regimes

2026-03-17

AI Summary

This work addresses gradient distortion in existing differentiable simulators under frictional contact and large deformations, which stems from mathematical inconsistencies and leads to optimization failure. We propose the first unified, fully GPU-accelerated differentiable simulator that enables stable, high-fidelity gradient computation across contact states. Our approach integrates a rigorously Markovian position-velocity manifold coupling, a mass-aligned preconditioner, a soft Fischer–Burmeister friction operator, and a finite element singularity resolution technique. We further introduce a long-horizon consistency mechanism and a unified contact stability strategy, enabling—for the first time—mathematically rigorous modeling of both frictional contact and hyperelastic materials within a differentiable framework. The resulting low-noise, high-fidelity gradients significantly narrow the Sim-to-Real gap and enhance the reliability of physical system identification and control in tasks such as dexterous manipulation and cloth folding.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web applications in cross-disciplinary domains and verticals such as mixed reality, smart cities, and digital health

Abstract

Differentiable simulation establishes the mathematical foundation for solving challenging inverse problems in computer graphics and robotics, such as physical system identification and inverse dynamics control. However, rigor in frictional contact remains the "elephant in the room." Current frameworks often avoid contact singularities via non-Markovian position approximations or heuristic gradients. This lack of mathematical consistency distorts gradients, causing optimization stagnation or failure in complex frictional contact and large-deformation scenarios. We introduce our unified fully GPU-accelerated differentiable simulator, which establishes a rigorous theoretical paradigm through: Long-Horizon Consistency: enforcing strict Markovian dynamics on a coupled position-velocity manifold to prevent gradient collapse; Unified Contact Stability: employing a mass-aligned preconditioner and soft Fischer--Burmeister operator for smooth frictional optimization; Robust Material Identification: resolving FEM singularities via a derived "Within-block Commutation" condition. Our experiments demonstrate our solver efficacy in bridging the Sim-to-Real gap, delivering precise, low-noise gradients in contact-rich tasks like dexterous manipulation and cloth folding. By mitigating the gradient instability issues common in conventional approaches, our framework significantly enhances the fidelity of physical system identification and control.

Problem

• differentiable simulation
• frictional contact
• gradient instability
• inverse problems
• physical system identification

Innovation

• differentiable simulation
• frictional contact
• gradient consistency
• soft Fischer–Burmeister
• within-block commutation