An accurate, physically-based, and differentiable model of soft robots can unlock downstream applications in optimal control. The Finite Element Method (FEM) is an expressive approach for modeling highly deformable structures such as dynamic, elastomeric soft robots. In this paper, we compare virtual robot models simulated using differentiable FEM with measurements from their physical counterparts. In particular, we examine several soft structures with different morphologies: a clamped soft beam under external force, a pneumatically actuated soft robotic arm, and a soft robotic fish tail. We benchmark and analyze different meshing resolutions and elements (tetrahedra and hexahedra), numerical damping, and the efficacy of differentiability for parameter calibration using a simulator based on the fast Differentiable Projective Dynamics (DiffPD). We also advance FEM modeling in application to soft robotics by proposing a predictive model for pneumatic soft robotic actuation. Through our recipes and case studies, we provide strategies and algorithms for matching real-world physics in simulation, making FEM useful for soft robots

翻译：精确、物理和不同的软机器人模型可以在最佳控制下解开下游应用。 有限元素法(FEM)是模拟高度变形结构(如动态、弹性软机器人)的一种直观方法。 在本文中,我们比较了使用不同式FEM模拟的虚拟机器人模型与物理模型的测量结果。 特别是,我们检查了几种不同形态的软结构:外部力量下的紧固软光束、气动软机器人臂和软机器人尾鱼。 我们通过我们的食谱和案例研究,对不同网格分辨率和元素(trahedra和Hexhedra)进行基准和分析,用基于快速差异投影动态的模拟器(DiffPD)对参数校准、数字阻隔和参数校准的不同性效果进行了数据测试和分析。 我们还在软机器人应用中推进了FEM模型,为软式机器人提出了一个预测模型。 通过我们的食谱和案例研究,我们提供了在模拟中匹配真实世界物理学(trahedra和Hexhedra)、数字和算法,使FEM对软机器人有用。