  Finite element methods have been successfully used to develop physics-based
models of soft robots that capture the nonlinear dynamic behavior induced by
continuous deformation. These high-fidelity models are therefore ideal for
designing controllers for complex dynamic tasks such as trajectory optimization
and trajectory tracking. However, finite element models are also typically very
high-dimensional, which makes real-time control challenging. In this work we
propose an approach for finite element model-based control of soft robots that
leverages model order reduction techniques to significantly increase
computational efficiency. In particular, a constrained optimal control problem
is formulated based on a nonlinear reduced order finite element model and is
solved via sequential convex programming. This approach is demonstrated through
simulation of a cable-driven soft robot for a constrained trajectory tracking
task, where a 9768-dimensional finite element model is used for controller
design.
