Modeling and Analysis of Chaos and Bifurcations for the Attitude System of a Quadrotor Unmanned Aerial Vehicle

Abstract

A model of the attitude system for a quadrotor unmanned aerial vehicle (QUAV), assumed to be a rigid body, is developed. For specific parameter configurations, a chaotic region with a saddle and two stable node-focus equilibrium points is identified. The chaotic model provides an important reference for dynamic analysis and a challengeable task of controller design once the flight enters the chaotic region of parameters. The pitchfork bifurcation of the equilibrium points is provided. Rich dynamics of the system are revealed by two bifurcation regions, which demonstrates the diversity of the flight behaviors as the parameters vary. One bifurcation analysis is with respect to the speed of the front propeller and the speed difference of the front and left propellers, and another one is with respect to the speed of the front propeller and moment of inertia. The dynamic characteristics of the QUAV are further verified by the Casimir power bifurcations. The trajectories of three settings with different structural parameters are analyzed in detail. The stability of the QUAV is found to be enhanced for certain optimized values of the structural parameters. Finally, using the Casimir power and Lagrange multiplier method, a supremum bound of the chaotic attractor is presented.