Real-Time Disturbance-Aware Koopman Model Predictive Control for Quadrotors in Spatially Varying Winds

Stella Kombo; Masih Haseli; Alejandro A. Stefan-Zavala; Peter I. Renn; Morteza Gharib; Joel W. Burdick

cs.ROOct 20, 2026

Real-Time Disturbance-Aware Koopman Model Predictive Control for Quadrotors in Spatially Varying Winds

Authors: Stella Kombo, Masih Haseli, Alejandro A. Stefan-Zavala, Peter I. Renn, Morteza Gharib, Joel W. Burdick

Organizations: Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA.

Abstract

Reliable quadrotor flight in disturbed environments requires predictive models that remain accurate as unmodeled aerodynamic effects change during deployment. We introduce a disturbance-aware Koopman Control Family (DA-KCF) framework that preserves an offline-identified nominal model while learning only a disturbance-induced correction online. A reference-dependent KCF is first learned from simulation data and calibrated using limited hardware data. During deployment, the nominal KCF remains fixed while a lightweight residual ensemble learns a low-dimensional disturbance correction from causal state-command-state transitions. The Adaptive DA-KCF model is incorporated into MPC, where disturbance corrections are evaluated along the prediction horizon to optimize position and yaw references sent to the onboard stabilizing controller. Hardware experiments on a nano-quadrotor under uniform wind and a spatially varying wake demonstrate that online adaptation improves multi-step prediction and trajectory tracking as disturbance-induced model mismatch increases, while satisfying real-time control requirements.

Figures & tables

Fig. 1 : Drone figure-eight trajectory tracking under aerodynamic disturbance. The fan array seen on the left side of the photo generates a predominantly unidirectional flow (red arrows). The overlaid trajectories illustrate the adaptive (green) and non-adaptive (red) controller responses.

Fig. 2 : Overview of the proposed disturbance-aware KCF pipeline: nominal KCF identification in simulation, sim-to-real fine-tuning and online disturbance adaptation for predictive control.

Fig. 3 : Experimental figure-eight trajectories under increasing aerodynamic disturbance. Columns correspond to PID, Nominal KCF-MPC, and Adaptive DA-KCF-MPC, while rows correspond to fan-array flow speeds of $0$ m/s, $3.75$ m/s, and $5.0$ m/s. Trajectories are shown in the $x$ – $z$ projection relative to the center $(x_{c},z_{c})$ of the desired trajectory. The dashed black curve denotes the desired path, while the measured trajectory is colored by the instantaneous three-dimensional position-tracking error $e_{p}(k)=1000\|p_{k}-p_{k}^{d}\|_{2}$ [mm]. Each panel shows a representative experimental trial. Aggregate performance over repeated trials is reported in Table I .

Wind	PID	Nominal	Adaptive
$0$	$5.70\pm 0.19$	$3.66\pm 0.18$	$\mathbf{3.59\pm 0.05}$
$3.75$	$10.72\pm 0.08$	$9.39\pm 0.05$	$\mathbf{7.70\pm 0.33}$
$5.00$	$13.15\pm 2.03$	$12.63\pm 0.27$	$\mathbf{9.95\pm 0.41}$

TABLE I : Three-dimensional position-tracking RMSE [cm] under increasing wind speed [m/s]. Nominal and Adaptive denote Nominal KCF-MPC and Adaptive DA-KCF-MPC, respectively. Values report mean

\pm

one sample standard deviation across

4

repeated trials.

Fig. 4 : Online adaptation during sustained

5.0

m/s wind hover. The orange dashed line marks disturbance onset, the dark-purple line the first adaptation trigger, and the light-purple lines subsequent candidate-update cycles. Dashed black lines denote the commanded hover position.

Fig. 5 : Online residual adaptation during sustained $5.0$ m/s wind hover. The light-blue trace shows the $x$ -component of the observed one-step velocity prediction mismatch $\Delta v_{k,x}$ , the black trace its causal $1$ s trailing mean, and the dark-blue trace the learned $x$ -component of the ensemble correction $\Gamma_{k,x}$ . Vertical lines indicate wind onset (orange), the first online training attempt (purple), and deployment of the first validated residual model (green). Time is referenced to wind onset.

Fig. 6 : Adaptive DA-KCF-MPC flight through a spatially varying wake generated by an obstacle representative of an urban building under a $2.5$ m/s free-stream condition. Top: representative snapshots at $t=\{0.5,4,12\}$ s as the vehicle follows the $\pm 0.5$ m, $16$ s lateral trajectory along the $y$ -axis through different regions of the wake. Bottom: lateral tracking error for representative PID and Adaptive DA-KCF-MPC trials. Aggregate tracking performance is evaluated over 4 repeated trials per controller.

Horizon $h_{p}$	Sim. KCF	Cal. KCF	Adap. DA-KCF
$1$	2.48	2.83	2.83
$5$	10.58	12.31	12.43
$10$	22.59	24.28	24.82
$25$	120.58	88.83	82.09

TABLE II: Multi-step position prediction RMSE [mm] on held-out disturbed hardware sequences using identical measured initial states and recorded reference commands.

Horizon $h_{p}$	Sim. KCF	Cal. KCF	Adap. DA-KCF
$1$	9.42	6.89	4.97
$5$	46.18	27.04	21.46
$10$	102.57	40.08	45.64
$25$	486.23	186.96	147.79

TABLE III: Multi-step velocity prediction RMSE [mm/s] on held-out disturbed hardware sequences using identical measured initial states and recorded reference commands.

Adaptive MPC

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Jun 10, 2025J/K move · Enter open · S save

Differentiable Physics-Informed Adaptive Koopman Control for Stable Flight under Unknown Disturbances

Ao Jin, Qiujin Liang, Tao Zhang, Panfeng Huang+1

Research Center for Intelligent Robotics, School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China · Department of Automation, Tsinghua University, Beijing 100080, China

Robot Trajectory Tracking Robust Control Feedback Control Quadrotor Control Disturbance Rejection Adaptive Control

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Uncertainties and disturbances in robotic systems, such as aerodynamic forces, are fundamentally outcomes of physical interactions with the environment, manifesting as learnable spatiotemporal sequences rather than random noise. However, achieving high-precision control for robotic systems operating in unstructured environments is often hindered by complex unmodeled dynamics and external disturbances. While learning-based methods offer powerful approximation capabilities, they typically suffer from heavy reliance on offline training and lack theoretical guarantees. Conversely, traditional robust control strategies are predominantly reactive, limited to instantaneous estimation without the foresight to anticipate future disturbance trends. To bridge this gap, this paper proposes a differentiable data-enabled Koopman control framework termed DEKC. Unlike black-box approaches, DEKC adopts a hybrid modeling strategy that retains the nominal physics model while employing a deep neural network to parameterize the lifting function of Koopman operator for unknown residual dynamics. Crucially, the framework formulates disturbances as a dynamical system, learning their temporal evolution in a global linear space. This enables the prediction of future disturbance trajectories, which are explicitly integrated into controller for preemptive compensation. Furthermore, an online backward gradient update mechanism is introduced to ensure real-time adaptation to time-varying uncertainties. Numerical simulations on a tethered space robot demonstrate the efficacy of the proposed DEKC in mitigating highly coupled uncertainties. Complementing these results, real-world experiments on a quadrotor substantiate its superiority in tracking agile trajectories under uncertainties induced by aerodynamics and suspended payload.

Abstract

Adaptive MPC

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