## 5 Case Studies: Localization in a Real-World Indoor Environment
### Case Study 2: Kidnapped Robot Scenario  
Kidnapped robot tests were performed to evaluate how fast and accurately a robot can determine its position in the map when the robot was moved to arbitrary locations. As shown in Figure 10b, six stations were selected for different kidnapped positions. The initial pose represents the initial belief about the current pose from which the robot should recover. For station 1 in a foyer area, a set of sub-tests was performed because there are multiple possible states due to six doors that can be either correctly or incorrectly represented in the map. The doors were either fully open or closed in real life, and the map was altered to show the doors being fully open or closed. At station 1, the robot was placed in the center of the foyer and rotated until it could localize itself. If a full minute of rotation was undertaken without the robot being able to locate itself, the experiment was stopped and marked as a failure. For each case, a total of five identical iterations of the experiment was performed. Each of the cases resulted in the robot being able to localize itself after rotating multiple times. The average time and standard deviations for each iteration are given in Table 3. As shown in the results, all kidnapped robot positioning-utilizing maps accurately presenting the actual door states successfully determined the current positions, and the location error ranged from 2 cm to 8 cm, averaging 5 cm, for all successful localizations. For example, in the case where the map showed all doors open, the robot failed to locate itself regardless of the actual door configurations. However, for each case where the map matched the real-life door configuration, the robot was able to localize itself within the 60 s cut-off. While some of the localization trials were faster for maps that did not match the door layout, localization was more successful and fastest when the maps matched reality. Figure 13 shows how the AMCL particle swarms evolve during rotation searching for the  
Figure 12: Traditional localization scenario: navigation without map updating (**top**) and traditional navigation with map updating (**bottom**). best match between the map and 2D LiDAR scans. Due to the AMCL setting in Table 1, the initial swarm was spread in a wide area around the initial belief. Then, the swarm converged to the most likely positions making the robot jump to different locations. While the robot was able to accurately determine the location when it used an accurate map, a wrong location was determined after four rotations when it used a map with inaccurate door states. The robot's position could not recover from the incorrect localization regardless of many rotations were made. All adjacent doors were closed for the remainder of the kidnapped localization at stations 2-6. A comparison of the average time necessary for localization using the updated map versus the original map was undertaken, with the results being presented in Table 4. Error ranged from 2 cm to 8 cm, averaging 5 cm, for all successful localizations. All of the scenarios relying on the original map failed in localization, except for station 6. This is likely due to the simple rectangular rooms that do not provide enough geometric differentiation for the AMCL algorithm to correctly localize it if it is rotating in one place. This was also found to be the case even if an updated map was used for stations 3 and 5. Station 4 took  
Figure 13: Evolution of particle swarms for actual door configuration OOOOXO using an accurate map (OOOOOXO) and inaccurate map (OOOOOO).