Where am I?: indoor localization based on range measurements

Nowadays, robotics plays an important role in increasing fields of application. There exist many environments or situations where mobile robots instead of human beings are used, since the tasks are too hazardous, uncomfortable, repetitive, or costly for humans to perform. The autonomy and the mobility of the robot are often essential for a good solution of these problems. Thus, such a robot should at least be able to answer the question “Where am I?”. This thesis investigates the problem of self-localizing a robot in an indoor environment using range measurements. That is, a robot equipped with a range sensor wakes up inside a building and has to determine its position using only its sensor data and a map of its environment. We examine this problem from an idealizing point of view (reducing it into a pure geometric one) and further investigate a method of Guibas, Motwani, and Raghavan from the field of computational geometry to solving it. Here, so-called visibility skeletons, which can be seen as coarsened representations of visibility polygons, play a decisive role. In the major part of this thesis we analyze the structures and the occurring complexities in the framework of this scheme. It turns out that the main source of complication are so-called overlapping embeddings of skeletons into the map polygon, for which we derive some restrictive visibility constraints. Based on these results we are able to improve one of the occurring complexity bounds in the sense that we can formulate it with respect to the number of reflex vertices instead of the total number of map vertices. This also affects the worst-case bound on the preprocessing complexity of the method. The second part of this thesis compares the previous idealizing assumptions with the properties of real-world environments and discusses the occurring problems. In order to circumvent these problems, we use the concept of distance functions, which model the resemblance between the sensor data and the map, and appropriately adapt the above method to the needs of realistic scenarios. In particular, we introduce a distance function, namely the polar coordinate metric, which seems to be well suited to the localization problem. Finally, we present the ROLOPRO software where most of the discussed algorithms are implemented (including the polar coordinate metric).