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.
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References
Betke, M., Gurvits, L.: Mobile robot localization using landmarks. IEEE Transactions on Robotics and Automation 13(2), 251–263 (1997)
Borenstein, J., Everett, H., Feng, L.: Where am I? Systems and methods for mobile robot positioning. Tech. rep., University of Michigan (March 1996)
Borenstein, J., Everett, H., Feng, L., Wehe, D.: Mobile robot positioning - sensors and techniques. Journal of Robotic Systems 14(4), 231–249 (1997)
Borenstein, J., Feng, L.: Umbmark: A benchmark test for measuring odometry errors in mobile robots. SPIE, Philadelphia (1995)
Briechle, K., Hanebeck, U.: Localization of a mobile robot using relative bearing measurements. IEEE Transactions on Robotics and Automation 20(1), 36–44 (2004)
Casanova, E., Quijada, S., Garcia-Bermejo, J., González, J.: A new beacon-based system for the localization of moving objects. In: IEEE International Conference on Mechatronics and Machine Vision in Practice. Chiang Mai, Tailand (2002)
Cohen, C., Koss, F.: A comprehensive study of three object triangulation. In: Mobile Robots VII, vol. 1831, pp. 95–106. SPIE, San Jose (1993)
Demaine, E.D., López-Ortiz, A., Munro, J.I.J.: Robot localization without depth perception. In: Penttonen, M., Schmidt, E.M. (eds.) SWAT 2002. LNCS, vol. 2368, pp. 177–194. Springer, Heidelberg (2002)
Eiden, J.D.: Géometrie analytique classique. Calvage & Mounet, Paris (2009)
Esteves, J., Carvalho, A., Couto, C.: Generalized geometric triangulation algorithm for mobile robot absolute self-localization. In: International Symposium on Industrial Electronics (ISIE), vol. 1, pp. 346–351. Rio de Janeiro, Brazil (2003)
Esteves, J., Carvalho, A., Couto, C.: Position and orientation errors in mobile robot absolute self-localization using an improved version of the generalized geometric triangulation algorithm. In: IEEE International Conference on Industrial Technology (ICIT), Mumbai, India, pp. 830–835 (December 2006)
Font-Llagunes, J., Batlle, J.: Mobile robot localization. Revisiting the triangulation methods. In: International Federation of Automatic Control (IFAC), Bologna, Italy. Symposium on Robot Control, vol. 8 (September 2006)
Font-Llagunes, J., Batlle, J.: Consistent triangulation for mobile robot localization using discontinuous angular measurements. Robotics and Autonomous Systems 57(9), 931–942 (2009)
Hu, H., Gu, D.: Landmark-based navigation of industrial mobile robots. International Journal of Industry Robot 27(6), 458–467 (2000)
Lee, C., Chang, Y., Park, G., Ryu, J., Jeong, S.G., Park, S., Park, J., Lee, H., Hong, K.S., Lee, M.: Indoor positioning system based on incident angles of infrared emitters. In: Conference of the IEEE Industrial Electronics Society (IECON), vol. 3, pp. 2218–2222 (November 2004)
McGillem, C., Rappaport, T.: A beacon navigation method for autonomous vehicles. IEEE Transactions on Vehicular Technology 38(3), 132–139 (1989)
Pierlot, V., Van Droogenbroeck, M.: A simple and low cost angle measurement system for mobile robot positioning. In: Workshop on Circuits, Systems and Signal Processing (ProRISC), pp. 251–254. Veldhoven, The Netherlands (November 2009)
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Pierlot, V., Urbin-Choffray, M., Van Droogenbroeck, M. (2011). A New Three Object Triangulation Algorithm Based on the Power Center of Three Circles. In: Obdržálek, D., Gottscheber, A. (eds) Research and Education in Robotics - EUROBOT 2011. EUROBOT 2011. Communications in Computer and Information Science, vol 161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21975-7_22
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DOI: https://doi.org/10.1007/978-3-642-21975-7_22
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