Real-time trajectory tracking and stabilization of quadrotors using deep Koopman-based model predictive control

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Abstract
Purpose: This study aims to develop a data-driven Deep Koopman-based model predictive control (DK-MPC) framework for real-time trajectory tracking and stabilization of quadrotor systems. The objective is to overcome the computational limitations of conventional nonlinear model predictive control (NMPC) while preserving high-accuracy control performance. Design/methodology/approach: A deep neural network-based Koopman operator is employed to map the nonlinear quadrotor dynamics into a globally linear latent space, enabling the formulation of a computationally efficient linear model predictive control (MPC) problem. The Koopman embeddings are trained using the publicly available WaveLab Pelican dataset to capture the coupled and nonlinear dynamics of the quadrotor. The proposed DK-MPC framework is evaluated through numerical simulations involving point stabilization and trajectory tracking tasks, including previously unseen helical trajectories. Performance is assessed in terms of tracking accuracy, computational efficiency and real-time feasibility, with comparisons made against conventional NMPC. Findings: Simulation results demonstrate that the proposed DK-MPC framework achieves high-precision control with a coefficient of determination (R2) of 99%. The method requires approximately 10% of the computation time per control step compared to NMPC. For a prediction horizon of H = 50, DK-MPC maintains real-time feasibility with an average computation time of 15 ms per control step, while NMPC frequently fails to converge within the required time constraints. These findings confirm the effectiveness of the Koopman-based linear embedding in reducing computational burden without compromising control accuracy. Originality/value: The study presents a scalable and computationally efficient integration of deep Koopman operator learning with MPC for quadrotor systems. By combining data-driven nonlinear system representation with linear MPC optimization, the proposed framework bridges the gap between advanced learning-based modeling and real-time predictive control implementation.

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