Abstract
We propose scale-free coordinates as an alternative coordinate system for multi-robot systems with large robot populations. Scale-free coordinates allow each robot to know, up to scaling, the relative position and orientation of other robots in the network.We consider a weak sensing model where each robot is only capable of measuring the angle, relative to its own heading, to each of its neighbors. Our contributions are three-fold. First, we derive a precise mathematical characterization of the computability of scale-free coordinates using only bearing measurements, and we describe an efficient algorithm to obtain them. Second, through simulations we show that even in graphs with low average vertex degree, most robots are able to compute the scale-free coordinates of their neighbors using only 2-hop bearing measurements. Finally, we present an algorithm to compute scale-free coordinates that is tailored to low-cost systems with limited communication bandwidth and sensor resolution. Our algorithm mitigates the impact of sensing errors through a simple yet effective noise sensitivity model. We validate our implementation with real-world robot experiments using static accuracy measurements and a simple scale-free motion controller.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
McLurkin, J.: Analysis and Implementation of Distributed Algorithms for Multi-Robot Systems. Ph.D. thesis, Massachusetts Institute of Technology (2008)
McLurkin, J., Lynch, A.J., Rixner, S., Barr, T.W., Chou, A., Foster, K., Bilstein, S.: A low-cost multi-robot system for research, teaching, and outreach. In: Proc. of the Tenth Int. Symp. on Distributed Autonomous Robotic Systems, DARS 2010 (October 2010)
Wei, R., Mahony, R., Austin, D.: A bearing-only control law for stable docking of unicycles. In: Proceedings of the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), vol. 3, 4, pp. 3793–3798 (2003)
Lemaire, T., Lacroix, S., Sola, J.: A practical 3D bearing-only SLAM algorithm. In: 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), pp. 2449–2454 (2005)
Scheding, S., Dissanayake, G., Nebot, E.M., Durrant-Whyte, H.: An experiment in autonomous navigation of an underground mining vehicle. IEEE Transactions on Robotics and Automation 15(1), 85–95 (1999)
Cortes, J., Martinez, S., Karatas, T., Bullo, F.: Coverage control for mobile sensing networks. In: Proceedings of the IEEE International Conference on Robotics and Automation, ICRA 2002, vol. 2, pp. 1327–1332 (2002)
McLurkin, J., Lynch, A., Rixner, S., Barr, T., Chou, A., Foster, K., Bilstein, S.: A low-cost multi-robot system for research, teaching, and outreach. In: Proc. of the Tenth Int. Symp. on Distributed Autonomous Robotic Systems, DARS 2010, p. 200 (2010)
Hendrickson, B.: The molecule problem: Exploiting structure in global optimization. SIAM Journal on Optimization 5(4), 835–857 (1995)
Eren, T., Goldenberg, D.K., Whiteley, W., Yang, Y.R., Morse, A.S., Anderson, B.D.O., Belhumeur, P.N.: Rigidity, computation, and randomization in network localization. In: Proc. 23rd IEEE Conference on Computer Communications, vol. 4, pp. 2673–2684 (2004)
Bekris, K.E., Argyros, A.A., Kavraki, L.E.: Angle-based methods for mobile robot navigation: Reaching the entire plane. In: Proc. EEE International Conference on Robotics and Automation (ICRA), pp. 2373–2378 (2004)
Nagpal, R., Shrobe, H.E., Bachrach, J.: Organizing a Global Coordinate System from Local Information on an Ad Hoc Sensor Network. In: Zhao, F., Guibas, L.J. (eds.) IPSN 2003. LNCS, vol. 2634, pp. 333–348. Springer, Heidelberg (2003)
Ranganathan, P., Morton, R., Richardson, A., Strom, J., Goeddel, R., Bulic, M., Olson, E.: Coordinating a team of robots for urban reconnaisance. In: Proceedings of the Land Warfare Conference (LWC) (November 2010)
Moore, D., Leonard, J., Rus, D., Teller, S.: Robust distributed network localization with noisy range measurements. In: Proc. 2nd International Conference on Embedded Networked Sensor Systems, pp. 50–61 (2004)
Priyantha, N.B., Chakraborty, A., Balakrishnan, H.: The cricket location-support system. In: Proceedings of the 6th Annual International Conference on Mobile Computing and Networking, Boston, Massachusetts, United States, pp. 32–43. ACM (2000)
Lee, S., Amato, N.M., Fellers, J.: Localization based on visibility sectors using range sensors. In: Proc. IEEE Int. Conf. Robot. Autom. (ICRA), pp. 3505–3511 (2000)
Sundaram, B., Palaniswami, M., Reddy, S., Sinickas, M.: Radar localization with multiple unmanned aerial vehicles using support vector regression. In: Third International Conference on Intelligent Sensing and Information Processing, ICISIP 2005, pp. 232–237 (2005)
Montesano, L., Gaspar, J., Santos-Victor, J., Montano, L.: Cooperative localization by fusing vision-based bearing measurements and motion. In: 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2005), pp. 2333–2338 (August 2005)
Loizou, S.G., Kumar, V.: Biologically inspired bearing-only navigation and tracking. In: 2007 46th IEEE Conference on Decision and Control, pp. 1386–1391 (2007)
Ghrist, R., Lipsky, D., Poduri, S., Sukhatme, G.S.: Surrounding Nodes in Coordinate-Free Networks. In: Skella, S., Amato, N.M., Huang, W.H., Mishra, B. (eds.) Algorithmic Foundations of Robotics VII. STAR, vol. 47, pp. 409–424. Springer, Heidelberg (2006)
Bilò, D., Disser, Y., Mihalák, M., Suri, S., Vicari, E., Widmayer, P.: Reconstructing Visibility Graphs with Simple Robots. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 87–99. Springer, Heidelberg (2010)
Whiteley, W.: Matroids from Discrete Geometry. AMS Contemporary Mathematics 197, 171–312 (1996)
Bruck, J., Gao, J., Jiang, A.(A.): Localization and routing in sensor networks by local angle information. ACM Transactions on Sensor Networks 5(1), 1–7 (2009)
Cornejo, A., Khabbazian, M., McLurkin, J.: Theory of scale-free coordinates for multi-robot system with bearing-only sensors. Technical Report (2011), http://mrsl.rice.edu/publications
Horton, J.D.: A Polynomial-Time algorithm to find the shortest cycle basis of a graph. SIAM Journal on Computing 16(2), 358 (1987)
Olson, E.: Apriltag: A robust and flexible multi-purpose fiducial system. Technical report, University of Michigan APRIL Laboratory (May 2010)
McLurkin, J.: Measuring the accuracy of distributed algorithms on Multi-Robot systems with dynamic network topologies. In: 9th International Symposium on Distributed Autonomous Robotic Systems (DARS) (2008)
Rykowski, J.B.: Pose Estimation With Low-Resolution Bearing-Only Sensors. M.S. thesis, Rice University (2011)
O’Kane, J.M., LaValle, S.M.: Comparing the power of robots. The International Journal of Robotics Research 27(1), 5 (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cornejo, A., Lynch, A.J., Fudge, E., Bilstein, S., Khabbazian, M., McLurkin, J. (2013). Scale-Free Coordinates for Multi-robot Systems with Bearing-Only Sensors. In: Frazzoli, E., Lozano-Perez, T., Roy, N., Rus, D. (eds) Algorithmic Foundations of Robotics X. Springer Tracts in Advanced Robotics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36279-8_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-36279-8_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36278-1
Online ISBN: 978-3-642-36279-8
eBook Packages: EngineeringEngineering (R0)