## 3 Experiments and Discussions
### Production Environment Navigation
The additional computation effort needed to determine the right-hand driving cells at each expansion step does not increase the overall processing time. Quite the opposite, the approach A*zone needs approximately 11% less average processing time. This decrease correlates with the number of expanded cells, which is also approximately 11% smaller than that of A*. The same applies to the approach Dijkstrazone, which results in 9% less expanded cells and a corresponding decrease in the overall processing time. Table 2 shows a comparison of the five start-goal-position tuple groups by evaluating the number of expanded cells normalized to the resulting path length for each tuple. The goal zone has a high impact on the efficiency of the evaluated path planners. If the goal position lies within the corridor zone (\(T_{\text{SC}}\), \(T_{\text{CC}}\)), the number of expanded cells is significantly lower compared to a goal position outside the corridor zone (\(T_{RR}\), \(T_{\text{SS}}\), \(T_{\text{CS}}\)), by comparing columns \(T_{\text{SC}}\), \(T_{\text{CC}}\) with other columns of Table 2. This behavior is caused by the cost levels of the zones and the nature of the path planning algorithms. Since the cost level of the corridor zone is relatively low the planners will expand inside the corridor zone with a high preference, before starting to expand inside a restricted or station zone. The A* and A*zone implementations provide a lower number of expanded cells for each paths group, as highlighted by the bold font in Table 2, which is caused by the additional heuristic. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Approach** & **aMSE** & **Processing Time** & **Expanded Cells** & **Path Length** \\  & **[m]** & **[ms]** & **Expanded Cells** & **[m]** \\ \hline A* & 15.72 & 56.2 & 401,497 & 62.43 \\ Dijkstra & 13.78 & 53.3 & 596,325 & 62.22 \\ A*zone & 0.11 & 49.8 & 355,200 & 71.04 \\ Dijkstrazone & 0.06 & 49.1 & 545,255 & 72.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the evaluated planning approaches. Performance parameters averaged over 100 start-goal-position tuples in 10 simulated environments. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Approach** & \(T_{RR}\) & \(T_{\text{SS}}\) & \(T_{\text{SC}}\) & \(T_{\text{CS}}\) & \(T_{CC}\) \\ \hline A* & 7643 & 9801 & **2836** & 8852 & **3298** \\ Dijkstra & 10,366 & 11,294 & 6261 & 11,663 & 6425 \\ A*zone & 6170 & 7745 & **1695** & 7963 & **1623** \\ Dijkstrazone & 8219 & 8818 & 4401 & 10,115 & 4496 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The number of expanded cells normalized to the path length. Our right-hand driving approach results in an additional decrease in the number of expanded cells. This is caused by the effect of our method on the behavior of the path planning algorithms. Figure 12 shows a comparison of a path \(p\in T_{SC}\) and the corresponding expansion potentials for each of the evaluated approaches. The relatively low-cost cells at the edge between the corridor zone and the guard rail zone let the path planning algorithms concentrate their expansion towards a particular direction. Since the corridor zone is designed to connect typical station areas in the industrial environment, our method reduces the number of cells that are expanded in the corridor zone. Therefore, our method provides a higher expansion efficiency which results in lower computational effort compared to standard implementations of Dijkstra or A*.