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:我们提出了一种新的凸形式,该形式建模了通过摩擦接触耦合的刚性和可变形体。该公式包括具有正半定性 Hessian 的新的共旋转材料模型,该模型使我们得以将我们之前关于可变形体接触凸形式的工作扩展到模拟大的变形。我们严格地描述了我们的逼近,并提供了实现细节。具有全局收敛性、有效的热启动、大时间步长的能力以及专门的稀疏代数,我们的方法以交互速率稳健地运行。我们提供了与机器人应用相关的具有挑战性的模拟的验证结果和性能指标。我们的方法在开源机器人工具包 Drake 中提供。