## 3 Path Planning in Robotics and Additive Manufacturing
### Requirements on New Path Planning Algorithm  
The path planning for AM processes and the algorithms used are characterized by the material build-up process. This proves to be sensible, as optimal component quality is the goal of AM. The extrusion process in the FDM process and the optimal setting of the welding parameters in WAAM, in conjunction with suitable path planning, have the greatest influence on component quality. [PERSON] et al. [27] highlighted key challenges for path planning when performing additive welding processes. The robustness of the planning algorithm must be ensured in order to be able to automatically plan paths in complex geometries. WAAM processes pose a particular challenge in this respect, since the width of the material fed and thus the width of the path is large in comparison to the slice area to be filled, unlike in comparable AM processes. Conventional path planners are therefore found  
Figure 5: Example applications of path planning in AM: (**a**) AM of a hollow wing structure [7]; (**b**) path optimization with regard to heat input during welding [8]; and (**c**) slicing software Simplify3D with visible outer contour and filling structure [23]. to be unsuitable as they do not meet the subsequent requirements. A complete coverage of the slice through path planning must be guaranteed. Non-uniform weld bed profiles can occur over the entire path and lead to accumulated defects in the course of the process. The greatest non-uniformities occur at the beginning and end of a weld path [28]. It can therefore be deduced that a path planning algorithm should produce a continuous path whenever possible. [PERSON] et al. further highlighted path crossing as a challenge [27]. Since crossovers in the manufacturing process lead to undesired material accumulation and stress induction [29], a path planner should avoid them if possible. The analysis of whether a crossover is preferable to setting down and restarting the weld path remains open. These challenges do not lose their importance in the specific case of MDAM. However, the implementation brings the kinematic and dynamic properties of the robot movement and their effects on the welding result to the fore. MDAM opens up a multitude of freedoms and possibilities that enable complex path planning for AM. However, the robot is subject to natural limitations. For example, it must be taken into account that paths planned on a geometric basis in the component coordinate system usually lead to robot movements with high velocities and accelerations, or the robot must adopt configurations that are not achievable from a design point of view or lead to collisions with itself and the environment. Manipulator- and process-specific path planning should consider requirements from both robotics and AM together in one path planning algorithm. The following requirements are to be defined for the path planner:  
* Process slices in any spatial orientation. * Consideration of robot kinematics, joint limits and corresponding assurance of feasibility. * Geometrical outward approximation of the cross-section. * Search for the best possible overall path based on defined criteria (from robotics and welding process). * Minimize calculation time. * Cover the entire slice without gaps. * Include path elements that favor continuous and uniform trajectory execution by the robot. * Modular implementation (extensibility and interchangeability of components). It can be stated that path planning algorithms essentially perform the optimization within a single slice in order to improve, for example, mechanical properties. Position and orientation of the slice or kinematic movements are not taken into account. The integration of the kinematic system into the path planning as well as a targeted path smoothing are only introduced in the preliminary work of this contribution. The planning of a completely six-dimensional manufacturing process does not exist.