  The study of systems whose movement is both geometric and dissipative offers
an opportunity to quickly both identify models and optimize motion. Here, the
geometry indicates reduction of the dynamics by environmental homogeneity while
the dissipative nature minimizes the role of second order (inertial) features
in the dynamics. In this work, we extend the tools of geometric system
identification to "Shape-Underactuated Dissipative Systems (SUDS)" -- systems
whose motions are kinematic, but whose actuation is restricted to a subset of
the body shape coordinates. A large class of SUDS includes highly damped robots
with series elastic actuators, and many soft robots. We validate the predictive
quality of the models using simulations of a variety of viscous swimming
systems. For a large class of SUDS, we show how the shape velocity actuation
inputs can be directly converted into torque inputs suggesting that, e.g.,
systems with soft pneumatic actuators or dielectric elastomers, could be
controlled in this way. Based on fundamental assumptions in the physics, we
show how our model complexity scales linearly with the number of passive shape
coordinates. This offers a large reduction on the number of trials needed to
identify the system model from experimental data, and may reduce overfitting.
The sample efficiency of our method suggests its use in modeling, control, and
optimization in robotics, and as a tool for the study of organismal motion in
friction dominated regimes.
