# Testing Procedure of Unmanned Aerial Vehicles (UAVs) Trajectory in Automatic Missions
## 3 Results
### Task 2--ISO Standards for Industrial Robots  
The accuracy of an industrial robot is determined by its functional characteristics [59], the most important of which are the accuracy and repeatability of reaching a position. The guidelines for testing the accuracy of robots are described by PN-EN ISO 9283:2003 [43; 60]. Different measuring methods can be used for examining the positioning of such devices [61; 62; 63; 64]. In task 2, all of the tests have been carried out, so that the central point of the test base reached the four independent directions consistent with the Cardinal Directions. The UAV has been programmed to carry out the mission, so as to reach the set central position at least 25 times. The test has been conducted at a flight altitude of 30 m, so that the measurement results have not been affected by turbulence that is associated with trees or other infrastructure located in the vicinity of the measurement base. The calculations have been performed so that the description of the results is related to the direction of reaching the central point from the north (N), south (S), east (E), and west (W), respectively. The reference data have been the measurement results of the MS50 instrument as absolute position sources. Task 2 discusses the works allowing for defining the parameters listed below:  
* positioning accuracy (\(AP_{P}\)), which is understood as the difference between the set position and the average position reached by the robot when reaching the set position following from the same direction: \[AP_{P}\ =\ \sqrt{\left(\overline{x}-x_{c}\right)^{2}+\left(\overline{y}-y_{c} \right)^{2}+\left(\overline{z}-z_{c}\right)^{2}}\] (12) \[AP_{x}\ =\ \left(\overline{x}-x_{c}\right)\] (13) \[AP_{y}\ =\ \left(\overline{y}-y_{c}\right)\] (14) \[AP_{z}\ =\ \left(\overline{z}-z_{c}\right)\] (15) \[\overline{x}\ =\ \frac{1}{n}\sum_{j=1}^{n}x_{j}\] (16) \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**MS50**} & \multicolumn{4}{c}{**LOG**} \\  & & **N [m/min]** & **E [m/min]** & **A [m/min]** & **N [m/min]** & **E [m/min]** & **A [m/min]** \\ \hline LIGHT & COM-1 & 0.009 & 0.000 & \(-\)0.055 & \(-\)0.012 & 0.002 & 0.003 \\ WIND & COM-2 & \(-\)0.035 & \(-\)0.046 & \(-\)0.152 & 0.001 & \(-\)0.002 & 0.003 \\ \hline STRONG & COM-1 & \(-\)0.187 & 0.116 & \(-\)0.057 & \(-\)0.013 & 0.015 & 0.002 \\ WIND & COM-2 & 0.130 & \(-\)0.057 & \(-\)0.278 & \(-\)0.021 & \(-\)0.007 & 0.010 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of time drifts calculated for all tests for each coordinate for data from MS50 and LOG in task 1. \[\overline{y} = \frac{1}{n}\sum_{j\ =\ 1}^{n}y_{j}\] (17) \[\overline{z} = \frac{1}{n}\sum_{j\ =\ 1}^{n}z_{j}\] (18) where \(\overline{x},\ \overline{y},\ \overline{z}\)--coordinates of average position reached by the robot; \(x_{c},\ y_{c},\ z_{c}\)--coordinates of set position; \(x_{j},\ y_{j},\ z_{j}\)--coordinates of the \(j\)-th position reached; and, \(n\)--number of cycles measured. * positioning repeatability (\(RP_{l}\)), i.e., a measurement of the scatter of deviations between the positions reached after \(n\) number of repetitions, when reaching the same position set from the same direction: \[RP_{l}=\overline{l}+3S_{l}\] (19) \[\overline{l}\ =\ \frac{1}{n}\sum_{j\ =\ 1}^{n}l_{j}\] (20) \[l_{j}\ =\ \sqrt{\left(x_{j}-\overline{x}\right)^{2}+\left(y_{j}- \overline{y}\right)^{2}+\left(z_{j}-\overline{z}\right)^{2}}\] (21) \[S_{l}\ =\ \sqrt{\frac{\sum_{j\ =\ 1}^{n}\left(l_{j}-\overline{l}\right)^{2}} {n-1}}\] (22) where \(\overline{x},\ \overline{y},\ \overline{z}\)--average coordinates of points reached \(n\) times in response to the reference position; \(l\)--the distance between the achieved position and the average of all achieved positions; \(x_{j},\ y_{j}\), \(z_{j}\)--coordinates of the \(j\)-th position reached.