  A new, and extremely fast, computational modeling 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, and
significant effort has been devoted to the development of intricate
constitutive models for finite elasticity, we show that in the kinds of
large-strain mechanics problems arising in soft robotics, many of the
parameters in constitutive models are irrelevant. For the most part, the
isochoric (locally volume-preserving) constraint dominates behavior, and this
can be built into closed-form kinematic deformation fields before even
considering other aspects of constitutive modeling. We therefore focus on
developing and applying primitive deformations that each observe this
constraint. It is shown that by composing a wide enough variety of such
deformations that the most common behaviors observed in soft robots can be
replicated. Case studies include an inflatable rubber chamber, a slender rubber
rod, and a rubber block subjected to different boundary conditions. We show
that this method is at least 50 times faster than the ABAQUS implementation of
the finite element method (FEM). Physical experiments and measurements show
that both our method and ABAQUS have approximately 10% error relative to
experimentally measured displacements, as well as to each other. Our method
provides a real-time alternative to FEM, and captures essential degrees of
freedom for use in feedback control systems.

Robotics