## 5 Testbed Environment Setups  
To evaluate the preformation of the proposed global path and shape planner to cover the predefined areas, experimental environments are set up as Figure 15. The shape and size of the experimental environments are changed to create different maps. The small testbed map with simple shape obstacles has the size 4.5 m \(\times\) 2.5 m. The large tested maps with moderate obstacles shapes and complicated obstacles shapes have the size 4.5 m \(\times\) 4.8 m.  
Static obstacles are placed arbitrarily in the testbed maps to create some narrow spaces. The scenarios with the dynamic obstacles are not taken in to account in this paper. The Hector mapping-based SLAM method is used to build maps for ROS navigation. The proposed method with the components of both the path plan and the shape plan was compared with the traditional A-star algorithm of ROS navigation and A-star based method [29]. The method A-star ROS navigation can be considered as heuristic approaches where A-star are used to find the shortest path to connect the left and right boundary waypoints staying on the same horizontal lines. In the future, more heuristic approaches will be taken in to account when considering the dynamic obstacles.  
Waypoints are defined to create the roadmap by applying these methods before hTetro performs the navigation to clear the planned waypoints. During the hTetro navigation, the position of the robot after being finely tuned with AMCL was recorded to compute the area covered by the robot. To measure the covered areas, while the robot navigates, the path of the robot is widened to the size that corresponds to the actual width \(w_{r}\) and marked in green color. Once the robot has completed the navigation of each test, the ratio \(A_{r}\) between the covered areas and the need-to-be-covered areas and the ratio \(R_{r}\) between the revisited areas and the covered areas will be calculated as Equations (9) and (10) respectively. Specifically, the areas covered by the robot during navigation are measured by the number of blue pixels (excluding blue pixels generated by the robot positions noise overlapped with obstacles, map borders and unidentified areas). The need-to-be-covered areas are the number of pixels corresponding to the free space areas with the value = 0 in the map on the ROS map server. The revisited areas are the overlapped areas of robot location during navigation. Since the percentage of the covered area showed differences between the tested methods, total path lengths can be evaluated through revisited areas. The higher the value of \(A_{r}\), the better the tested method. The smaller \(R_{r}\)  
Figure 15: Testbed environment setups. (**a**) Real testbed environment, (**b**) small map with simple obstacles, (**c**) large map with moderate obstacles, (**d**) large maps with complicated obstacles.  
the better the tested method. The processes are conducted ten times for each of these tested methods on each testbed map. The \(A_{r}\) and \(R_{r}\) ratios of all tested times are averaged to compare.  
\[A_{r}=\frac{Number\ of\ covered\ pixels}{Number\ of\ free\ space\ pixels}\times 100\% \tag{9}\]  
\[R_{r}=\frac{Number\ of\ covered\ pixels}{Number\ of\ free\ space\ pixels}\times 100\% \tag{10}\]