Sim-to-Real for Projective Dynamics on Soft Robots via Differentiability: Meshing, Damping, and Actuation

An accurate, physically-based 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. Recently, Projective Dynamics (PD) has been proposed as a fast FEM; however, PD lacks rigorous benchmarking against reality. In this paper, we compare virtual robot models simulated using PD with measurements from their physical counterparts. In particular, we examine several soft structures with different morphologies: a clamped 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 differentiability of PD through a differentiable solution (DiffPD). We also advance PD in application to soft robotics by proposing a predictive model for pneumatic soft robot actuation. Through our case-studies, we provide strategies and algorithms for matching real-world physics in simulation, making PD useful for soft robots.