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arXiv · 1709.01568

Model-Based Control Using Koopman Operators

Ian Abraham·Gerardo De La Torre·Todd D. Murphey
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Abstract

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.

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Ian Abraham, Gerardo De La Torre, Todd D. Murphey. 2017-09-05. Model-Based Control Using Koopman Operators. https://doi.org/10.15607/rss.2017.xiii.052

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