A new three object triangulation algorithm based on the power center of three circles

Abstract

Positioning is a fundamental issue in mobile robot applications that can be achieved in multiple ways. Among these methods, triangulation is a proven technique. As it exists for a long time, many variants of triangulation have been proposed. Which variant is most appropriate depends on the application because some methods ignore the beacon ordering while other have blind spots. Some methods are reliable but at a price of increasing complexity or special cases study. In this paper, we present a simple and new three object triangulation algorithm. Our algorithm works in the whole plane (except when the beacons and the robot are concyclic or colinear), and for any beacon ordering. Moreover, it does not need special cases study and has a strong geometrical meaning. Benchmarks show that our algorithm is faster than existing and comparable algorithms. Finally, a quality measure is intrinsically derived for the triangulation result in the whole plane, which can be used to identify the pathological cases, or as a validation gate in Kalman filters. © 2011 Springer-Verlag.