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Distance-based Formation Control: Background, Principal Results and Issues

거리기반 편대 제어: 기초지식, 주요결과 및 이슈

  • Kang, Sung-Mo (School of Mechatronics, Gwangju Institute of Science and Technology) ;
  • Park, Myoung-Chul (School of Mechatronics, Gwangju Institute of Science and Technology) ;
  • Lee, Byung-Hun (School of Mechatronics, Gwangju Institute of Science and Technology) ;
  • Oh, Kwang-Kyo (Digital Convergence Research Center, KETI) ;
  • Ahn, Hyo-Sung (School of Mechatronics, Gwangju Institute of Science and Technology)
  • 강성모 (광주과학기술원 기전공학부) ;
  • 박명철 (광주과학기술원 기전공학부) ;
  • 이병훈 (광주과학기술원 기전공학부) ;
  • 오광교 (전자부품연구원) ;
  • 안효성 (광주과학기술원 기전공학부)
  • Received : 2013.02.20
  • Accepted : 2013.03.15
  • Published : 2013.05.01

Abstract

This paper provides an overview of distance-based formation control. Firstly, in this paper, we introduce preliminary background materials that are used in defining the distance-based formation control. Then, based on the preliminary background, we briefly review main results developed thus far in this field. Lastly, we provide some issues that need to be studied further in future works.

Keywords

References

  1. J.-S. Kim and Y.-H. Joo, "Asynchronous behavior control algorithm of the swarm robot for surrounding intruders," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 18, no. 9, pp. 812-818, Sep. 2012. https://doi.org/10.5302/J.ICROS.2012.18.9.812
  2. S.-H. Kim, S.-O. Cho, S.-B. Cho, and C.-B. Park, "Development of operation network system and processor in the loop simulation for swarm flight of small UAVs," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 18, no. 5, pp. 401-508, May 2012. https://doi.org/10.5302/J.ICROS.2012.18.5.433
  3. K.-K. Oh, M.-C. Park, and H.-S. Ahn, "A survey of multi-agent formation control: Position-, displacement-, and distance-based approaches," Number: Gist DCASL TR 2012-02, Dec. 2012.
  4. L. Asimow and B. Roth, "The rigidity of graphs, II," Journal of Mathematical Analysis and Applications, vol. 68, no. 1, pp. 171-190, 1979. https://doi.org/10.1016/0022-247X(79)90108-2
  5. B. Hendrickson, "Conditions for unique graph realizations," SIAM Journal on Computing, vol. 21, no. 1, pp. 65-84, 1992. https://doi.org/10.1137/0221008
  6. R. Connelly, "Generic global rigidity," Discrete and Computanional Geometry, vol. 33, no. 4, pp. 549-563, 2005. https://doi.org/10.1007/s00454-004-1124-4
  7. J. M. Hendrickx, B. D. O. Anderson, J.-C. Delvenne, and V. D. Blondel, "Directed graphs for the analysis of rigidity and persistence in autonomous agent systems," International Journal of Robust and Nonlinear Control, vol. 17, no. 10-11, pp. 960-981, 2007. https://doi.org/10.1002/rnc.1145
  8. C. Yu, J. M. Hendrickx, B. Fidan, B. D. O. Anderson, and V. D. Blondel, "Three and higher dimensional autonomous formations: Rigidity, persistence and structural persistence," Automatica, vol. 43, no. 3, pp. 387-402, 2007. https://doi.org/10.1016/j.automatica.2006.08.025
  9. H.-S. Ahn and K.-K. Oh, "Command coordination in multiagent formation: Euclidean distance matrix approaches," in Proceedings of the IEEE International Conference on Control Automation and Systems, pp. 1592-1597, Oct. 2010.
  10. K.-K. Oh and H.-S. Ahn, "A survey of formation of mobile agents," in IEEE Multi-conference on Systems and Control, pp. 1470-1475, Sep. 2010.
  11. B. D. O. Anderson, C. Yu, B. Fidan, and J. M. Hendrickx, "Rigid graph control architectures for autonomous formations," IEEE Control Systems Magazine, vol. 28, no. 6, pp. 48-63, 2008. https://doi.org/10.1109/MCS.2008.929280
  12. L. Krick, M. E. Broucke, and B. A. Francis, "Stabilisation of infinitesimally rigid formations of multi-robot networks," International Journal of Control, vol. 82, no. 3, pp. 423-439, 2009. https://doi.org/10.1080/00207170802108441
  13. F. Dorfler and B. Francis, "Formation control of autonomous robots based on cooperative behavior," in Proceedings of the 2009 European Control Conference, pp. 2432-2437, Aug. 2009.
  14. K.-K. Oh and H.-S. Ahn, "Distance-based undirected formations of single-integrator and double-integrator modeled agents in ndimensional space," International Journal of Robust and Nonlinear Control (published online), 2013.
  15. D. V. Dimarogonas and K. H. Johansson, "On the stability of distance-based formation control," in Proc. of the 47th IEEE Conference on Decision and Control, pp. 1200-1205, Dec. 2008.
  16. D. V. Dimarogonas and K. H. Johansson, "Further results on the stability of distance-based multi-robot formations," in Proceedings of the American Control Conference, pp. 2972-2977, Jun. 2009.
  17. D. V. Dimarogonas and K. H. Johansson, "Stability analysis for multi-agent systems using the incidence matrix: quantized communication and formation control," Automatica, vol. 46, no. 4, pp. 695-700, 2010. https://doi.org/10.1016/j.automatica.2010.01.012
  18. B. D. O. Anderson, C. Yu, S. Dasgupta, and T. H. Summers, "Controlling four agent formations," in Proceedings of the 2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems, pp. 139-144, Sep. 2010.
  19. S. Dasgupta, B. D. O. Anderson, C. Yu, and T. H. Summers, "Controlling rectangular formations," in Proceedings of the Australian Control Conference, pp. 44-49, Nov. 2011.
  20. T. H. Summers, C. Yu, S. Dasgupta, and B. D. O. Anderson, "Formation shape control: global asymptotic stability of a fouragent," in Proceedings of the 48th IEEE Conference on Decision and Control and the 28th Chinese Control Conference, pp. 3002-3007, Dec. 2009.
  21. K.-K. Oh and H.-S. Ahn, "Distance-based formation control using Euclidean distance dynamics matrix: Three-agent case," in Proceedings of the American Control Conference, pp. 4810-4815, Jun. 2011.
  22. K.-K. Oh and H.-S. Ahn, "Distance-based formation control using Euclidean distance dynamics matrix: General cases," in Proceedings of the American Control Conference, pp. 4816-4821, Jun. 2011.
  23. K.-K. Oh and H.-S. Ahn, "Formation control of mobile agents based on inter-agent distance dynamics," Automatica, vol. 47, no. 10, pp. 2306-2312, 2011. https://doi.org/10.1016/j.automatica.2011.08.019
  24. R. Olfati-Saber and R. M. Murray, "Distributed cooperative control of multiple vehicle formations using structural potential functions," in Proceedings of the 15th IFAC World Congress, pp. 495-500, Jul. 2002.
  25. J. Baillieul and A. Suri, "Information patterns and hedging brocketts theorem in controlling vehicle formations," in Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 556-563, Dec. 2003.
  26. T. Eren, B. D. O. Anderson, A. S. Morse, and P. N. Belhumeur, "Information structures to secure control of rigid formations with leader-follower architecture," in Proceedings of the American Control Conference, pp. 2966-2971, Jun. 2005.
  27. K.-K. Oh and H.-S. Ahn, "Distance-based control of cycle-free persistent formations," in IEEE Multi-conference on Systems and Control, pp. 816-821, Sep. 2011.
  28. K.-K. Oh and H.-S. Ahn, "Local asymptotic convergence of a cycle-free persistent formation of double-integrators in threedimensional space," in IEEE Multi-conference on Systems and Control, pp. 692-696, Oct. 2012.
  29. C. Yu, B. D. O. Anderson, S. Dasgupta, and B. Fidan, "Control of minimally persistent formations in the plane," SIAM Journal on Control and Optimization, vol. 48, no. 1, pp. 206-233, 2009. https://doi.org/10.1137/060678592
  30. T. H. Summers, C. Yu, S. Dasgupta, and B. D. O. Anderson, "Control of minimally persistent leader-remote-follower and coleader formations in the plane," IEEE Transactions on Automatic Control, vol. 56, no. 12, pp. 2778-2792, 2011. https://doi.org/10.1109/TAC.2011.2146890
  31. B. D. O. Anderson, C. Yu, S. Dasgupta, and A. S. Morse, "Control of a three-coleader formation in the plane," Systems & Control Letters, vol. 56, no. 9-10, pp. 573-578, 2007. https://doi.org/10.1016/j.sysconle.2007.04.004
  32. M. Cao, A. S. Morse, C. Yu, B. D. O. Anderson, and S. Dasgupta, "Controlling a triangular formation of mobile autonomous agents," in Proc. of the 46th IEEE Conference on Decision and Control, pp. 3603-3608, Dec. 2007.
  33. M. Cao, B. D. O. Anderson, A. S. Morse, and C. Yu, "Control of acyclic formations of mobile autonomous agents," in Proceedings of the 47th IEEE Conference on Decision and Control, pp. 1187-1192, Dec. 2008.
  34. M. Cao, C. Yu, A. S. Morse, B. D. O. Anderson, and S. Dasgupta, "Generalized controller for directed triangle formations," in Proceedings of the 17th IFAC World Congress, pp. 6590-6595, Jul. 2008.
  35. M. Cao, A. S. Morse, C. Yu, B. D. O. Anderson, and S. Dasgupta, "Maintaining a directed, triangular formation of mobile autonomous agents," Communications in Information and Systems, vol. 11, no. 1, pp. 1-16, 2011. https://doi.org/10.4310/CIS.2011.v11.n1.a1
  36. F. Dorfler and B. Francis, "Geometric analysis of the formation problem for autonomous robots," IEEE Transactions on Automatic Control, vol. 55, no. 10, pp. 2379-2384, 2010. https://doi.org/10.1109/TAC.2010.2053735
  37. M.-C. Park, B.-Y. Kim, K.-K. Oh, and H.-S. Ahn, "Control of inter-agent distances in cyclic polygon formations," in IEEE Multi-conference on Systems and Control, pp. 951-955, Oct. 2012.
  38. M.-C. Park, K.-K. Oh, and H.-S. Ahn, "Modified gradient control for acyclic minimally persistent formations to escape from collinear position," in Proceedings of the 51st IEEE Conference on Decision and Control, pp. 1423-1427, Dec. 2012.
  39. A. Belabbas, S. Mou, A. S. Morse, and B. D. O. Anderson, "Robustness issues with undirected formations," in Proceedings of the 51st IEEE Conference on Decision and Control, pp. 1445-1450, Dec. 2012.
  40. J. Aspnes, T. Eren, D. K. Goldenberg, A. S. Morse, W. Whiteley, R. Yang, B. D. O. Anderson, and P. N. Belhumeur, "A theory of network localization," IEEE Transactions on Mobile Computing, vol. 5, no. 12, pp. 1663-1677, 2006. https://doi.org/10.1109/TMC.2006.174
  41. H. Hur and H.-S. Ahn, "Active localization in distributed networks: A framework," in Proceedings of the 2010 International Conference on Control Automation and Systems, pp. 1586-1591, Oct. 2010.
  42. H.-S. Ahn, "Formation coordination for self-mobile localization: framework," in Proceedings of the IEEE International Symposium on Computational Intelligence in Robotics and Automation, pp. 340-348, Dec. 2009.
  43. R. Olfati-Saber, J. A. Fax, and R. M. Murray, "Consensus and cooperation in networked multi-agent systems," Proceedings of the IEEE, vol. 95, no. 1, pp. 215-233, 2007. https://doi.org/10.1109/JPROC.2006.887293
  44. W. Ren, R. W. Beard, and E. M. Atkins, "Information consensus in multivehicle cooperative control," IEEE Control Systems Magazine, vol. 27, no. 2, pp. 71-82, 2007. https://doi.org/10.1109/MCS.2007.338264
  45. K.-K. Oh and H.-S. Ahn, "Formation control of mobile agent groups based on localization," in IEEE Multi-conference on Systems and Control, pp. 822-827, Sep. 2011.
  46. K.-K. Oh and H.-S. Ahn, "Formation control of mobile agents without an initial common sense of orientation," in Proceedings of the 51st IEEE Conference on Decision and Control, pp. 1428-1432, Dec. 2012.
  47. K.-K. Oh and H.-S. Ahn, "Formation control of mobile agents based on distributed position estimation," Accepted for the publication in IEEE Transactions on Automatic Control.
  48. M. Cao, C. Yu, and B. D. O. Anderson, "Formation control using range-only measurements," Automatica, vol. 47, no. 4, pp. 776-781, 2011. https://doi.org/10.1016/j.automatica.2011.01.067
  49. M. Basiri, A. N. Bishop, and P. Jensfelt, "Distributed control of triangular formations with angle-only constraints," Systems & Control Letters, vol. 59, no. 2, pp. 147-154, 2010. https://doi.org/10.1016/j.sysconle.2009.12.010
  50. A. N. Bishop, I. Shames, and B. D. O. Anderson, "Stabilization of rigid formations with direction-only constraints," in 50th IEEE Conference on Decision and Control and European Control Conference, pp. 746-752, Dec. 2011.