Some geometric localization problems with applications in
robotics

Abstract: In this survey, two different kinds of geometrical localization problems
with applications in robotics are studied. First, the Robot Localization
Problem, which is the problem of determining a robot's unknown position in a
known environment, is studied. Then, the Robot Search Problem, in which the
position of a hidden item in an unknown environment is searched for, is
considered. Throughout the survey mainly two different kinds of sensors are
used to gather data about the robot's surrounding, namely Angle Meters and
Range Meters. Both problems are formulated as geometrical problems, and are
solved using algorithms and data structures from the field of Computational
Geometry. Some aspects crucial to implementing robust algorithms in
practical applications are also considered.