## 3 Experiments and Discussions  
### Production Environment Navigation  
We evaluated the presented zone-based navigation concept in the multi-robot simulator Gazebo [48]. Therefore, we created 10 different production environments of the size  
Figure 10: Task management system. State machines in blue and ROS nodes in orange. 60 \(\times\) 60 m. Each simulated production environment features an individual navigation zone layout, comparable to the layout shown in Figure 6. In each simulated production environment, we defined 10 start-goal-position tuples, which resulted in a total of 100 tuples. The tuples were divided into five groups:  
* [noitemsep,topsep=0 pt]
* Tuples \(T_{RR}\) from restricted-to-restricted zone;
* Tuples \(T_{5S}\) from station-to-station zone;
* Tuples \(T_{5C}\) from station-to-corridor zone;
* Tuples \(T_{CS}\) from corridor-to-station zone;
* Tuples \(T_{CC}\) from corridor-to-corridor zone. The five groups are equally distributed across the 10 simulated environments, resulting in two tuples for each group per environment. For each tuple, we manually annotated the desired path \(P_{i}\) with \(i=\{1,2,\ldots,100\}\). Each path \(P_{i}\) fulfills two criteria. The first one is the reduction in the overall costs of the path by preferring the corridor zone. The second one respects the desired right-hand driving behavior alongside the corner between the corridor zone and the guard rail zone. The experiment compares the performance of the default A* and Dijkstra implementation of the robot operating system (ROS) [49] with our adapted version, later called A*zone and Dijkstrazone. The deviation between a planned path \(A\) and the corresponding manually annotated path \(B\)\(e\)\(P_{i}\) is represented by the average mean square error \(aMSE\). The calculation is given in Equation (5):  
\[aMSE=\frac{\sum_{i=0}^{n}d_{i}^{2}}{n}, \tag{5}\]  
where \(d_{i}\) is the Euclidean distance between each of the \(n\) positions \(a_{i}\)\(e\)\(A\) and its closest neighbored position \(b_{i}\)\(e\)\(B\). Figure 11 shows the experimentally determined results for each of the 10 simulated production environments averaged over all five start-goal-position tuple groups. As expected, the \(aMSE\) is significantly higher for the default implementations of A* and Dijkstra. This result is caused by the right-hand driving criteria of the manually annotated reference paths. In addition to the \(aMSE\), we analyzed the following performance parameters:  
1. [noitemsep,topsep=0 pt]
2. The required process time;
3. The number of expanded cells; and
4. [noitemsep,topsep=0 pt]  
Figure 11: Average mean square error over all paths for each simulated environment. The path length. The required process time indicates the additional computation effort caused by the implementation of Algorithm 1. The number of expanded cells reflects the efficiency of reaching the goal cell. The overall path length shows the additional path caused by the desired right driving behavior. Table 1 shows the performance parameters averaged over all 100 start-goal-position tuples. The default implementations of A* and Dijkstra provide the most cost-efficient path. The cost efficiency is mainly influenced by the cost levels of the different zones. Inside a zone, the length of the path is the factor of influence. Therefore, the average path length of the default implementations is approximately 14% smaller compared to our approach. With an average \(aMSE\) of 0.11 m for A*zone and 0.06 m for Dijkstrazone, our approach proved to provide consistent paths following the concept of right-hand driving. The general difference in processing time between the approaches A*, A*zone and Dijkstra, and Dijkstrazone is caused by the calculation of the heuristic. Therefore, the average processing time for A*zone is 2.5% greater than that for Dijkstrazone, even though the number of expanded cells is approximately 35% smaller.