## 3 Path Planning in Robotics and Additive Manufacturing
### Path Planning in Additive Manufacturing
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **Relevant Developments** & **Advantages** & **Disadvantages** \\ \hline [PERSON] et al. [7] & change of building direction and curves surfaces/slices (cf. Figure 5a) & necessary subvolumization approach & restricted range for building direction \\ \hline [PERSON] et al. [8] & segmented consideration of paths (cf. Figure 5b) & include process parameter into optimization, optimize robot motion & use of rotational degree of freedom around the welding head \\ \hline Simplify3D [9] & subdivision of objects to be printed into an outer shell and an infill structure & - & 2.5D Slicer without any optimization \\ \hline [PERSON] et al. [10] & raster infill strategy & easy process handling & 2.5D Slicer \\ \hline [PERSON] et al. [11] & zigzag infill strategy & continuous path, reduced number of sub-paths, fewer transition movements & many changes in printing direction \\ \hline [PERSON] [12] & dividing slices into many convex polygons, optimization algorithm generates optimal zigzag in direction & minimal number of changes - \\  & infill orientation & in direction & - \\ \hline [PERSON] et al. [13] & contour infill strategy (Figure 4) & reduce mistakes near the contour & orientation changes more then 180 deg \\ \hline [PERSON] et al. [14] & spiral infill strategy & used in 5D numerically controlled (NC) machining, solve the limitations of zigzag infill & only suitable for special geometric model, orientation changes more then 180 deg \\ \hline [PERSON] et al. [15] & hybrid infill structure, zigzag+contour & combine the advantages of several strategies & orientation changes more than 180 deg \\ \hline [PERSON] et al. [16] & hybrid infill structure, zigzag+contour & combine the advantages of several strategies & orientation changes more than 180 deg \\ \hline [PERSON] et al. [17] & Hilbert infill structure & cover complex polygons, reducing shrinkage in AM processes & large number of path orientation changes, not suitable for WSAM processes [18] \\ \hline [PERSON] et al. [19] & fractal-like path planning using a simulated annealing algorithm, area to be deposited is broken down into nodes & possible path optimization & for large areas and high accuracy requirements, the processing time required is unacceptably long \\ \hline [PERSON] and [PERSON] [20] & hybrid infill structure, zigzag + continuous path strategies, decomposed into a set of monotone polygons & reduces the number of welding paths & - \\ \hline [PERSON] et al. [21] & hybrid infill structure, zigzag + contour + continuous path patterns & continuous path pattern is suitable for WSAM of solid structures & orientation changes more than 180 deg \\ \hline [PERSON] et al. [22] & maze-like structure, decompose slice and map volumes in weighted graph, find optimal path by backtracking algorithm & increase the isotropy of the mechanical properties in the component & many orientation changes, not suitable for WSAM processes [18] \\ \hline [PERSON] et al. [6] & Hamilton graph search, decompose slice and map pixels in weighted graph, find optimal path using a backtracking algorithm & evaluate robot motion along printing path & many orientation changes, calculation effort not suitable, hard to find a single Hamilton path \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the state of the art of path planning algorithms. Advantages and disadvantages are summarized in the context of robotic MDAM using WAAM.