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

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.

Quadrotor trajectory tracking under unmodeled disturbances often relies on online residual adaptation, but short out-domain residuals can corrupt the learned disturbance model when constant-step updates treat every residual gradient uniformly. We propose Dual Gradient Consensus (DGC), an adaptive-learning method for mixed in-domain/out-domain disturbances that retains the random Fourier feature model, offline BPTT policy, and least-squares adaptation of a prior domain-adaptive residual policy (DAPL) while modifying the online update step size. DGC compares each residual gradient with long- and short-term gradient memories, classifies the current adaptation regime, and uses a confidence map to suppress unreliable updates while recovering adaptation after persistent domain shifts. We evaluate DGC in numerical quadrotor trajectory tracking under four residuals that mix an in-domain component with short out-domain events. Compared with $L_1$-augmented MPC, RFF-based MPC, constant-step DAPL, and a frozen-parameter baseline, DGC achieves the lowest mean position RMSE in all four cases.

We present an algorithm for efficient domain-adaptive policy learning via kernel representations. Learning domain-adaptive policies is challenging since it requires an environment representation that is both sufficiently expressive to model complex sim-to-real gaps during offline training, and computationally efficient enough to support rapid online adaptation during deployment. For instance, a quadrotor may encounter time-varying, non-stationary disturbances, such as sudden gusts of wind, payload shifts, or transitions between distinct flight regimes with and without ground effects. To address these challenges, we model unknown disturbances using a differentiable kernel approximation based on random Fourier features. During the offline training phase, we randomly sample kernel coefficients and bandwidth parameters to generate a rich diversity of disturbance profiles. We then optimize the control policy via differentiable simulation with analytical gradients, a process that takes only 50 seconds of training time on an RTX 4090 GPU. During hardware deployment, the policy adapts to non-stationary environments in real time by updating both the kernel coefficients and bandwidth through online least-squares estimation. We evaluate our method on quadrotor trajectory tracking tasks across high-fidelity numerical simulations and hardware experiments using Crazyflie, subjected to various disturbances, including complex aerodynamic effects, wind, ground effects, and payload fluctuations.