### State of the Art in Path Generation with Skeletonization
The authors of [43] introduced a so-called fuzzy logic, where uncertainties about the position of individuals are taken into account. While the distance to obstacles is checked locally in this work, a global distance measurement is carried out in this work. A global measurement offers the advantage that it can be decided before the start of the journey whether the destination can be reached at all with sufficient distance to existing obstacles. Similarly, instead of a fixed safety distance, the maximum possible distance to the obstacle should be implicitly calculated for each path alternative. Another scenario is the misalignment of the robot. Since along a path the uncertainty of the robot position is constantly increasing in the global model, a constant correction of the robot position is necessary [9]. To guide these robots back to the individual paths, heuristic methods or, as in our case, skeletonization can be used. These skeletonization methods allow finding of suitable centered paths for the recalibration of the robots using the same procedure as in the path simplification step without affecting the original path model. Furthermore, while the works in [25; 26; 27] focus on path generation and the works in [2; 10] concentrate on the use of path generation of existing twins, this work is mainly concerned with the connection between path generation and digital twin. For example, if the path changes due to altering environmental conditions, this directly leads to an adjustment in the twin. This flexibility enables the fully automated generation of digital twins based on simple map layouts. All combinations of path algorithms and digital twins are based on the use of pathfinding in the digital twin, which does not change during operation as a virtual model (only the states and values in the twin). In this work, however, the digital twin is generated directly from pathfinding, which consider changes in the environment. In contrast to the alternative works, a holistic approach to trajectory generation as well as repositioning of the robot is presented here. In the following, a comprehensive investigation of virtual and real 2D environments as well as virtual 3D environments is performed. A crucial factor is the linking of trajectory generation with information such as trajectory width from the environment itself. So the main scientific contribution can be summed up as an concept which covers:  
* Implicit path finding and clearance width estimation;
* Implicit retracking of robots;
* Implicit multiple tasks and robots in environmental simplification;
* Deterministic path algorithm in 2D and 3D;
* Local updating property;* Digital twin with state graphs for passability redundant path options and embedded process time (task and path). At once in one concept. In the following, a method for constructing the environment based on 2D maps is presented first. Then the modification as well as the incorporation of the markers for the maps are explained. Finally, a digital twin is derived based on the path model. The creation of the digital twins is then tested using different map configurations as well as modifications to the map. It should also be possible to return lost robots directly to the existing paths (back to track). In the following drones and mobile robots are referred to as robots.