22 research outputs found
Modeling, Reduction, and Control of a Helically Actuated Inertial Soft Robotic Arm via the Koopman Operator
Soft robots promise improved safety and capability over rigid robots when
deployed in complex, delicate, and dynamic environments. However, the infinite
degrees of freedom and highly nonlinear dynamics of these systems severely
complicate their modeling and control. As a step toward addressing this open
challenge, we apply the data-driven, Hankel Dynamic Mode Decomposition (HDMD)
with time delay observables to the model identification of a highly inertial,
helical soft robotic arm with a high number of underactuated degrees of
freedom. The resulting model is linear and hence amenable to control via a
Linear Quadratic Regulator (LQR). Using our test bed device, a dynamic,
lightweight pneumatic fabric arm with an inertial mass at the tip, we show that
the combination of HDMD and LQR allows us to command our robot to achieve
arbitrary poses using only open loop control. We further show that Koopman
spectral analysis gives us a dimensionally reduced basis of modes which
decreases computational complexity without sacrificing predictive power.Comment: Submitted to IEEE International Conference on Robotics and
Automation, 202
Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation
Effective and causal observable functions for low-order lifting linearization
of nonlinear controlled systems are learned from data by using neural networks.
While Koopman operator theory allows us to represent a nonlinear system as a
linear system in an infinite-dimensional space of observables, exact
linearization is guaranteed only for autonomous systems with no input, and
finding effective observable functions for approximation with a low-order
linear system remains an open question. Dual Faceted Linearization uses a set
of effective observables for low-order lifting linearization, but the method
requires knowledge of the physical structure of the nonlinear system. Here, a
data-driven method is presented for generating a set of nonlinear observable
functions that can accurately approximate a nonlinear control system to a
low-order linear control system. A caveat in using data of measured variables
as observables is that the measured variables may contain input to the system,
which incurs a causality contradiction when lifting the system, i.e. taking
derivatives of the observables. The current work presents a method for
eliminating such anti-causal components of the observables and lifting the
system using only causal observables. The method is applied to excavation
automation, a complex nonlinear dynamical system, to obtain a low-order lifted
linear model for control design