We present a novel convex formulation that models rigid and deformable bodies coupled through frictional contact. The formulation incorporates a new corotational material model with positive semi-definite Hessian, which allows us to extend our previous work on the convex formulation of compliant contact to model large body deformations. We rigorously characterize our approximations and present implementation details. With proven global convergence, effective warm-start, the ability to take large time steps, and specialized sparse algebra, our method runs robustly at interactive rates. We provide validation results and performance metrics on challenging simulations relevant to robotics applications. Our method is made available in the open-source robotics toolkit Drake.

翻译：我们提出了一种新型凸优化框架，用于描述通过摩擦接触耦合的刚性与可变形体系统。该框架采用了一种具有半正定Hessian矩阵的新型共旋材料模型，从而将我们先前关于柔顺接触凸优化公式的研究扩展至大变形场景。我们对近似方案进行了严格的理论刻画，并给出了具体的实现细节。得益于全局收敛性证明、高效的热启动策略、大时间步长处理能力以及专用稀疏代数求解器，该方法能够在交互速率下稳健运行。我们提供了针对机器人学领域挑战性模拟的验证结果与性能指标。本方法已在开源机器人工具包Drake中发布。