On the Geometry of Some Localisation Problems in Robotics

In this work a couple of localisation problems for mobile robots are revisited. Specifically the problem of finding the location of the robot from the distances to fixed beacons and using time differences of arrivals of signals at several stations are addressed. The aim is to study the geometry of these problems. In particular, tetracyclic coordinates are used to represent circles in the plane. These coordinates are an old idea that have not been used for these types of problem before. The coordinates help to simplify expressions and hence expose the underlying geometric ideas involved in these problems.