Dual Quaternion-Based Neural Network Control for AAVs: Dynamic Modeling and Trajectory Tracking

The use of dual quaternions in the dynamic modeling of Unmanned Aerial Vehicles (UAVs) provides an elegant and singularity-free alternative to Euler angle-based representations, thereby eliminating the gimbal lock problem and enabling compact formulations of rigid body motion. Despite their advantages, dual quaternions have been underutilized in the explicit dynamic modeling and control design of multirotor UAVs, particularly in the presence of external disturbances and system uncertainties. To bridge this gap, this paper introduces a novel dual quaternion-based dynamic model that clearly decouples Coriolis, gravitational, control input, and disturbance components. Additionally, a set of mathematical identities analogous to classical matrix-based robotic systems is derived in the dual quaternion framework, which facilitates the Lyapunov-based stability analysis and could enable the future development of new control laws based on dual quaternions. Furthermore, a radial basis function neural network (RBFNN) control strategy is developed to estimate and reject lumped uncertainties in real time. The proposed method is rigorously analyzed using Lyapunov theory, and the boundedness of all closed-loop signals is formally established. Simulation results are presented for three trajectory tracking scenarios and benchmarked against two baseline controllers: a conventional proportional-derivative (PD) controller and a robust controller based on a second-order filter. Quantitatively, the proposed control scheme achieves a reduction of up to 47.5% in the mean squared tracking error under external disturbances, demonstrating its superior performance in uncertain environments. The key contributions of this work include: (i) the development of a structurally rich dual quaternion-based dynamic model for multirotor UAVs; (ii) the derivation of dual quaternion-based dynamic identities inspired by robotic matrix models, which simplify stability proofs and pave the way for future controller designs; (iii) the design of an online RBFNN-based control strategy to adaptively estimate and mitigate dynamic uncertainties; and (iv) the derivation of a formal proof ensuring the uniform ultimate boundedness of both tracking and estimation errors. These contributions represent a significant advancement in the robust and efficient control of UAVs operating in nonlinear and disturbed conditions.