# Robotic Coverage Path Planning for Ultrasonic Inspection
## 7 Results  
To determine the effectiveness of the proposed method, we evaluate it on different geometries. Our evaluation focuses on the Cartesian path planning phase, or more precisely, on the method used to mark a part of the surface as inspected. The algorithm proposed in Section 6 (later called papp-adaptive) iteratively generates streamlines and deploys a ray-tracing algorithm after each iteration. The obtained volumetric inspection is then projected back onto the surface, marking surface points that are above a column of fully inspected voxels as inspected. This approach is compared to a baseline algorithm (papp-base-\(d\)) that does not consider the volumetric inspection, but simply considers surface points in a certain proximity \(d\) to the streamline as inspected. Four different values for \(d\) are tested: 30 mm, 40 mm, 50 mm and 60 mm. The phased array sensor has a width of 114 mm, and thus, an inspection radius of 60 mm still yields good results on slightly curved surfaces. The algorithm variants are compared using the Cartesian path length, i.e., the total length of all streamlines. The quality of the path is measured as the percentage of the (voxelized) mesh-volume that is covered by the given path. For the baseline algorithm, the ray tracing algorithm is used to derive the volumetric inspection once all streamlines are calculated. The evaluation is conducted, using four mesh objects shown in Figure 5. These objects are the following: WAVE, a moderately wavy plate with increasing wall thickness; EDGE1,an edge which is bent at its center with thinner walls towards the ends; and EDGE2, an edge that bends twice in two different directions and BEAM: a complex U-shaped beam. The surface curvature has a big impact on the size of the inspected volume. A large fraction of energy is lost when the surface normal is not parallel to the sensors' z-axis. Challenging areas are also those with thick walls and/or non-parallel back walls. The wall thickness for all objects is in a range between 15 mm to 55 mm. All mesh objects are available online ([[https://zenodo.org/record/5173521#.YRIJECxVPY](https://zenodo.org/record/5173521#.YRIJECxVPY)]([https://zenodo.org/record/5173521#.YRIJECxVPY](https://zenodo.org/record/5173521#.YRIJECxVPY))). Streamlines calculated in the first phase of the coverage planning algorithm papp-adaptive are illustrated in Figure 5.  
Table 1 shows the path length and achieved coverage for the different algorithms. For flat areas, such as the object depicted in Figure 4(a), the baseline algorithms achieve full coverage with short paths. However, for more challenging areas, e.g., for the highly curved center area on the mesh EDGE1, the baseline algorithms require an even smaller inspection radius to achieve full coverage. Figure 6 visualizes the voxels that are missed by algorithm papp-base-60. Table 1 summarizes path length and coverage for different versions of our algorithm on the four different test geometries. The papp-adaptive version of the algorithm performs quite well in the sense that it delivers full coverage for all test geometries. For WAVE, there is little advantage of using the adaptive method as the respective geometry contains only moderate curvature. For EDGE1 and EDGE2, the adaptive method outperforms all other variants of the algorithm. For these geometries, papp-adaptive delivers full coverage  
Figure 5: Test objects used to evaluate the proposed algorithm. The streamlines (in red) are generated with the following variants of the algorithm (from top-left to bottom-right): papp-base-60, papp-adaptive, papp-base-40, papp-adaptive. Figure 6: Visualization of the 163 missed voxels on the mesh EDGE1 for the path planned, using papp-base-60. with a shorter path length. For BEAM, the two algorithm variants papp-adaptive and papp-base-30 both achieve full coverage. However, in this case, the papp-adaptive version requires a slightly larger path length than papp-base-30. For this evaluation, we only considered parts for which the complete volume can be inspected.