Abstract
This paper describes an intuitive geometric algorithm for the localization of mobile nodes in networks of sensors and robots using range-only or angle-only measurements. The algorithm is a minimalistic approach to localization and tracking when dead reckoning is too inaccurate to be useful. The only knowledge required about the mobile node is its maximum speed. Geometric regions are formed and grown to account for the motion of the mobile node. New measurements introduce new constraints which are propagated back in time to refine previous localization regions. The mobile robots are passive listeners while the sensor nodes actively broadcast making the algorithm scalable to many mobile nodes while maintaining the privacy of individual nodes. We prove that the localization regions found are optimal–that is, they are the smallest regions which must contain the mobile node at that time. We prove that each new measurement requires quadratic time in the number of measurements to update the system, however, we demonstrate experimentally that this can be reduced to constant time.
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References
Briechle, K., Hanebeck, U.D.: Localization of a mobile robot using relative bearing measurements. IEEE Transactions on Robotics and Automation 20(1), 36–44 (2004)
Butler, Z., Corke, P., Peterson, R., Rus, D.: From animals to robots: virtual fences for controlling cattle. In: International Symposium on Experimental Robotics, New Orleans, pp. 4429–4436 (2004)
Castelnovi, M., Sgorbissa, A., Zaccaria, R.: Markov-localization through color features comparison. In: Proceedings of the 2004 IEEE International Symposium on Intelligent Control, pp. 437–442 (2004)
Deans, M., Hebert, M.: Experimental comparison of techniques for localization and mapping using a bearings only sensor. In: Proc. of the ISER 2000 Seventh International Symposium on Experimental Robotics, pp. 395–404. Springer, Heidelberg (2000)
Deffenbaugh, M., Bellingham, J.G., Schmidt, H.: The relationship between spherical and hyperbolic positioning. In: OCEANS 1996. MTS/IEEE. Prospects for the 21st Century. Conference Proceedings, vol. 2, pp. 590–595 (1996)
Dellaert, F., Fox, D., Burgard, W., Thrun, S.: Monte carlo localization for mobile robots. In: IEEE International Conference on Robotics and Automation (ICRA 1999), vol. 2, pp. 1322–1328 (May 1999)
Djugash, J., Singh, S., Corke, P.I.: Further results with localization and mapping using range from radio. In: International Conference on Field and Service Robotics (July 2005)
Dobkin, D.P., Hershberger, J., Kirkpatrick, D.G., Suri, S.: Computing the intersection-depth of polyhedra. Algorithmica 9(6), 518–533 (1993)
Doherty, L., Pister, K.S.J., Ghaoui, L.E.: Convex optimization methods for sensor node position estimation. In: INFOCOM, pp. 1655–1663 (2001)
Eagle, N., Pentland, A.: Reality mining: Sensing complex social systems. Personal and Ubiquitous Computing, 1–14 (September 2005)
Erdmann, M.: Using backprojections for fine motion planning with uncertainty. IJRR 5(1), 19–45 (1986)
Isler, V., Bajcsy, R.: The sensor selection problem for bounded uncertainty sensing models. In: Fourth International Symposium on nformation Processing in Sensor Networks, 2005. IPSN 2005, pp. 151–158 (April 2005)
Johnson, D., Dudgeon, D.: Array Signal Processing. Prentice Hall, Englewood Cliffs (1993)
Kantor, G.A., Singh, S.: Preliminary results in range-only localization and mapping. In: Proceedings of the IEEE Conference on Robotics and Automation (ICRA 2002), vol. 2, pp. 1818–1823 (May 2002)
Kurth, D.: Range-only robot localization and SLAM with radio. Master’s thesis, Robotics Institute Carnegie Mellon University, Pittsburgh PA (May 2004)
McLauchlan, P.F.: A batch/recursive algorithm for 3d scene reconstruction. In: Computer Vision and Pattern Recognition, vol. 2, pp. 738–743 (2000)
Meizel, D., Leveque, O., Jaulin, L., Walter, E.: Initial localization by set inversion. IEEE Transactions on Robotics and Automation 18(3), 966–971 (2002)
Moore, D., Leonard, J., Rus, D., Teller, S.: Robust distributed network localization with noisy range measurements. In: Proc. 2nd ACM Sen.Sys., Baltimore, pp. 50–61 (November 2004)
Olson, E., Leonard, J., Teller, S.: Robust range-only beacon localization. In: Proceedings of Autonomous Underwater Vehicles, pp. 66–75 (2004)
Olson, E., Walter, M., Leonard, J., Teller, S.: Single cluster graph partitioning for robotics applications. In: Robotics Science and Systems, pp. 265–272 (2005)
Priyantha, N.B., Chakraborty, A., Balakrishnan, H.: The cricket location-support system. In: MobiCom 2000: Proceedings of the 6th annual international conference on Mobile computing and networking, pp. 32–43. ACM Press, New York (2000)
Smith, A., Balakrishnan, H., Goraczko, M., Priyantha, N.: Tracking moving devices with the cricket location system. In: MobiSys 2004: Proceedings of the 2nd international conference on Mobile systems applications and services, pp. 190–202. ACM Press, New York (2004)
Spletzer, J.R., Taylor, C.J.: A bounded uncertainty approach to multi-robot localization. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), vol. 2, pp. 1258–1265 (2003)
Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. MIT Press, Cambridge (2005)
Vasilescu, I., Kotay, K., Rus, D., Dunbabin, M., Corke, P.: Data collection, storage, and retrieval with an underwater sensor network. In: SenSys 2005: Proceedings of the 3rd international conference on Embedded networked sensor systems, pp. 154–165. ACM Press, New York (2005)
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Detweiler, C., Leonard, J., Rus, D., Teller, S. (2008). Passive Mobile Robot Localization within a Fixed Beacon Field. In: Akella, S., Amato, N.M., Huang, W.H., Mishra, B. (eds) Algorithmic Foundation of Robotics VII. Springer Tracts in Advanced Robotics, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68405-3_27
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DOI: https://doi.org/10.1007/978-3-540-68405-3_27
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