A Summary of the Application of Mathematics in the Design of Quadrotor UAV

Abstract

With the rapid development of UAV technology, mathematical methods play a vital role in the design of quadrotor UAV. This paper systematically expounds the application of mathematical tools in mathematical modeling, control algorithm and optimization method of quadrotor UAV. Aiming at the nonlinear characteristics of UAV, such as the torque model has no driving force characteristics and strong coupling, Euler-Lagrange equation is used to establish a six-degree-of-freedom model of UAV, and coordinate transformation theory is used to accurately describe the motion of UAV. In the control algorithm, the classical PID control, adaptive control, modern model predictive control (MPC), sliding mode control and other technologies are integrated, among which nonlinear MPC(NMPC) combined with sequential quadratic programming (SQP) algorithm significantly improves the trajectory tracking accuracy. Intelligent control field, neural network and fuzzy control also increase the possibility of independent judgment for complex environment. By optimizing the route design and voyage duration, this paper effectively improves the efficiency and stability of flight. The research shows that the comprehensive application of mathematical methods lays a good mathematical foundation for the control accuracy and flight endurance of quadrotor UAV.