Trajectory study of power inspection quadcopter based on Udwadia–Kalaba theory

In this study, the dynamic model of the quadrotor is constructed by introducing the Udwadia–Kalaba theory, and the Moore–Penrose inverse is used to simplify the dynamic equations during the modeling process, avoiding the complexity of the traditional Lagrangian calculation methods. By transforming the three jobs of quadrotor pitch, roll, and yaw into independent motions in X– Y, X– Z, and Y– Z planes, respectively, a simpler way of 3D trajectory presentation is realized. The Udwadia–Kalaba equation is simulated by MATLAB software, and the simulation results show that the dynamic model based on the Udwadia–Kalaba theory has high accuracy and stability, and its trajectory error is within the allowable error tolerance of ±0.01, which is suitable for the dynamic modeling needs in many complex scenarios. In addition, the Udwadia–Kalaba theory is compared with the traditional PID control method and the emerging deep reinforcement learning (DRL) method. The DRL method also shows relatively excellent trajectory error control capability, with the overall error fluctuation range being controlled within ±0.05, while the PID exhibits error fluctuation of about ±0.1 and insufficient robustness. The results provide a new reference in the control modeling of quadrotor UAVs on the one hand and extend the application of Udwadia–Kalaba theory to the study of vehicle trajectories on the other.