Efficient Differentiable Contact Model with Long-range Influence

2025-09-25

AI Summary

In differentiable physics simulation, conventional contact models impede gradient-based optimization convergence due to discontinuous or vanishing gradients. This paper introduces the first long-range differentiable contact model that simultaneously ensures theoretical soundness and computational efficiency. We first formalize three essential properties—continuity, non-degeneracy, and local sensitivity—that guarantee well-behaved gradients. Building upon these, we construct an implicit, continuous contact force model fully integrated into a differentiable rigid-body dynamics framework via implicit differentiation. Experiments on complex, contact-intensive control tasks—including multi-stage motion planning and dexterous manipulation—demonstrate that our model achieves stable convergence without careful initialization, significantly improving optimization success rates while maintaining tractable gradient computation overhead.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Low Level & Physics-based Vision
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

With the maturation of differentiable physics, its role in various downstream applications: such as model predictive control, robotic design optimization, and neural PDE solvers, has become increasingly important. However, the derivative information provided by differentiable simulators can exhibit abrupt changes or vanish altogether, impeding the convergence of gradient-based optimizers. In this work, we demonstrate that such erratic gradient behavior is closely tied to the design of contact models. We further introduce a set of properties that a contact model must satisfy to ensure well-behaved gradient information. Lastly, we present a practical contact model for differentiable rigid-body simulators that satisfies all of these properties while maintaining computational efficiency. Our experiments show that, even from simple initializations, our contact model can discover complex, contact-rich control signals, enabling the successful execution of a range of downstream locomotion and manipulation tasks.

Problem

• Differentiable simulators provide erratic gradients that impede optimization convergence
• Contact model design causes abrupt gradient changes or vanishing gradients
• Need contact model ensuring smooth gradients while maintaining computational efficiency

Innovation

• Developed differentiable contact model with smooth gradients
• Established properties for stable gradient-based optimization
• Maintained computational efficiency while handling complex contacts