Position and Orientation Errors in Mobile Robot Absolute Self-Localization Using an Improved Version of the Generalized Geometric Triangulation Algorithm

Triangulation with active beacons is widely used in the absolute localization of mobile robots. The original generalized geometric triangulation algorithm suffers only from the restrictions that are common to all algorithms that perform self-localization through triangulation. But it is unable to compute position and orientation when the robot is over the segment of the line that goes by beacons 1 and 2 whose origin is beacon 1 and does not contain beacon 2. An improved version of the algorithm allows self-localization even when the robot is over that line segment. Simulations results suggest that a robot is able to localize itself, with small position and orientation errors, over a wide region of the plane, if measurement uncertainty is small enough.