Koopman-LQR Controller for Quadrotor UAVs from Data

Quadrotor systems are common and beneficial in 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 an approach based on data to identify the dynamics of a given quadrotor system using Koopman operator theory which offers a linear, but infinite dimensional representation of nonlinear dynamics. This facilitates the use of globally linear models to get an approximation for the nonlinear systems, which can be analyzed and controlled using standard linear optimal control techniques. We leverage the method of extended dynamic mode decomposition (EDMD) to identify the Koopman operator from data. We demonstrate that the identified model can be stabilized and controlled by designing a controller using the linear quadratic regulator (LQR).