# Active Learning of Dynamics for Data-Driven Control Using Koopman Operators

## TL;DR

This paper introduces an active learning approach for robotic control that leverages Koopman operator theory to efficiently learn system dynamics and improve control performance, demonstrated on quadcopters and real robots.

## Contribution

It develops an active learning controller based on Koopman operators that accelerates system identification and control synthesis for nonlinear robotic systems.

## Key findings

- Enhanced control performance with Koopman-based models
- Active learning increases information gain about system dynamics
- Successful implementation on quadcopters and real robots

## Abstract

This paper presents an active learning strategy for robotic systems that takes into account task information, enables fast learning, and allows control to be readily synthesized by taking advantage of the Koopman operator representation. We first motivate the use of representing nonlinear systems as linear Koopman operator systems by illustrating the improved model-based control performance with an actuated Van der Pol system. Information-theoretic methods are then applied to the Koopman operator formulation of dynamical systems where we derive a controller for active learning of robot dynamics. The active learning controller is shown to increase the rate of information about the Koopman operator. In addition, our active learning controller can readily incorporate policies built on the Koopman dynamics, enabling the benefits of fast active learning and improved control. Results using a quadcopter illustrate single-execution active learning and stabilization capabilities during free-fall. The results for active learning are extended for automating Koopman observables and we implement our method on real robotic systems.