Trajectory Tracking Control Based on Generalized Rodrigues Parameter for Underactuated VTOL UAVs

In this paper, we design two trajectory tracking control schemes based on generalized Rodrigues parameters (GRPs) for underactuated vertical take-off and landing (VTOL) unmanned aerial vehicle (UAV). In the attitude loop, we use rotation matrix to describe the attitude to ensure the global motion of the attitude, and use Rodrigues parameters (RPs) to describe the attitude error to make the attitude error have almost global convergence and avoid unwinding. At the same time, we design the GRP to extend the generalization ability of the attitude error description scheme and improve the control accuracy. Unlike the existing attitude constraint schemes, GRP only needs a constraint boundary to constrain the error angle of PR. The thrust error caused by underactuated characteristics is compensated in the attitude controller by position–attitude cascade decomposition. The controller based on backstepping is designed to exponentially stabilize the zero equilibrium of the error system. In order to simplify the controller structure and reduce the difficulty of engineering application, a control scheme with saturation property is proposed. Finally, numerical simulation is carried out to verify the effectiveness of the proposed algorithm.