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.

翻译：我们提出了一种生成复杂接触模型凸近似框架的方法，该方法融合了经实验验证的模型（如Hunt & Crossley模型与库仑摩擦定律的结合）以及最大耗散原理。我们的方法在广泛的刚度值范围内具有鲁棒性，适用于柔性表面和刚性近似场景。我们通过多种测试案例评估这些近似方法，详细阐述其特性与局限。我们在开源机器人工具包Drake中实现了完全可微分的求解方案。这种新颖的混合方法能够在复用接触求解因式分解的同时，为复杂几何模型计算梯度。我们展示了以交互速率实现机器人任务的鲁棒仿真，其中静摩擦与接触转换均得到精确求解，有效支持了仿真到现实的迁移应用。