On the Geometry of Some Localisation Problems in Robotics

Conference paper

Selig, J.M. On the Geometry of Some Localisation Problems in Robotics. 2nd IMA Conference on the Mathematics of Robotics. Online 08 - 10 Sep 2021 Springer.
AuthorsSelig, J.M.
TypeConference paper
Abstract

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.

KeywordsLocalisation; Tetracyclic coordinates; Cyclographic coordinates; Osculating circles
PublisherSpringer
Accepted author manuscript
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Print08 Sep 2021
Publication process dates
Accepted01 Jul 2021
Deposited22 Sep 2021
Additional information

To appear in Proceedings of the 2nd IMA conference on Mathematics for Robotics, published by Springer Verlag.

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