## 4 Experimental Validation Framework  
For the purpose of the experimental validation of the presented model and the proposed procedure for the analysis of configuration parameters, it is necessary to realize an experimental aircraft and experimental firmware. The experimental aircraft was designed in the SOLIDWORKS software package (Dassault Systemes SE, Velizy-Villacoublay, France). As mentioned before, the aircraft assembly consists of four modules. The modular approach to aircraft design aims to enable the easy assembly of the aircraft and the propulsion module with a different number of rotors. Rapid prototyping technologies are used in the development phase where important requirements are high strength and the rigidity of parts and low specific weight. The parts are made from composite plates utilizing a 3-axis computer-controlled milling machine. On the other hand, plastic parts are made by additive manufacturing, using fused deposition modeling (FDM) and a selective laser sintering (SLS) 3D printing process. The three-axis gimbal joint shown in the previous study [28] is used in laboratory tests. The concept of gimbal design enables the implementation with a six-axis force and torque sensor, which will be achieved in the future phase of research. The open-source Pixhawk FC was selected to perform the control of the experimental multirotor UAV. The selected FC supports a variety of communication protocols to connect to peripheral devices, such as the global positioning system (GPS) module, telemetry, or remote control (RC). The FC communicates with GPS and telemetry via the UART protocol, while the RC receiver communicates via the S.BUS protocol. Pixhawk FC has an integrated redundant accelerometer, gyroscope, and magnetometer sensors. The heart of FC is a powerful 32-bit 168 MHz STM32F427 Cortex M4 processor with 256 kB of RAM, and 2 MB of flash memory. The control system is based on a PX4 [31] ecosystem with modular software architecture and a permissive license. The PX4 is written in C and C++ languages, and, in recent years, PX4 has been supported through the MATLAB/Simulink toolbox. This fact allows for the faster execution of custom firmware that allows for experimental testing. For the purpose of aircraft experimental testing, custom firmware based on the model of the control allocation scheme was designed, which enabled the testing of configurations with different parameters. A preliminary configuration experiment was first performed to test the control commands for each of the six DOF. The tests were performed using an experimental setup consisting of a 3-axis gimbal joint that allowed for the safe testing of the multirotor UAV orientation. Figure 10 shows a part of the roll and pitch angles of the aircraft orientation in the case of the preliminary testing of a passively tilted hexarotor configuration (PTX6) using a remote control. Figure 11 shows the PWM signals sent by the FC to the EPUs. The goal of preliminary tests was to show the functionality of and to get acquainted with the experimental aircraft. The first experimental testing relates to attitude control of PTX6 configuration with respect to the reference orientation during the testing cycle. A second rotors setup was chosen for the considered configuration (Table 1), and for the needs of laboratory tests; instead of a battery, a 12 V DC power source was used. A cascade PID controller was implemented, whose gain parameters for the outer and inner control loop were chosen empirically. In order to tune the gain parameters, the custom firmware also contained a module for adjusting the control algorithm parameters in real time. Figure 12 shows multirotor attitude with respect to different reference orientations determined by the roll angle (\(\phi\)) around the X\({}_{\text{B}}\) axis, pitch angle (\(\theta\)) around the Y\({}_{\text{B}}\) axis, and yaw angle (\(\psi\)) around the Z\({}_{\text{B}}\) axis. Figure 13 shows the testing results for the orientation tracking of the case of reference.