Nonlinear backstepping control design for miniature helicopters using the rotation matrix

This paper presents a backstepping control design for small scale helicopters. The objective is for the helicopter to autonomously track predefined position and yaw trajectories. The position reference trajectories are arbitrary, possibly aggressive, with some constraints in their higher order time derivatives. The main idea of the algorithm is to control the direction and magnitude of the thrust vector appropriately in order to stabilize the position dynamics. In contrast with most control schemes that use Euler angles or quaternions for the control of the attitude dynamics, this design use the elements of the rotation matrix. The intermediate pseudo controls related with the directional dynamics are enhanced with terms that guarantee that the helicopter will not overturn while tracking the position reference signals.