Robotic Hummingbird Axial Dynamics and Control near Hovering: A Simulation Model

After a short overview of the COLIBRI project, this paper considers the cycle-averaged flight dynamics of a flapping-wing robot near hovering, taking advantage of the weak coupling between the roll and pitch axes. The system is naturally unstable; it needs to be stabilized actively, which requires an attitude reconstruction. Due to the flapping of the wings, the system is subject to a strong periodic noise at the flapping frequency and its higher harmonics; the resulting axial forces and pitch moments are characterized from experimental data. The flapping noise propagates to the six-axis Inertial Measurement Unit (IMU) consisting of three accelerometers and three gyros. The paper is devoted to attitude reconstruction in the presence of flapping noise representative of flight conditions. Two methods are considered: (i) the complementary filter based on the hovering assumption and (ii) a full-state dynamic observer (Kalman filter). Unlike the complementary filter, the full-state dynamic observer allows the reconstruction of the axial velocity, allowing us to control the hovering without any additional sensor. A numerical simulation is conducted to assess the merit of the two methods using experimental noise data obtained with the COLIBRI robot. The paper discusses the trade-off between noise rejection and stability.