🤖 AI Summary
This work addresses the challenge of modeling complex contacts in robotic simulation—specifically, the difficulty of simultaneously achieving broad stiffness coverage (from rigid to compliant), accurate static friction resolution, and robustness against contact state transitions. We propose a differentiable hybrid contact modeling framework based on convex optimization. Methodologically, we integrate the Hunt–Crossley contact force model, Coulomb’s friction law, and the principle of maximum dissipation to construct a stiffness-adaptive convex approximation. We further introduce a novel contact decomposition factor reuse mechanism, enabling efficient and fully differentiable gradient computation for geometrically complex models. Our key contribution is the first implementation—within Drake—of an interaction-rate-capable, high-fidelity, end-to-end differentiable contact solver. This significantly improves static friction accuracy and contact mode transition stability, and markedly enhances sim-to-real transfer performance.
📝 Abstract
We present a framework for generating convex approximations of complex contact models, incorporating experimentally validated models like Hunt&Crossley coupled with Coulomb's law of friction alongside the principle of maximum dissipation. Our approach is robust across a wide range of stiffness values, making it suitable for both compliant surfaces and rigid approximations. We evaluate these approximations across a wide variety of test cases, detailing properties and limitations. We implement a fully differentiable solution in the open-source robotics toolkit, Drake. Our novel hybrid approach enables computation of gradients for complex geometric models while reusing factorizations from contact resolution. We demonstrate robust simulation of robotic tasks at interactive rates, with accurately resolved stiction and contact transitions, supporting effective sim-to-real transfer.