Koopman-LQR Controller for Quadrotor UAVs from Data

TL;DR

This paper introduces a data-driven control method for quadrotor UAVs using Koopman operator theory to linearize nonlinear dynamics, enabling the design of effective LQR controllers based on data-derived models.

Contribution

It presents a novel approach combining Koopman operator theory with LQR control for quadrotors, using EDMD for system identification from data.

Findings

Koopman-based models accurately represent quadrotor dynamics.

LQR controllers designed on Koopman models stabilize the UAV.

The method reduces reliance on complex nonlinear modeling.

Abstract

Quadrotor systems are common and beneficial for many fields, but their intricate behavior often makes it challenging to design effective and optimal control strategies. Some traditional approaches to nonlinear control often rely on local linearizations or complex nonlinear models, which can be inaccurate or computationally expensive. We present a data-driven approach to identify the dynamics of a given quadrotor system using Koopman operator theory. Koopman theory offers a framework for representing nonlinear dynamics as linear operators acting on observable functions of the state space. This allows to approximate nonlinear systems with globally linear models in a higher dimensional space, which can be analyzed and controlled using standard linear optimal control techniques. We leverage the method of extended dynamic mode decomposition (EDMD) to identify Koopman operator from data with total least squares. We demonstrate that the identified model can be stabilized and controllable by designing a controller using linear quadratic regulator (LQR).