# Algorithm for Base Action Set Generation Focusing on Undiscovered Sensor Values
## 4 Experimental Results
### Visualization of Robot's Motion Vectors  
Next, we enumerated heat maps of the robot's motion vectors at a regular time interval for each algorithm. The motion vectors were calculated once every 50 steps; in other words, 50 * 0.02 s = 1 s. The horizontal axis in these maps denotes the relative angle \(\theta(t)\) and the vertical axis denotes the magnitude \(|\vec{q}(t)|\). The results of Algorithms A, A', and Random are shown in Figure 8. These results show all the vectors of ten trials for each algorithm. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Standard Deviation** \\ \hline Algorithm A & 0.0261 \\ Algorithm A’ & 0.1443 \\ Algorithm Random & 0.0102 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Final standard deviation of each algorithm. Figure 7: Sensor cover rate of each algorithmIn the results for Algorithm A (Figure 8a), strong responses were shown in four sections: \"Go forward\" (1 in Figure 8a), \"Go backward\" (2 in Figure 8a), \"Turn 90 degrees right\" (3 in Figure 8a), and \"Turn 90 degrees left\" (4 in Figure 8a). This means the robot used these four locomotions frequently. These locomotion selections were comparable to typical wheeled robot locomotions. However, strong responses were observed evenly from turning 90 degrees right to 90 degrees left except for \"Go forward\" and \"Go backward\" (6 in Figure 8c) in the results of Algorithm Random (5 in Figure 8c). This means that the robot could only find about 10% fewer box allocation patterns even though Algorithm Random made more locomotion patterns than Algorithm A. All the heat maps of the ten trials for each algorithm are shown in Figure 9. The distributions of the ten trials were almost the same in Algorithms A and Random. However, the distributions were unstable and variable in Algorithm A'. These results show that discarding action fragments was executed correctly in Algorithm A. Therefore, Algorithm A could determine effective base actions to find undiscovered sensor values. Moreover, Algorithm A discarded actions that did not contribute to finding new sensor values correctly and stabilized its performance. Next, we divided experiment time \(t_{max}\)(=200(10\({}^{3}\) s)) into four parts and enumerated heat maps of the robot's motion vectors at each part. The four heat maps of Algorithm A with \(r_{r}=0.3\), which are the results of ten trials, are shown in Figure 10.  
Figure 8: Motion vector heat map of each algorithm. (**a**) Algorithm A; (**b**) Algorithm A’; (**c**) Algorithm Random. As shown in Figure 10, a heat map in the early phase (\([0,t_{max}/4]\)) showed strong responses only near the \"Go forward\" and \"Go backward\" areas. However, strong responses near \"Turn right 90 degrees\" and \"Turn left 90 degrees\" appeared from the second part (\([t_{max}/4,t_{max}/2]\)) and remained almost the same from the third part (\([t_{max}/2,3t_{max}/4]\)). These results mean that actions of strong responses in the heat maps were used repeatedly. Therefore, Algorithm A finished extracting the appropriate action fragments until (\([t_{max}/2,3t_{max}/4]\)) and then maintained. Next, we changed the action generation random rate \(r_{r}\) and evaluated its effect on acquiring the appropriate action set in Algorithm A. Average sensor cover rates of Algorithm A with various \(r_{r}\) are given in Figure 11, which includes the average results of ten trials. Average sensor cover rate increased for the entire time in accordance with the decrease of \(r_{r}\) from 0.7 to 0.3. In contrast, they remained almost the same when \(r_{r}\) decreased from 0.3 to 0.1. Heat maps of the robot's motion vectors for each \(r_{r}\) value are shown in Figure 12. Here, as the action generation random rate increases, the results show distributions similar to the result of Algorithm Random (\(r_{r}=1.0\)) that distributed between angle \(\theta=-\pi/2\) to \(\theta=\pi/2\) uniformly. However, the heat maps of \(r_{r}=0.1\) and 0.3 are almost the same and showed strong responses in all four areas, as in Figure 8a.