Robotics: Science and Systems XIII

Model-Based Control Using Koopman Operators

Ian Abraham, Gerardo de la Torre, Todd Murphey


This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting model-based control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis. Simulated results show that with increasing complexity in the choice of the basis functions, a closed-loop controller is able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore, the specification of the basis function are shown to be of importance when generating a Koopman operator for specific robotic systems. Experimental results with the Sphero SPRK robot explore the utility of the Koopman operator in a reduced state representation setting where increased complexity in the basis function improve open- and closed-loop controller performance in various terrains, including sand.



    AUTHOR    = {Ian Abraham AND Gerardo de la Torre AND Todd Murphey}, 
    TITLE     = {Model-Based Control Using Koopman Operators}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2017}, 
    ADDRESS   = {Cambridge, Massachusetts}, 
    MONTH     = {July}, 
    DOI       = {10.15607/RSS.2017.XIII.052}