Title :
Revisiting trilateration for robot localization
Author :
Thomas, Federico ; Ros, Lluís
Author_Institution :
Inst. de Robotica i Informatica Ind., Barcelona, Spain
Abstract :
Locating a robot from its distances, or range measurements, to three other known points or stations is a common operation, known as trilateration. This problem has been traditionally solved either by algebraic or numerical methods. An approach that avoids the direct algebrization of the problem is proposed here. Using constructive geometric arguments, a coordinate-free formula containing a small number of Cayley-Menger determinants is derived. This formulation accommodates a more thorough investigation of the effects caused by all possible sources of error, including round-off errors, for the first time in this context. New formulas for the variance and bias of the unknown robot location estimation, due to station location and range measurements errors, are derived and analyzed. They are proved to be more tractable compared with previous ones, because all their terms have geometric meaning, allowing a simple analysis of their asymptotic behavior near singularities.
Keywords :
determinants; error analysis; mobile robots; position control; Cayley Menger determinant; error analysis; position control; range measurement; robot localization; robot location estimation; trilateration; Analysis of variance; Computer graphics; Crystallography; Equations; Error analysis; Measurement errors; Position measurement; Robot kinematics; Robot localization; Roundoff errors;
Journal_Title :
Robotics, IEEE Transactions on
DOI :
10.1109/TRO.2004.833793