### State of the Art in Path Generation with Skeletonization  
If an environment is available, a path to minimize travel time can be found by a common path algorithm based on cost functions such as A*- [14] or Dijkstra-algorithm [15]. Furthermore genetic-based [1], bio-inspired [16; 17], or more recently machine learning-based path-finding methods [4; 18; 19] can also be found. For a more detailed overview in the domain of path-finding, we refer to the review articles [9; 20]. In the following, the A*-algorithm is explained in detail as it constitutes a widely used variant. The A*-algorithm is a heuristic method to find a path from a given source to a given destination [14]. It uses a cost function that chooses the distance of a point to both the source and the destination as the evaluation criterion. However, if a path with the shortest possible distance is chosen as the evaluation criterion, these paths often cut the corners of obstacles, on which for example the digital twin of [10] may touch its obstacles head-on. In addition to the A*-method, a variety of other methods such as Probabilistic Roadmaps (PRM) [21], Rapid Exploring Random Tree (RRT) [22] or Rapid Exploring Random Tree Connect (RRT-C) [23] and Artificial Potential Field (APF) [24] can be used, on which we refer for more details to [24]. These algorithms are used for comparison in Section 3.8 to the proposed path simplification. Although these paths are often the shortest paths to position tools, it may touch the non-passable area. Moreover, since in reality component deformations due to centrifugal forces or path deviations due to tolerances occur in the robot kinematics, a conservative path detection with a certain distance to the non-passable areas should be rather preferred. Another major drawback of the A*-algorithm is the lack of consideration of multiple targets and sources. Classically, a single optimal path is computed for each target-source combination, rather than planning a holistic route. A more holistic approach to reduce the environment to a subset of paths can be achieved by so-called skeletonization, where multiple destinations and sources can be implicitly considered [12]. The authors of [9] narrowed down the possible paths by a so-called thinning procedure to obtain the most centered path suggestions on which the shortest path is processed with A*. While A* processed on the whole 2D or 3D image environment leads to a massive amount of path possibilities, the reduction with skeletonization leads to an environment consisting only of a few topologically connected path suggestions fur A*. Classical trajectory algorithms can capture the shortest path from a source to a target quite efficiently. For this reason, an approach based on skeletonization is used in this work to constrain the possible paths that can also respond to a dynamically changing environment and tackle multiple targets and sources. Furthermore, it is ensured, that the maximum distance of a path to the non-passable areas is implicit embedded in the environment simplification. The authors of [12; 25; 26; 27] used a so-called skeletonization to simplify the path search environment. Skeletonization describes a topic in which centered lines (curve skeletons) of 2D geometric objects or centered surfaces/curves of 3D objects can be determined [28]. Such skeletons can be calculated by using for example [PERSON]'s concept of the maximal inscribed balls [29]. The center points of circles in 2D or spheres in 3D that touch the boundary of the geometric object at least at two points are used to build the skeleton. However, since this type of calculation is not practical, a number of other concepts have been developed based on these medial skeletons as an analogy, such as the grassfire analogy, Maxwell sets, or symmetry sets [28]. Such skeletonization can now be computed for a variety of geometric descriptions such as images [13; 30], point clouds [31], polygon meshes [32], or algebraic functions [33].