Robust control of non-linear systems is a challenging task, notably in the presence of external disturbances and uncertain parameters. The main focus of this paper is to solve the trajectory tracking problem of an unconventional quadrotor with rotating arms (also known as a foldable drone), while overcoming some of the challenges associated with this type of vehicle. Therefore, in a first step, the model of this vehicle is presented, taking into account the change of the inertia, the centre of gravity, and the control matrix. The theoretical foundations of backstepping control, based on the finite time Lyapunov stability theory and enhanced by a Super-Twisting algorithm, are then discussed. Numerical simulations are performed to demonstrate the efficiency of the suggested control approach. Finally, a qualitative and quantitative comparative study of the proposed controller with the conventional backstepping controller is performed. Overall, the obtained results show that the proposed control strategy outperforms in terms of accuracy and resilience.