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

Abstract

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.

Hovering Flight of a Robotic Hummingbird: Dynamic Observer and Flight Tests

“…The above equation includes the flapping drag noise d and the pitch flapping torque noise t p that enter the system at the input. Time-histories of the lift L, the drag d and the pitch torque t p have been studied in experiments reported in [11]. The signals are periodic but very complex, involving a lot of harmonic components and peak values at least one order of magnitude larger than their cycle-averaged values.…”

“…f g is particularly important, because its output qg is directly used in the construction of the control torque τ; it has a direct impact on the stability margins. Extensive numerical studies [11] have shown that f g = 8 Hz offers a good compromise between stability and noise rejection. The frequencies f s (accelerometer output) and the complementary filter corner frequency f c are less critical; they have been selected f s = 2 Hz and f c = 0.1 Hz.…”

“…A new control board has been developed including a ARM processor with a clockspeed of 168 MHz and two IMU sensors, one with six axes and one with nine axes, including a magnetometer. The board also includes a Bluetooth link, for a total weight of 1.4 gr; it is briefly described in [11]. The IMUs are particularly critical components in view of the noisy environment due to the flapping of the wings; the flapping noise is analysed in [11].…”

“…The board also includes a Bluetooth link, for a total weight of 1.4 gr; it is briefly described in [11]. The IMUs are particularly critical components in view of the noisy environment due to the flapping of the wings; the flapping noise is analysed in [11].…”

“…In hovering, a = 0 and the specific acceleration s = (s x , s y , s z ) T indicates the position of the gravity vector in the robot frame, from which the robot attitude (roll-pitch) can (in principle) be calculated. However, the acceleration and angular velocity data are subject to intense flapping noise at the flapping frequency and higher harmonics (the harmonic content of the lift and drag forces and the aerodynamic torque is documented in [11], together with a brief description of the control board).…”