An Experimental Study on Response and Control of a Flapping-Wing Aerial Robot Under Wind Gusts

Abstract

Bioinspired flapping-wing micro-air-vehicles (FWMAVs) have the potential to be useful aerial tools for gathering information in various environments. With recent advancements in manufacturing technologies and better understanding of aerodynamic mechanisms behind of the flapping flight, outdoor flights have become a reality. However, to fully realize the potential of FWMAVs, further improvements are necessary, particularly in terms of stability and robustness under gusty conditions. In this study, the response and control of a tailless two-winged FWMAV under the wind gusts are investigated. Physical experiments are conducted with a one-degree-of-freedom gimbal to focus on effects of wind gusts on the rotational motion of the FWMAV. Proportional-derivative and sliding-mode controls are adopted for the attitude control. Results present that the body angles changed in time and reached approximately 50${}^\circ$ at the maximum due to the wing gusts. The sliding-mode controller can more effectively control the rotational angle in the presence of disturbances and both the wing speed and changes in wind speed have an impact on the effectiveness of attitude control. These results contribute to the development of of tailless two-winged, single-motor driven FWMAVs in terms of the design of attitude controller and testing apparatus.

Appendices

Appendix 1: Design of Wing Planform

Effects of wing planform on the lift and the lift-to-power ratio of the FWMAV were investigated. Figure 12 showed three tested wing planforms that had wing areas of 1,757 mm$^2$ and the length of leading edge of the wing, R of 75 mm, 2,000 mm$^2$ and R = 80 mm, and 2,258 mm$^2$ and R = 85 mm, respectively. The range of wing size and area was chosen based on that of FWMAVs having similar weight to that of the robot used in this study. Figure 13 presented the experimental setup of simultaneous measurement of lift and lift-to-power ratio. The lift force generated by the FWMAV was measured by a 6-axis force transducer (Nano 17, ATI Industrial Automation Inc.) and the input power was measured by a two-channel oscilloscope (TBS1000C, Tekronix Inc.) and a resistor (2 Ohm, tolerance = ±1%). An external power supply (PW8-3AQP, Texio Corp.) was used to drive the wings. The flapping frequency varied from 13 Hz to 22 Hz. Figure 14 showed the experimental results and the wing with the highest power efficiency (R = 80 mm and wing area of 2,000 mm$^2$) at the robot’s weight. Thus, the wing with R of 80 mm and wing area of 2,000 mm$^2$ were adopted for all the experiments of this study.

Fig. 12

Schematics of tested wing planforms

Fig. 13

Experimental apparatus of simultaneous lift and power measurements

Fig. 14

Results of lift-to-power and lift for three tested wings

Appendix 2: Relationship Between Control Command and Control Torque

The relationship between the control commands and the control torques generated by the FWMAV was explored. Figures 15 and 16 show the experimental results. For the pitch control, changing the control input $\theta _{S}$ from -60${}^\circ$ to +60${}^\circ$, the measured $M_{Y,B}$ varied from $-$0.83 N$\cdot$mm to 1.18 N$\cdot$mm, while for the roll control, changing the control input $\phi _{S}$ from -60${}^\circ$ to +60${}^\circ$, the measured $M_{X,B}$ varied from $-$1.07 N$\cdot$mm to 0.69 N$\cdot$mm. It was also seen that torque was generated even when the command to the servomotor was zero in both pitch and roll directions. This was because the vehicle was made by hand and not perfectly symmetrical. From the experimental data (Figs. 15 and 16), a linear approximation of the relationship (Eqs. 3 and 4) between torque and servomotor input was obtained for the pitch and roll motion.

Fig. 15

Experimental results of the relationship between pitch torque ($\tau _{\theta }$) and pitch command ($\theta _S$)

Fig. 16

Experimental results of the relationship between roll torque ($\tau _{\phi }$) and roll command ($\phi _S$)

Appendix 3: Effects of Filters on Body Angle Estimation of FWMAV

The impact of filtering on the accuracy of the body angle estimation in the FWMAV was discussed. Measurements were performed with the FWMAV mounted on a gimbal with one degree of freedom (1-DOF) that rotated only either in the pitch direction or the roll direction. The attitudes estimated by the inertial measurement unit (MPU9250) attached to the FWMAV were compared with the attitudes tracked by the digital camera (RX10VII, Sony). Here, the Kalman filter, Madgwick filter, and Complementary filter were considered to estimate body rotational angles from the internal sensors together with the moving average filter. Figure 17 illustrates the schematics and time-histories of pitch ($\theta$) and roll ($\phi$) angles of FWMAV. For the pitch angle control, the RMSE of three filters with the actual angles from the camera were 15.71${}^\circ$ (Kalman filter), 3.30${}^\circ$ (Madgwick filter), and 19.81${}^\circ$ (complementary filter), while for the roll angle control, the RMSE of three filters with the actual angles from the camera were 8.21${}^\circ$ (Kalman filter), 2.66${}^\circ$ (Madgwick filter), and 12.43${}^\circ$ (complementary filter). Therefore, a filter combining the Madgwick filter with the moving average filter was employed to estimate body rotational angles for the attitude control in this study.

Fig. 17

Schematics of experimental setup of measurement of body angle of 1-DOF gimbal and comparison of three filters of estimated values: a pitch angle ($\theta$) and b roll angle ($\phi$)