## 3 Experiment
### Experimental Setup  
Figure 4a shows the prototype of the proposed TM-UAV, Tilt-X. The body frame is printed with a 3D printer using ABS-A100 material with a filling density of 100%. Tilt  
Figure 3: Channels (CH) mapping on RC. X has a mass of 2048 g, and the maximum thrust of all four propellers exceeds 7200 g. Figure 4b illustrates the wiring diagram of Tilt-X. All four rotors and all four servo motors are connected to the same power module. Electronic speed controllers (ESCs) are used to control the speed and direction of the rotors, adjusting the current based on commands from the flight controller. BECs are used to convert battery voltage to a stable lower voltage, supplying power to the flight controller and servo motors. Propellers 1 and 2 are CCW propellers, and propellers 3 and 4 are CW propellers. Thus, rotors 1 and 2 are connected to ESCs 1 and 2 differently from the way rotors 3 and 4 are connected to ESCs 3 and 4. Telemetry is used to transmit real-time data, including the positions and status of Tilt-X to the Mission Planner, for monitoring and control purposes. In terms of the design of Tilt-X, to ensure that there is no airflow interference between adjacent propellers, the distance between the center of each propeller should be greater than \(0.1r_{max}\)[28]. The maximum propeller radius is calculated as in (14), where max(_i_) is 4 for Tilt-X as a quadcopter. \[r_{\max}=ds\bigg{(}\frac{180}{\max(i)}\bigg{)}. \tag{14}\]  
The experimental setups are shown in Figure 5. The base of a force/torque (F/T) sensor is fixed to a heavy table to ensure it does not move. A fixed part is attached to the top of the F/T sensor, on which the Tilt-X is placed. This setup allows the F/T sensor to obtain the vertical component of thrust force, \(F_{z}^{e}\), horizontal pulling force, \(F_{x}^{e}\), and yaw moment, \(M_{z}^{e}\), of Tilt-X in the ECF. The experiment of tilting all the propellers in the same direction to apply the horizontal pulling force to the environment is shown in Figure 5a, which is the translation experiment. The experiment of tilting two pairs of propellers symmetrically in opposite directions to maximize yaw moment is shown in Figure 5b, which is the rotation experiment. The horizontal pulling force and yaw moment can be simplified according to Equations (7) and (13) as:  
\[F_{x}^{e}=-F_{z}^{b}t\hat{b}_{i}^{b}\ \theta c\psi-F_{z}^{b}(c\psi s\theta c \varphi+s\psi s\varphi), \tag{15}\]  
\[M_{z}^{e}=\left(-\frac{\sqrt{2}}{2}dF_{z}^{b}t\hat{b}_{i}^{b}\right)\frac{c \varphi}{c\theta}, \tag{16}\]  
where \(F_{z}^{b}t\hat{b}_{i}^{b}\), i.e., \(F_{x}^{b}\), is represented this way because, as mentioned in Section 3.1, both the translation experiment and rotation experiment are conducted under AltHold mode. This mode keeps the attitude angles of Tilt-X very small. Therefore, Equations (15) and (16) can be further simplified. Additionally, in AltHold mode, the rotational speeds of each  
Figure 4: (**a**) Prototype of Tilt-X, and (**b**) its wiring diagram. propeller are nearly equal to keep the body's attitude level, so the moments generated by each propeller cancel each other out. Therefore, Equation (16) is valid only under this condition. In other words, when the attitude angles of Tilt-X are very small and can be ignored, the vertical component of thrust force \(F_{z}^{e}\) obtained by the F/T sensor in the ECF is equal to the vertical component of thrust force \(F_{z}^{b}\) in the BCF. In this case, Equations (15) and (16) can be simplified to:  
\[F_{x}^{e}=-F_{z}^{e}t\beta_{i}^{b}, \tag{17}\]  
\[M_{z}^{e}=-\frac{\sqrt{2}}{2}dF_{z}^{e}t\beta_{i}^{b}. \tag{18}\]  
To calculate the maximum tilt angle of the propellers, the thrust required for hovering should be considered. An excessive tilt angle will result in insufficient thrust.