Model Reduction in Soft Robotics Using Locally Volume-Preserving Primitives

A new, and extremely efficient, computational mod- eling paradigm is introduced here for specific finite elasticity problems that arise in the context of soft robotics. Whereas continuum mechanics is a very classical area of study that is broadly applicable throughout engineering, and significant effort has been devoted to the development of intricate constitutive models for finite elasticity, we show that for the most part, the isochoric (locally volume-preserving) constraint dominates behavior in common soft robotics contexts, and this can be built into closed-form kinematic deformation fields before even consid- ering other aspects of constitutive modeling. We therefore focus on developing and applying primitive deformations that each observe this constraint. By composing a wide enough variety of such deformations, many of the most common behaviors observed in soft robots can be replicated. Case studies include isotropic ob- jects subjected to different boundary conditions, a non-isotropic helically-reinforced tube, and a not-purely-kinematic scenario with gravity loading. We show that this method is at least 50 times faster than the ABAQUS implementation of the finite element method (FEM), and has speed comparable with the real- time FEM framework SOFA. Experiments show that both our method and ABAQUS have approximately 10% error relative to experimentally measured displacements, as well as to each other. And our method outperforms SOFA when the deformation is highly nonlinear. Our method provides a real-time alternative to FEM, and captures essential degrees of freedom for potential use in feedback control systems.