We present a framework that enables to write a family of convex approximations of complex contact models. Within this framework, we show that we can incorporate well established and experimentally validated contact models such as the Hunt & Crossley model. Moreover, we show how to incorporate Coulomb's law and the principle of maximum dissipation using a regularized model of friction. Contrary to common wisdom that favors the use of rigid contact models, our convex formulation is robust and performant even at high stiffness values far beyond that of materials such as steel. Therefore, the same formulation enables the modeling of compliant surfaces such as rubber gripper pads or robot feet as well as hard objects. We characterize and evaluate our approximations in a number of tests cases. We report their properties and highlight limitations. Finally, we demonstrate robust simulation of robotic tasks at interactive rates, with accurately resolved stiction and contact transitions, as required for meaningful sim-to-real transfer. Our method is implemented in the open source robotics toolkit Drake.

翻译：我们提出一个框架，能够为复杂接触模型构建一系列凸近似。在该框架下，我们展示了如何融入诸如亨特-克罗斯利模型等经过实验验证的成熟接触模型。此外，我们还展示了如何利用正则化摩擦模型纳入库仑定律与最大耗散原理。与普遍推崇刚性接触模型的传统观点相反，我们的凸公式即使在远超钢材等材料刚度的条件下依然具有鲁棒性和高效性。因此，同一公式既能对橡胶夹爪垫或机器人足部等柔性表面进行建模，也能处理硬质物体。我们通过多个测试案例对所提近似方法进行了表征与评估，报告其特性并指出局限性。最终，我们以交互速率实现了机器人任务的鲁棒仿真，精确解析了粘滞滑动与接触状态转换——这正是实现有意义的仿真到现实迁移的关键。该方法已部署于开源机器人工具包Drake中。