# Topological Navigation and Localization in
## 5 Results and Discussion
that these were done during development, and small tweaks and adjustments, some of them that worked and some of them did not, were made in between. To further assess the driving abilities of the autonomous system, the smoothness of its operation is considered. For this, two different metrics are used. The first measures the change between two consecutive command inputs (propel and steering), as is shown in equation (22). The second, in a similar way, measures the difference between two consecutive measures of the dynamic state of the LHD, namely, its speed and the angle of its articulation, as is shown in Equation (23). \[E_{u}(k)=(u_{v}(k+1)-u_{v}(k))^{2}\Delta t+(u_{\omega}(k+1)-u_{\omega}(k))^{2} \Delta t \tag{22}\]  
\[E_{LHD}(k)=(v(k+1)-v(k))^{2}\Delta t+(\gamma(k+1)-\gamma(k))^{2}\Delta t \tag{23}\]  
The average and maximum values of both metrics for all datasets are presented in Table 4. Again, the human operator shows a better performance than the autonomous system. The consistency of the human operator is quite remarkable, and it shows its expertise and knowledge of the machine and the tunnel. The autonomous system is also quite consistent on these metrics, but that is usually expected of an automation system. In order to have a better idea of the difference between them, Figures 17-20 show the machine inputs (propel and steering) as well as the instant speed and steering angle of the LHD. Figures 17 and 19 show dataset 14, while Figures 18 and 20 show dataset M1. For clarity, Steering command and steering angle have been plotted separately from and propel command and LHD's speed. Both were made with the LHD having a fully loaded bucket, and with the vehicle moving backward, towards the dump point of the tunnel. Straight lines can be seen in Figure 16 on the propel command line, showing a constant output by the autonomous system. Looking at both figures, it can be seen that the human operator uses fewer steering commands, perhaps showing a better understanding of the LHD kinematics, and, therefore, greater abilities to predict the behavior of the vehicle. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**ID** & **ACD** & **MCD** & **ASD** & **MSD** & **ADLW [m]** & **MDLW [m]** & **ADRW [m]** & **MDRW [m]** \\ \hline
1 & 0.0060 & 0.2776 & 0.0451 & 5.0400 & 0.62 & 0.19 & 0.67 & 0.16 \\
2 & 0.0053 & 0.3941 & 0.0358 & 3.4620 & 0.84 & 0.10 & 0.47 & 0.10 \\
3 & 0.0066 & 0.2510 & 0.0380 & 4.7157 & 0.62 & 0.12 & 0.64 & 0.19 \\
4 & 0.0043 & 0.3777 & 0.0347 & 6.8018 & 0.71 & 0.10 & 0.43 & 0.10 \\
5 & 0.0068 & 0.2184 & 0.0484 & 5.4908 & 0.62 & 0.20 & 0.61 & 0.23 \\
6 & 0.0058 & 0.2607 & 0.0323 & 1.9258 & 0.55 & 0.10 & 0.46 & 0.10 \\
7 & 0.0059 & 0.3070 & 0.0309 & 5.3291 & 0.61 & 0.10 & 0.64 & 0.12 \\
8 & 0.0058 & 0.2110 & 0.0558 & 5.8182 & 0.68 & 0.10 & 0.41 & 0.10 \\
9 & 0.0071 & 0.3096 & 0.0514 & 7.8898 & 0.63 & 0.17 & 0.65 & 0.11 \\
10 & 0.0056 & 0.2268 & 0.0717 & 6.1329 & 0.71 & 0.11 & 0.50 & 0.10 \\
11 & 0.0059 & 0.2157 & 0.0583 & 5.7393 & 0.56 & 0.10 & 0.65 & 0.17 \\
12 & 0.0056 & 0.2526 & 0.0361 & 3.4673 & 0.73 & 0.10 & 0.51 & 0.10 \\
13 & 0.0072 & 0.3440 & 0.0359 & 4.3282 & 0.64 & 0.16 & 0.63 & 0.11 \\
14 & 0.0048 & 0.1749 & 0.0383 & 4.5030 & 0.78 & 0.13 & 0.49 & 0.10 \\ M1 & 0.0018 & 0.0406 & 0.0076 & 0.1779 & 0.60 & 0.10 & 0.56 & 0.10 \\ M2 & 0.0016 & 0.0339 & 0.0090 & 0.1044 & 0.47 & 0.10 & 0.63 & 0.11 \\ M3 & 0.0016 & 0.0452 & 0.0091 & 0.2017 & 0.48 & 0.10 & 0.69 & 0.10 \\ M4 & 0.0013 & 0.0260 & 0.0070 & 0.1617 & 0.44 & 0.10 & 0.70 & 0.12 \\ \(\mu\)(1–14) & 0.0053 & 0.2711 & 0.0435 & 4.5901 & 0.66 & 0.13 & 0.55 & 0.13 \\ \(\sigma\)(1–14) & 0.0006 & 0.0834 & 0.0147 & 1.7500 & 0.08 & 0.04 & 0.10 & 0.04 \\ \(\mu\)(M1–M4) & 0.0016 & 0.0364 & 0.0082 & 0.1614 & 0.50 & 0.10 & 0.65 & 0.11 \\ \(\sigma\)(1–M44) & 0.0002 & 0.0083 & 0.0010 & 0.0414 & 0.07 & 0.00 & 0.06 & 0.01 \\ \hline \end{tabular}
\end{table} 
Table 4: LHD input difference, state difference and distance to the walls for autonomous navigation and manual operation. ID: Dataset Identifier. ACD: Average Command Difference (\(E_{u}\)).