Data-Driven Geometric System Identification for Shape-Underactuated Dissipative Systems

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.