Comprehensive study of three-object triangulation

Charles J. Cohen; Frank V. Koss

doi:10.1117/12.143782

4 May 1993 Comprehensive study of three-object triangulation

Charles J. Cohen, Frank V. Koss

Author Affiliations +

Proceedings Volume 1831, Mobile Robots VII; (1993) https://doi.org/10.1117/12.143782
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States

Abstract

Given three landmarks whose location in Cartesian space is known, and a robot with the ability to detect each landmark's heading with respect to the robot's internal orientation, the task is to determine the robot's location and orientation in Cartesian space. Although methods are mentioned in literature, none are completely detailed to the point where useful algorithms to compute the solution are given. This paper presents four methods: (1) Iterative search, (2) Geometric circle intersection, (3) Geometric triangulation, and (4) Newton-Raphson iterative method. All four methods are presented in detail and compared in terms of robustness and computation time. For example, circle intersection fails when all three landmarks lie on a circle, while the Newton-Raphson method fails when the initial guess of the robot's position and orientation is beyond a certain bound. The shortcomings and strengths of each method are discussed. A sensitivity analysis is performed on each method, with noise added to the landmark locations. The authors were involved in a mobile robotics project that demanded a robust three landmark triangulation algorithm. None of the above methods alone was adequate, but an intelligent combination of each method served to overcome their individual weaknesses. The implementation of this overall absolute positioning system is detailed.

Citation Download Citation

Charles J. Cohen and Frank V. Koss "Comprehensive study of three-object triangulation", Proc. SPIE 1831, Mobile Robots VII, (4 May 1993); https://doi.org/10.1117/12.143782

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

;

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE