Data-Driven and Nonlinear Control Methods for Autonomous Quadrotor Systems: Development and Evaluation of a Koopman-Based Predictive Control Framework

Accurate prediction and control of quadrotor systems are challenging because their dynamics are nonlinear, coupled, and influenced by embedded flight-control behavior and environmental disturbances. This work investigates whether finite-dimensional bilinear Koopman models can provide sufficiently accurate short-horizon representations of nonlinear quadrotor dynamics for nonlinear model predictive control (NMPC), and whether the resulting predictive framework can improve trajectory tracking under previously unseen disturbances. The methodology progresses from an analytical nonlinear pendulum to a reduced-order quadrotor with known governing equations, followed by data-driven identification and closed-loop control in PX4 Software-in-the-Loop with Gazebo, and finally prediction validation using physical DJI Tello EDU flight data. The pendulum and reduced-order studies establish the importance of bilinear state–input interactions introduced by nonlinear lifting. In a task-focused reduced-order comparison, the bilinear Koopman model reduced full-lap recursive three-dimensional position RMSE from 0.215 m to 0.005 m relative to an additive linear Koopman model, corresponding to a 97.66% reduction. In PX4–Gazebo, Koopman models were identified directly from simulated flight measurements and high-level velocity and yaw commands without explicitly supplying the complete rigid-body or embedded-controller equations. Under no-wind conditions, the learned model achieved a recursive approximately one-second three-dimensional position RMSE of 0.0081 m. A separate wind-conditioned proof-of-concept study showed that explicitly supplying wind information could substantially improve prediction under a tested disturbance. The final control architecture used a frozen no-wind-trained Koopman model as an outer predictive-correction layer while PX4 retained its cascaded stabilization loops. Wind speed and direction were not supplied to the predictor or optimizer during the final unseen-wind tests. Compared to the classical PX4 baseline under the same circular reference and wind conditions, the Koopman-NMPC architecture produced lower reported horizontal RMSE at every tested condition from 1 to 5 m/s East and under a diagonal 2 m/s East plus 2 m/s North disturbance. The largest observed reduction was 39.4% at 3 m/s East, while the benefit decreased to 7.4% at 5 m/s East. Finally, held-out DJI Tello flight data demonstrated physical short-horizon prediction accuracy, with position RMSE of approximately 5 mm over 0.22 s and below approximately 2 cm per axis over 0.55 s. The main contribution of this work is a practical progression from bilinear Koopman system identification to predictive quadrotor control, disturbance evaluation, baseline comparison, and physical-data validation within a unified framework. The results demonstrate that control-oriented bilinear Koopman representations can capture useful nonlinear command-response behavior directly from data while remaining suitable for short-horizon predictive optimization. This work lays the groundwork for future research in disturbance-conditioned and adaptive Koopman modeling, higher-dimensional vehicle representations, improved real-time optimization, and closed-loop physical-flight implementation. The framework therefore supports the continued development of data-driven nonlinear control methods for autonomous UAVs