  It is challenging to perform system identification on soft robots due to
their underactuated, high-dimensional dynamics. In this work, we present a
data-driven modeling framework, based on geometric mechanics (also known as
gauge theory) that can be applied to systems with low-bandwidth control of the
system's internal configuration. This method constructs a series of connected
models comprising actuator and locomotor dynamics based on data points from
stochastically perturbed, repeated behaviors. By deriving these connected
models from general formulations of dissipative Lagrangian systems with
symmetry, we offer a method that can be applied broadly to robots with
first-order, low-pass actuator dynamics, including swelling-driven actuators
used in hydrogel crawlers. These models accurately capture the dynamics of the
system shape and body movements of a simplified swimming robot model. We
further apply our approach to a stimulus-responsive hydrogel simulator that
captures the complexity of chemo-mechanical interactions that drive shape
changes in biomedically relevant micromachines. Finally, we propose an approach
of numerically optimizing control signals by iteratively refining models, which
is applied to optimize the input waveform for the hydrogel crawler. This
transfer to realistic environments provides promise for applications in
locomotor design and biomedical engineering.
