## 4 Verification on a Real Robot  
To experimentally verify the impact of the chosen fitness function on the real wear of the robot joints, it would be necessary to perform simultaneous long-term testing on multiple robots and then analyze the mechanical degradation of important components of the joint construction. This type of experiment was not feasible for us at this moment. Instead, we used experiments on a real robot to verify the accuracy of dynamical simulation in CoppeliaSim. The real experiments were performed on the same robot as was previously used for the simulations--the Universal Robots UR3 collaborative robot. The robotic arm was mounted on a table (Figure 2), and, instead of changing the robot base location relative to the trajectory, the trajectory was appropriately shifted in relation to the robot. There were no tools nor other equipment mounted to the output interface flange, which corresponds to the simulation model described above. The robot controller (CB3 controller, firmware version 3.10.0) provides state messages via the RTDE (Real-Time Data Exchange) protocol based on TCP/IP communication. This protocol allows reading the actual state of the robot with a frequency of 125 Hz. The RTDE messages can be configured and include the actual and target values of kinematic parameters, such as the position, velocity, and acceleration, as well as the currents of individual joints, the overall current of the whole robot, and the target torque values--which are needed for our experiment. The experiment was executed for the optimal (best) robot location found by the simulation, for the worst robot location, and for three other locations that were manually selected from the set of possible locations to cover various sections of the whole space. The locations are hereafter referred to as \"B\" (best), \"W\" (worst), and \"1\", \"2\", and \"3\" (the other locations). The three numbered locations are sorted from the lowest to the highest \(f_{f}\) values according to the simulation results (a lower \(f_{f}\) value indicates a better robot location). For each trajectory and robot location, the robot was programmed to go through the whole trajectory five times in a row. During this time, the integral (sum) was calculated according to (4), and the final value was then divided by five. All tested real robot locations are depicted in Figure 6. Numerical values of the \(f_{f}\) values in all five locations for all ten trajectories are listed in Tables 3 and 4. Table 3 shows the results from the simulation, the values here are sorted from lowest to highest (\"B\", \"1\", \"2\", \"3\", and \"W\"). Table 4 shows the values from real experiments--as can be seen, the  
Figure 8: Comparison of the angular velocity \(\omega_{3}\), torque \(\tau_{3}\), and immediate power \(\omega_{3}\tau_{3}\) of the third joint during the whole trajectories A1 and B1 for the best (\({}^{B}\)) and worst (\({}^{W}\)) robot locations. best locations were identical; the worst locations were also mostly identical, except for trajectory D2. Table 5 shows the ratios between the real and simulated values; ideally, these values should all be equal to 1. In general, it can be stated that the \(f_{f}\) values acquired by the real experiments were lower than the values from the simulation, and the average ratio was \(r=0.745\) with the standard deviation equal to \(\sigma_{r}=0.126\). Figure 9 displays a comparison of the simulated and real values in the form of a bar graph, together with the ratio \(r\). In this image, it can be observed that, for the same trajectory, the ratio \(r\) typically lowers (deteriorates) with increasing the \(f_{f}\) values. This will be further discussed in the Discussion section.