Validation of Quad Tail-sitter VTOL UAV Model in Fixed Wing Mode

study


I. INTRODUCTION
In recent years, the use of UAVs in the industry has been increasing rapidly, primarily for aerial mapping missions. Aerial mapping, such as precision farming, asset surveys, and monitoring, is the entrance to the industrial revolution 4.0 [1][2][3][4][5][6][7]. Fixed-wing UAVs are widely used in most industrial use cases. Although it has a coverage advantage, operating a fixed-wing UAV in a highly dense land-covered area, such as a forest and plantation, is challenging owing to the open space needed for take-off and landing. Operating a multi-copter is not optimal as its coverage is minimal, although it does not need open space for take-off and landing. The solution is a hybrid vertical take-off and landing (VTOL) UAV [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. This type of UAV can take off, land vertically like a multicopter, and transition to the fixed-wing mode for flight efficiency at a safe altitude [27][28][29][30][31][32]. The hybrid VTOL or usually just called VTOL UAV flight profile is illustrates in Fig. 1.  Fig. 2, was specifically designed for aerial mapping and survey missions. It is a quad tail-sitter with flying wing configuration [33]. The UX-7V VTOL UAV control system is being developed using a model-based design approach [34] [35]. Building a mathematical flight model is mandatory to facilitate aircraft attitude and motion studies [36][37][38][39][40]. Each flight model has its characteristics called model parameters [41]. A manned aircraft usually uses a wind tunnel test to obtain the model parameters [42]. This method has the best accuracy result, but limited wind tunnel test facilities in Indonesia and the associated high costs are the challenges to implement on small UAVs. The UX-7V UAV currently uses elevon to control the movement in fixed-wing mode [43]. The quad tail-sitter configuration [44] adopted in this UAV enables to use of differential thrust control [45]. So, in this study, the flight model will be used to develop a differential thrust control method in the subsequent research. This research focuses on a fixed-wing mode flight model using analytical modeling based on this requirement. Since the UX-7V is a successor of the UX-6 UAV [46], we used the same analytical modeling procedure as the previous study, but the tools used were different because the UX-6 UAV analytical model result is not good enough. Many tools can be used to build analytical models, such as OpenVSP [47], Datcom+Pro [48], Flow5 [49], and Tornado VLM [50]. OpenVSP software was used to develop and process the analytical model in this study. OpenVSP is widely used for preliminary design reviews on aircraft development. OpenVSP calculates aircraft aerodynamic derivatives using the vortex lattice and panel methods [50]. The aerodynamic derivatives are then used to derive model parameters. In the last step, the analytical model obtained from OpenVSP is validated with an empirical model built using system identification or reverse modeling [51][52][53][54][55][56]. This research has two contributions. The first is in the form of how the analytical model is generated and the tools used, in particular for the small VTOL quad tail-sitter UAV. The second is how to utilize off-the-shelf components for UAV empirical modeling.

II. MATERIALS AND METHODS
This research follows what we performed in a previous study [43]. There are three differences, the first is the aircraft type, change from UX-6 fixed-wing UAV to UX-7V VTOL UAV. The second is the type of electronic device used. We use a commercial flight controller with custom code to control the aircraft and flight data logging. The last, the software used, which previously used Datacom+ Pro, was replaced with OpenVSP. The general research flow shown in Fig. 3.

A. Quad Tail-sitter
Tail-sitter or tilt body is one of hybrid VTOL type [56], that had two orientations: -Vertical orientation for take-off and landing is similar to a copter. -Horizontal orientation for a forward flight is similar to a fixed-wing. Tail-sitters generally have two (dual) or four (quad) motors configuration. All tail-sitter motors keep running, both vertically and horizontally. In this research, the UX-7V UAV has a quad tail-sitter configuration. Quad tail-sitters typically use a flying-wing configuration. The airframe consists of a blended fuselage and wings. In the fixed-wing mode, elevons were used to control the flight. Elevons are two parts mixed on one control surface: elevators and ailerons. Elevators for up-down movements and ailerons for right-left turn movements. Fig. 4 shows the design of the quad tail-sitter UAV.

B. The Hardware
The three modules used in this research are a UX-7V aircraft, a remote controller (RC), and telemetry. UAV operator controls the UX-7V flight through an RC transmitter, and the ground control operator monitors the aircraft on a laptop via telemetry. Fig. 5 shows the connections and electronic devices. The UX-7V UAV uses PX4 based flight controller with a custom code. There are two commands to control UX-7V. First, control by a remote controller (RC), and second, by ground control/telemetry. Three modes are available: manual/stabilized, position-assisted, and autonomous. PX4 has the capability to log data, which is very useful because an operator input for actuators and output data (aircraft attitude) can be recorded at a specific rate. The PX4 data log is set to run at 5 Hz, whereas the maximum aircraft movement is at 2 Hz [57]. Fig. 6 shows aircraft electronic device block diagram, and Table I lists the aircraft hardware and specification details.

C. Analytical Modeling
In fixed-wing mode flight, many forces act, i.e., velocities, moments, and orientations. All could be summarized and visualized in Fig. 7. In flight, the aircraft is not always horizontally straight when flying ahead (on the X-axis, see Fig. 7) but has an angle of attack commonly written as α (alpha). The aircraft's angle of attack is the deflection angle of the aircraft on the x-axis caused by the wing geometry of the aircraft. Similar to the angle of attack, there is also a sideslip angle (Fig. 6), typically written as (beta). The difference is that the sideslip angle is the deflection on the y-axis owing to the air/wind from the side that concerns the aircraft's vertical stabilizer. Equations (1) and (2) are for finding α and β.  The Euler angle was used for the aircraft orientation as shown in Fig. 8, which has the following reference: a. The − leads downward (in the same direction as the gravity vector). The angle rotation on this axis is called the yaw ( ).
b. The − leads forward. The angle rotation on this axis is called the roll ( ). where: In addition to the angular velocity, translation velocities are required for the −, −, and − . The translational velocities of each axis are denoted as variables , , and . The variables , , and are determined by data changes in longitude, latitude, and altitude. It is then combined with the orientation of the Euler angle, thus producing ′, ′, and ′ derived in Equation (4).
where, S , S , S = sin , sin , sin C , C , C = cos , cos , The flight dynamics that work on a fixed wing can be divided into longitudinal and lateral modes [58][59][60][61][62]. The longitudinal modes include translational motion on the -and -axes and rotational motion around the -axis. The rotary motion around the y-axis changed the pitch angle. The motion in the longitudinal mode plays a role in the upward and downward movement of the aircraft. In the dynamics of aircraft flying, the longitudinal mode is influenced by the thrust and elevator. The longitudinal mode is determined using Equations (5), (6), (7), and (8). -Forces -Pitch orientation The lateral mode includes translational motion on the − and rotational motion along the − and − . The lateral mode is affected by the aileron. The lateral or directional mode is used for aircraft's turning movement. The lateral mode is determined using Equations (9), (10), (11), and (12). -Forces -Roll orientation Both longitudinal and lateral modes are necessary for all equations that work to elaborate and add flight assumptions (linear model and ignore flight disturbances such as wind, thermal, and weather). Then, we obtain the general equations of the longitudinal mode flight model in the form of a statespace model structure [63], [64] in Equation (13).
Furthermore, the lateral mode is the same as the longitudinal mode. Equation (14) represents the general equation for the lateral mode flight model.
The general linear equations of the longitudinal and lateral modes are obtained, and each variable is filled with values corresponding to the characteristics of the aircraft modeled using the OpenVSP software calculation.

D. Flight Data Acquisition
Flight data acquisition records an input signal given to the actuator, and the output data includes the aircraft's attitude, position, and speed. The input must be prepared. Several input scenarios are commonly used for identification systems, such as 3-2-1-1 and doublet input [65]. We use doublet input, a variety of inputs where a high position of the actuator was given during time and then changed to a low value of actuator during time . The signal is sent to the aircraft actuator through an RC transmitter. Doublet inputs are used by researchers and manufacturers to identify aircraft [66][67][68][69][70][71][72][73][74][75][76]. Fig. 9 shows the shape of the input doublet signal. Fig. 9. Doublet input Because this research divides the modeling into longitudinal and lateral modes, each mode is given a different doublet input, elevator in the longitudinal mode, and aileron in the lateral mode. The aircraft was conditioned in level flight condition during flight data acquisition before being given doublet input. Fig. 10 shows the flight data acquisition procedure.
The data log feature in the PX4 flight controller was customizable. The data groups selected for storage are as follows: -actuator_controls_1 -airspeed -vehicle_attitude -vehicle_gps_position The recorded flight data are then processed and converted into a variable used for system identification. Because the recorded vehicle attitude is in aircraft copter mode, while system identification uses fixed-wing mode attitude, quaternion rotation is required. It changes y-axis orientation by 90 degrees. Fig. 11 shows quaternion rotation.
where: ( 2  ) Thus, the attitude vehicle data, which rotates the aircraft by 90 degrees on the -axis is : If the copter mode attitude is , we can obtain the fixed-wing mode attitude by multiplying by Equation (16). = where: After the attitude data are appropriate, the next step is to convert the quaternion angle into an Euler angle [42] using Equation (17).

E. Empirical Modeling
An empirical model was built to validate the analytical model. The empirical model is based on flight data obtained through flight data acquisition, which is processed using a system identification technique [78]. Conceptually, system identification is a dynamic system shown in Fig. 13, modeling from the data generated in the experiment. This study uses a state-space model structure to build the empirical model, which has the same structure as the analytical model. The typical state-space model structure is different from the analytical model known as black-box system identification [79]. Fig. 14 shows MATLAB software used for system identification, precisely one of the sub-tools, the system identification toolbox.

A. Flight Data Acquisition
The flight data acquisition shown in Fig. 15 was performed at 7 AM to obtain clear and relatively no-wind conditions [80] [81]. We performed several flights; one determined the primary data and the other for backup. Fig. 16 shows the UX-7V main data flight path.

B. Empirical Model
The aircraft trim conditions [82] can be determined based on UX-7V UAV flight data. The trim condition is an aircraft condition when ≠ 0, = 0, = 0, and ≠ 0. The UX-7V UAV trim conditions are shown in Table II. After the flight data were processed using the system identification toolbox in MATLAB, an empirical model that represents UX-7V VTOL UAV was built, Equation (18)

C. Analytical Model
The analytical model used OpenVSP to obtain static and dynamic aerodynamic coefficients. This research use a panel method for the calculation [47]. The panel method models many elementary quadrilateral panels lying on an actual aircraft surface [83]. The OpenVSP calculation requires aircraft geometry data and aircraft flight conditions. The flight condition was equated with the UX-7V UAV level flight condition, obtained from flight data acquisition. The UX-7V UAV level flight condition was predicted at 7 degrees AoA, 17m/s velocity, and a 50-meter altitude. The UX-7V UAV geometry data and flight conditions input into OpenVSP generated the aircraft's calculated aerodynamic coefficients. Fig. 17 depicts the UX-7V UAV 3D. The static and dynamic aerodynamic coefficients generated by OpenVSP were used to calculate the stability derivative. The resulting stability derivative is organized into Equations (13) and (14). The analytical model of the UX-7V UAV is shown in Equation (20)

A. Empirical Model
The empirical model results were validated using simulation. The empirical model was compared with actual flight data in a simulation. The empirical model input was the aircraft input data. Then, the model's output was compared with the aircraft output data. The empirical model validation results showed that the model's accuracy was quite good: 90.97 percent on average for the longitudinal mode and 91.02 percent for the lateral mode. Fig. 18 and Fig. 19 shows the empirical model validation results for the longitudinal and lateral mode.
Generally, these empirical model results are better than previous research [46]. Previous research results showed an average accuracy of 73.95% for the longitudinal mode and 75.83% for the lateral mode. The UX-7V VTOL UAV already uses a flight controller, so the operator can use a position-assisted flight mode. This differs from previous research, which the operator manually controlled the aircraft movement. The UX-7V VTOL UAV operator can easily control the aircraft in a position-assisted flight mode [84] [85]. The altitude and position are locked in this mode by the computed trajectory of the flight controller [86][87] [88]. Therefore, the input to the empirical model of this research is not the remote-control input from the operator but the command given to the actuator from the flight controller. The accuracy of the empirical model increased drastically through this approach by approximately 20 percent.

B. Analytical Model Validation
The analytical models were built, validated using the empirical model. The process was performed by given the doublet input shown in Fig. 20 to both models. The input given is in the form of a control surface deflection of 0.6 (34.3775 degree) radians for 1 second and -0.6 radians (-34.3775 degree) for 1 second. In the longitudinal mode validation, the input doublet on the elevator is connected to the empirical and analytical models. Since the variation input is only elevator control surface, the input for throttle assumes as zero. Both models have a state-space model structure. The four output parameters of the model, namely forward velocity, angleof-attack, angular velocity, and angle, are then displayed in graphical form and stored for further analysis. For analytical model validation needs, MATLAB/Simulink software is used with a block diagram as shown in Fig. 21. For the other three parameters (alpha ( ), , and theta ( )), even though they have the same direction, the values are quite different. The main factor is the UX-7V longitudinal mode, in addition to using elevons for up and down motion, which also uses differential thrust. This is because the UX-7V longitudinal mode is less stable at the beginning of development. Therefore, it needs to be assisted by other actuators. The use of differential thrust is a tiny amount, a maximum of 10 percent of the total thrust of the brushless motor. Nevertheless, the effect is quite significant because it can be called active control [89]. This differential thrust factor was not modeled in analytical modeling; therefore, the three parameters (related to the angular velocity and angular position) in this longitudinal mode are not identical. Validation process of the lateral mode is similar with the longitudinal mode, but there is a little different in the doublet input that connected the empirical and analytical models, which is aileron control surface. Both models are also having a state-space model structure. The four output parameters of the model, namely sideslip angle, roll angular velocity, yaw angular velocity, and roll ( ) angle, are then also displayed in graphical form and stored for further analysis. An analytical model validation in lateral mode MATLAB/Simulink block diagram is shown in Fig. 23. where all four parameters (beta ( ), , , and roll ( )) are identical, showing only a slight delay or lower amplitude in the empirical model. It is normal and can be caused by natural factors, such as wind. Owing to the wind, the aircraft turn maneuver command will be affected, such that the aircraft's response will be a bit late or faster, depending on the wind direction and velocity. Flight data acquisition was designed to be performed in the morning when the weather was sunny and the wind was near zero. Unfortunately, the actual weather conditions of the flight level can differ from those of the ground level.
Based on the results obtained from this research, in general it is better than those produced by previous research [46]. In the empirical model. the improvement is very significant, then in the analytical model, especially in the lateral mode, it is also quite significant. In the longitudinal mode analytical model there are several things that might improve the accuracy and quality of the model, including by entering the propulsion and propeller models used. accuracy of the analytical model will be improved by considering the effect of using differential thrust control. Further studies also need to be carried out, although the modeling is more complex, which combines fixed wing [90][91] and copter control [92][93] [94], as well as aircraft transition phase [95]. The ultimate and main goal in UAV modeling and simulation is to create a safe and reliable system with a fast time [96]. The obtained model will use for simulation in the specific and even in dangerous condition [97][98] [99]. For example, in longitudinal mode will simulate altitude and speed control simulation, whereas in lateral mode will simulate heading control simulation. The simulation will be carried out in normal to dangerous environmental conditions such as strong winds [100].