This dataset contains recorded position, Euler angle XYZ, and the commanded voltages of the flights presented in the manuscript "Aerobatic maneuvers in insect-scale flapping-wing aerial robots via deep-learned robust tube model predictive control".

Data format

The data is saved in Comma-Separated Value (.csv) format. The first column of each .csv file represents the time (in seconds at 10 kHz) recorded during the flight for position and orientation, which are sampled at 10 kHz. The subsequent columns are organized in groups of six: the first three columns show the x, y, and z positions (in meters), and the next three columns contain the Euler angles in the XYZ convention (in radians). The column after the last Euler angles represents the time (in seconds at 1 kHz) recorded during the flight for commanded voltages, which are sampled at 1 kHz. The subsequent columns are organized in groups of four: each column shows the voltage (in Volts) computed by the controller for each of the flapping wing modules. The corresponding flight numbers are also included in the column names to demonstrate repeatability.

List of flight data

The following list shows the filenames and the corresponding flights (in terms of figure numbers) presented in the manuscript:

• "saccade.csv" - Fig. 2 (D-F) and Fig. S2
• "saccade_multi.csv" - Fig. 3 (A) (D) and Fig. S3 
• "saccade_multi_incorrect_mapping.csv" - Fig. 3 (B) (D) and Fig. S4
• "saccade_multi_disturbed.csv" - Fig. 3 (C) (D) and Fig. S5
• "x_shape.csv" - Fig. 4 (A-C) and Fig. S6
• "plus_sign.csv" - Fig. 4 (D-F) and Fig. S7
• "figure_8.csv" - Fig. 4 (G-H) (K) and Fig. S8
• "planar_circle.csv" - Fig. 4 (I-J) (L) and Fig. S9
• "flip_single.csv" - Fig. 5 (C-E) and Fig. S10
• "flip_multi.csv" - Fig. 5 (F) and Fig. 1 (D-E)
• "model-based_controller_saccade.csv" - Fig. S20
• "model-based_controller_saccade_multi.csv" - Fig. S21
• "model-based_controller_x_shape.csv" - Fig. S22
• "model-based_controller_plus_sign.csv" - Fig. S23
• "model-based_controller_figure_8.csv" - Fig. S24
• "model-based_controller_plannar_circle.csv" - Fig. S25

Data collection

The data was captured by a motion-capturing system (Vicon Vantage V5 and Vicon Tracker 3.9). The data was first retrieved from Vicon Tracker 3.9 and then transmitted in real-time to a target computer (Speedgoat) via asynchronous UDP. Position and orientation data was saved at 10 kHz on the target computer, with no post-processing applied; the commanded voltage data was saved at 1 kHz.

Post-processing used in the manuscript

While the data presented in this dataset is raw and without any post-processing, the plots shown in the manuscript have been post-processed. The following paragraphs explain the reasons and methods of post-processing used in the manuscript.

• The raw data received on the target computer does not update at exactly 400 Hz (Vicon system's refresh rate), as a result, a much higher sampling rate (10 kHz) was used to collect and save data. Lowpass filtering (e.g. Matlab filtfilt) is thus applied to smooth some of the signals presented in the manuscript.
• The Vicon system only provides position and Euler angle. Velocity and angular velocity shown in the manuscript were obtained through numerical differentiation of the post-lowpass-filtered data.
• The filtering of the orientation was done through the following steps: 1) convert the Euler angle into rotaton matrix; 2) applying lowpass filter to each of the element in the rotation matrix; and 3) convert the rotation matrix back to the Euler angle or take derivative numerically to obtain angular velocity. This process ensures continuous signal throughout the filtering, even for the somersault demonstrations.