Feedback Linearization of an Underactuated Miniature Blimp With Zero Dynamics Mitigation Using High Order Control Barrier Functions

In this letter we derive a tracking controller based on feedback linearization for a miniature blimp controlled by co-located fans on an undermounted gondola. We prove that feedback linearization of the underactuated blimp induces nontrivial zero dynamics corresponding to lightly damped oscillations in pitch and roll. To mitigate these oscillations we use high-order control barrier functions (HOCBFs) to limit the maximum allowable pitch and roll at the expense of tracking error. Experimental results are presented for three illustrative trajectories which demonstrate that the proposed controller outperforms a well-tuned LQR controller and a baseline nonlinear MPC controller, while the attitude oscillations are theoretically and empirically shown to be bounded by the HOCBFs.