# Robotic Coverage Path Planning for Ultrasonic Inspection
## 8 Conclusions and Future Work  
Coverage path planning for the inspection of complex 3D geometries is a challenging task. The exact solution of this problem is computationally not feasible. In this paper, we presented an approach that builds upon a heuristic using streamlines. Local curvature is taken as the measure to evolve individual streamlines. An important parameter of our algorithm is the distance at which streamlines are placed. This can either be a fixed value or can be adjusted adaptively. In the latter case, coverage is approximated via ray tracing in order to estimate the actual coverage for a path. While ray tracing is a relatively simple method to simulate ultrasound propagation, it provides a good trade-off between physical correctness and computational effort. An evaluation on four selected geometries shows that adaptive distances of streamlines can bring an improvement in the range of 17 to 22 percent shorter path length with the same or even better coverage on non-flat geometries. While the method does not provide an optimal solution to the computationally intractable coverage path planning problem, our method is well suited to many practical \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mesh** & **Algorithm** & **Path Length (mm)** & **Coverage (\%)** & **Missed Voxels** \\ \hline \multirow{6}{*}{WAVE} & papp-adaptive & 2048.0 & 100 & 0 \\ \cline{2-5}  & papp-base-30 & 3985.0 & 100 & 0 \\ \cline{2-5}  & papp-base-40 & 2009.0 & 100 & 0 \\ \cline{2-5}  & papp-base-50 & 2005.0 & 100 & 0 \\ \cline{2-5}  & papp-base-60 & 2006.0 & 100 & 0 \\ \hline \multirow{6}{*}{EDGE1} & papp-adaptive & 3985.9 & 100 & 0 \\ \cline{2-5}  & papp-base-30 & 4816.8 & 99.99 & 3 \\ \cline{2-5}  & papp-base-40 & 3226.9 & 99.98 & 7 \\ \cline{2-5}  & papp-base-50 & 3142.9 & 99.76 & 82 \\ \cline{2-5}  & papp-base-60 & 2441.9 & 99.52 & 163 \\ \hline \multirow{6}{*}{EDGE2} & papp-adaptive & 6906.4 & 100 & 0 \\ \cline{2-5}  & papp-base-30 & 8835.8 & 100 & 0 \\ \cline{1-1} \cline{2-5}  & papp-base-40 & 7147.8 & 99.96 & 37 \\ \cline{1-1} \cline{2-5}  & papp-base-50 & 5628.5 & 99.96 & 34 \\ \cline{1-1} \cline{2-5}  & papp-base-60 & 4723.8 & 99.92 & 71 \\ \hline \multirow{6}{*}{BEAM} & papp-adaptive & 1753.8 & 100 & 0 \\ \cline{1-1} \cline{2-5}  & papp-base-30 & 1558.0 & 100 & 0 \\ \cline{1-1} \cline{2-5}  & papp-base-40 & 1133.0 & 98.13 & 124 \\ \cline{1-1} \cline{2-5}  & papp-base-50 & 739.9 & 80.01 & 1329 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of different Cartesian path planning algorithms for four different mesh objects. The path length is the combined Cartesian path length in millimeters. The coverage indicates the percentage of voxels that are inspected using the generated path. The last column states the total number of missed voxels. robotic ultrasonic scanning problems. Moreover, the method of using streamlines lends itself well for adaptation of similar inspection tasks. Clearly, our method is not able to overcome physical limitations of ultrasonic inspection systems. Limitations relate to possibilities in the design of ultrasonic transducers (limited size of transducers, wavelengths/resolutions, etc.). For very complex configurations, full coverage might not be possible, due to the physical limitations. In some situations, a different layout of the transducer array might help, for example, using a curved instead of a linear layout. However, we do not take this degree of freedom into account in our present work. In any case, with the calculation of coverage, our method provides valuable information about the possibility to inspect individual regions. Future work will cover topics related to improvements of the ray tracing algorithm for better coverage calculation. Specifically, we plan to compare the calculated coverage with real ultrasound scans. Conceptualization and methodology, K.F., K.S. and S.Z. ; software, validation and formal analysis, K.F. and K.S. ; investigation, K.F. ; writing--review and editing, K.F., K.S. and S.Z. ; visualization, K.F. and S.Z.