Geometric Tracking Control of A Quadrotor with Tilted Propellers

This paper considers the control of the quadrotors with the unaligned thrust. Unlike the conventional quadrotor, the translational dynamics of these vehicles are sophisticatedly correlated with the rotational dynamics. This arises because the bearing of the total thrust in the body frame varies, in contrast to the unidirectional total thrust of regular quadrotors. This complexity poses a significant challenge to the control design for the quadrotor with the unaligned propellers. To address the challenge, we propose a geometric tracking control method that compensates for the thrust direction variation by incorporating additional vehicle inclination. The nonlinear tracking controller is characterized by defining the tracking error on the special Euclidean group SE(3). Through Lyapunov analysis, we proved almost globally exponential stability of zero equilibrium of the error dynamics. Simulation results illustrate the success of the proposed tracking control in achieving spiral trajectory tracking and recovering from the initial upside-down orientation for quadrotors with distinct propeller alignment configurations.