A physics-guided NARX-inspired network for accurate roll and pitch prediction of quadrotor UAVs

Purpose To develop a lightweight and physically interpretable approach for accurate one-step quadrotor attitude prediction. The study aims to reduce the learning burden of purely data-driven models by incorporating first-order rotational kinematics into a NARX-inspired neural architecture while retaining the ability to learn nonlinear dynamics and modeling errors. Design/methodology/approach A Physics-Guided NARX-inspired (PG-NARX) architecture is proposed, combining learnable autoregressive state propagation, a trainable physics-guided kinematic branch initialized using first-order rotational kinematics, and a neural residual branch. The approach is evaluated using flight-wise partitioned PX4-Gazebo Software-in-the-Loop data. PG-NARX is compared with MLP, NARX-inspired, Persistence, and Kinematic baselines using an unseen test trajectory, computational measurements, and angular-velocity noise experiments. Findings PG-NARX achieves roll and pitch RMSE values of 0.0206 rad and 0.0098 rad, with corresponding R2 values of 0.9558 and 0.9880. Compared with the Kinematic baseline, it reduces clean-test roll and pitch RMSE by approximately 10.8% and 17.6%, respectively. The model contains 18,602 trainable parameters and achieves a measured inference latency of 0.2667 ms. Additional experiments indicate relatively consistent performance under zero-mean Gaussian angular-velocity noise. Research limitations/implications The evaluation is limited to simulated PX4-Gazebo Software-in-the-Loop flight data and one-step attitude prediction, with roll and pitch as the primary targets. The results therefore do not establish performance under real-flight conditions, longer-horizon prediction, or more complex aerodynamic effects. Future research should validate the approach on real UAV hardware, investigate multi-step prediction and additional attitude states, and evaluate robustness across different flight conditions, disturbances, and sensor characteristics. Originality/value The study introduces a lightweight PG-NARX architecture that explicitly integrates first-order rotational kinematics into a NARX-inspired predictor through a trainable physics-guided branch and neural residual learning. Unlike purely data-driven NARX approaches, the proposed formulation assigns predictable short-term rotational behavior to a physics-guided component while allowing the neural network to learn remaining discrepancies. The resulting architecture provides a practical balance among prediction accuracy, computational efficiency, and physical interpretability for one-step quadrotor attitude prediction.