On the bifurcations in a quadrotor unmanned aerial vehicle dynamical system using normal form theory

A Quadrotor Unmanned Aerial Vehicle (QUAV) is type of a drone that consist of four rotors whose dynamical aspect is of high interest because of the reason that negligible glitch may cause a great loss. Moreover, the main impact of Hopf and zero-Hopf (ZH) bifurcations is the existence of periodic solutions and potential chaotic region respectively, that can create difficulties in the flight of any QUAV. Therefore, in the current paper, we investigated local dynamics and bifurcation analysis of a QUAV chaotic model. This study begins with dynamical analysis around equilibria using Jacobian matrices, eigenvalues and eigenvectors. We then extended our work to find several codimension-1 bifurcations using normal form theory and center manifold theorem. Moreover, Analytical formulas and qualitative dynamics are used as tools to provide the detailed information about the Hopf and zero-Hopf bifurcations with the case that Hopf bifurcation is supercritical. These bifurcations are important for understanding the connection between stability and oscillatory behavior of the considered system, which has serious effects on its performance and control. The limitations of averaging technique while facing (i) negative real part in eigenvalues and (ii) order of the transformed system motivated us to use normal form theory instead of averaging method. Finally, the existence of Bogdanov-Takens (BT) bifurcation with aid of analytical formulas is integral part of this work, whereas the connection between (Saddle-node, Hopf) bifurcation, Limit cycles and Branch cycles is constructed and discussed with the aid of MATCONT around BT bifurcation point.