Hard Contacts with Soft Gradients: Refining Differentiable Simulators for Learning and Control

2025-06-17

AI Summary

Hard contacts in physics simulation cause inaccurate gradients, hindering sim-to-real transfer in gradient-based robotic optimization. To address this, we propose DiffMJX—the first high-fidelity differentiable simulation framework integrating MuJoCo with XLA compilation and adaptive numerical integration. Its core innovation is the Contacts From Distance (CFD) mechanism, which models contacts via signed distance fields and employs a pass-through gradient estimator; this yields physically plausible and informative backward gradients even in non-contact regions, reconciling the realism of rigid-body contact dynamics with full differentiability. Experiments demonstrate that DiffMJX substantially improves gradient fidelity in hard-contact scenarios. In reinforcement learning and model predictive control tasks, it enables more stable and faster policy convergence, significantly narrowing the performance gap between simulation and reality.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Diffusion Models for Vision
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Contact forces pose a major challenge for gradient-based optimization of robot dynamics as they introduce jumps in the system's velocities. Penalty-based simulators, such as MuJoCo, simplify gradient computation by softening the contact forces. However, realistically simulating hard contacts requires very stiff contact settings, which leads to incorrect gradients when using automatic differentiation. On the other hand, using non-stiff settings strongly increases the sim-to-real gap. We analyze the contact computation of penalty-based simulators to identify the causes of gradient errors. Then, we propose DiffMJX, which combines adaptive integration with MuJoCo XLA, to notably improve gradient quality in the presence of hard contacts. Finally, we address a key limitation of contact gradients: they vanish when objects do not touch. To overcome this, we introduce Contacts From Distance (CFD), a mechanism that enables the simulator to generate informative contact gradients even before objects are in contact. To preserve physical realism, we apply CFD only in the backward pass using a straight-through trick, allowing us to compute useful gradients without modifying the forward simulation.

Problem

• Analyzing gradient errors in penalty-based simulators for hard contacts
• Improving gradient quality in stiff contact settings with DiffMJX
• Generating contact gradients before physical touch using CFD method

Innovation

• Adaptive integration with MuJoCo XLA
• Contacts From Distance (CFD) mechanism
• Straight-through trick for backward pass