Artificial Neural Network Simulation of a Cascaded PD Motor-Mixer for Quadrotor Trajectory Tracking

In this simulation study, a cascaded Proportional-Derivative (PD) controller and a motor mixer are used to generate training patterns for a forward-feedback Artificial Neural Network (ANN). The ANN is a multilayer perceptron with two hidden layers of 128 units, trained using the Adam optimizer (learning rate 1x10^-3) with batch size 2048 and early stopping. The dataset comprises 200,000 samples (160,000 training; 40,000 test) generated in MATLAB/Simulink using a fixed-step RK4 integrator (0.01 s step). Unlike previous ANN–PD comparative studies, the proposed ANN directly approximates actuator-level PD commands while providing explicit evaluation of both open-loop regression and closed-loop performance. The ANN achieves near-perfect open-loop fidelity (R^2~0.999) but exhibits different closed-loop behavior: the PD controller outperforms the ANN in hover stabilization (altitude RMSE 0.18 m vs 0.26 m), while the ANN shows superior performance in nonlinear trajectory tracking, reducing lateral RMSE along the x-axis from 0.47 m to 0.21 m (~55% improvement) and along the y-axis from 0.52 m to 0.19 m (~63% improvement). These results demonstrate that the ANN provides an adaptive nonlinear control approximation suitable for trajectory tracking, while the PD controller maintains robustness for stabilization tasks.