Model-Based Control Using Koopman Operators

TL;DR

This paper demonstrates how Koopman operator theory can be used to create data-driven, linearizable models for control of robotic systems, improving stability and performance across different terrains.

Contribution

It introduces a method to apply Koopman operators for model-based control in robotics, highlighting the importance of basis function selection and validating with simulations and real robot experiments.

Findings

Koopman operators enable linear control of complex robotic dynamics.

Choice of basis functions significantly affects control performance.

Experimental results show improved stability on varied terrains.

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.