# Recognition and Location Algorithm for Pallets in Warehouses Using RGB-D Sensor
## 4 Results
### Accuracy Test in Dynamic Experiment  
In Figure 10, the first row shows the coordination of the RGB-D sensor and the detection result of the pallet in {W} space. The third row shows the error of the pallet Ex, Ey, Ez, and Eagle in the approach process.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Distance** & **COF of Ex** & **COF of Ey** & **COF of Ez** & **COF of Eagle** \\ \hline
1000 & 0.9190 & 0.8059 & 0.8000 & 0.7473 \\
2000 & 0.8836 & 0.8320 & 0.8521 & 0.8843 \\
3000 & 0.7580 & \(-\)0.7414 & 0.5723 & \(-\)0.7307 \\
4000 & 0.8839 & \(-\)0.0472 & 0.9140 & 0.9283 \\ \hline \end{tabular}
\end{table}
Table 1: Correlation between parameter error and pallet angle.  
Figure 9: Measurement error curve of the algorithm for different distances and angles of the pallet. (**a**) Curve chart of measurement error in \(X\)-axis direction versus pallet angle. (**b**) Curve chart of measurement error in \(Y\)-axis direction versus pallet angle. (**c**) Curve chart of measurement error in \(Z\)-axis direction versus pallet angle. (**d**) Curve chart of angel measurement error versus pallet angle.  
When the sensor approached the pallet and the angle was in the range \(3.08^{\circ}-7.02^{\circ}\), as shown in Figure 8a, the estimated pallet position was (\(0.14\), \(-6.74\), \(58.16\)) and the angle was \(92.01^{\circ}\). The error became smaller when the sensor was closer to the pallet. The maximum errors in the \(X\) axis, \(Y\) axis, \(Z\) axis, and angle were \(6.38\) mm, \(15.92\) mm, \(54.56\) mm, and \(2.82^{\circ}\), respectively.  
When the sensor approached the pallet along a line, and the angle was in the range \(12.41^{\circ}-19.03^{\circ}\), as shown in Figure 9b, the estimated pallet position was (\(16.85\), \(-24.12\), \(61.08\)), and the angle was \(93.39^{\circ}\). The error became smaller when the sensor was closer to the pallet. The maximum errors in the \(X\) axis, \(Y\) axis, \(Z\) axis, and angle were \(46.37\) mm, \(48.42\) mm, \(33.09\) mm, and \(5.55^{\circ}\), respectively.  
When the sensor approached the pallet along a curve, as shown in Figure 9c, and the angle varied in the range \(2.84^{\circ}-35.98^{\circ}\), the estimated pallet position was (\(3.87\), \(40.50\), \(51.62\)), and the angle was \(90.91^{\circ}\). The error increased when the angle increased. The maximum error in the \(X\) axis, \(Y\) axis, \(Z\) axis, and angle were \(47.80\) mm, \(102.70\) mm, \(32.74\) mm, and \(6.51^{\circ}\), respectively.  
In the experiments, the angle changed in different ranges. The algorithm showed better performance, and the accuracy was less than \(50\) mm when the angle was steady and changed in \(\pm 20^{\circ}\). When the angle changed in a large range, the \(Y\) axis error had a dramatic variation because of the drift of pallet center recognition. As shown in Figure 9c, the algorithm recognized the pallet even when the angle reached \(35.98^{\circ}\), and the maximum \(Y\) error was \(102.70\) mm. The performance in the dynamic test matched the tendency observed in the static test.  
Figure 10: Verification of the algorithm’s performance in measuring accuracy when the angle dynamics change. (**a**) Sensor position as well as pallet positioning results data in the sensor angle range of \(0\)–\(10^{\circ}\) during sensor approach. (**b**) Sensor position as well as pallet positioning results data in the sensor angle range of \(10\)–\(20^{\circ}\) during sensor approach. (**c**) Sensor position as well as pallet positioning results data in the sensor angle range of \(0\)–\(40^{\circ}\) during sensor approach. (**d**) Error of pallet positioning results corresponding to Figure 9a. (**e**) Error of pallet positioning results corresponding to Figure 9b. (**f**) Error of pallet positioning results corresponding to Figure 9c.