Controlling robot formations by means of spatial reasoning based on rough mereology

  • Zmudzinski, Lukasz (Faculty of Mathematics and Computer Science University of Warmia and Mazury in Olsztyn Sloneczna) ;
  • Polkowski, Lech (Faculty of Mathematics and Computer Science University of Warmia and Mazury in Olsztyn Sloneczna) ;
  • Artiemjew, Piotr (Faculty of Mathematics and Computer Science University of Warmia and Mazury in Olsztyn Sloneczna)
  • 투고 : 2018.07.25
  • 심사 : 2018.11.05
  • 발행 : 2018.09.25


This research focuses on controlling robots and their formations using rough mereology as a means for spatial reasoning. The authors present the state of the art theory behind path planning, robot cooperation domains and ways of creating robot formations. Furthermore, the theory behind Rough Mereology as a way of implementing mereological potential field based path creation and navigation for single and multiple robots is described. An implementation of the algorithm is shown in simulation using RoboSim simulator. Five formations are tested (Line, Rhomboid, Snake, Circle, Cross) along with three decision systems (First In, Leader First, Horde Mode) as compared to other methods.



  1. Ahmed, A., Abdalla, T. and Abed A. (2015), "Path planning of mobile robot by using modified optimized potential field method", Int. J. Comput. Appl., 113(4).
  2. Alami, R., Robert, F., Ingrand, F. and Suzuki, S. (1995), "Multi-robot cooperation through incremental plan merging", Proceedings of the IEEE ICRA, Nagoya, Japan, May.
  3. Alonso-Mora, J., Montijano, E., Schwager, M. and Rus, D. (2016), "Distributed multi-robot formation control among obstacles: A geometric and optimization approach with consensus", Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May.
  4. Barraquand, J. and Latombe, J.C. (1990), "A Monte-Carlo algorithm for path planning with many degrees of freedom", Proceedings of the IEEE International Conference on Robotics and Automation, Cincinnati, Ohio, U.S.A., May.
  5. Brooks, R.A. (1991), "Intelligence without reason", Proceedings of the IJCAI, Sydney, New South Wales, Australia, August.
  6. Brumitt, B., Stentz, A. and Hebert, M. (2001), "CMU UGV group: Autonomous driving with concurrent goals and multiple vehicles: Mission planning and architecture", Autonom. Robot., 11, 103-115.
  7. Buckley, S.J. (1989), "Fast motion planning for multiple moving robots", Robot. Automat., 1, 322-326.
  8. Caloud, P., Choi, W., Latombe, J.C., Pape, L.C. and Yin, M. (1990), "Indoor automation with many mobile robots", Proceedings of the IEEE/RSJ IROS, Ibaraki, Japan, July.
  9. Cao Uny, Y., Fukunaga, A.S. and Kahng, A.B. (1997), "Cooperative mobile robotics: Antecedents and directions", Autonom. Robot., 4, 7-27.
  10. Das, A.K., Fierro, R., Kumar, V., Ostrowski, J.P., Spletzer, J. and Taylor, C.J. (2002), "A vision-based formation control framework", IEEE Trans. Robot. Automat., 18(5), 813-825.
  11. Desai, J.P., Ostrowski, J.P. and Kumar, V. (2001), "Modeling and control of formations of nonholonomic mobile robots", IEEE Trans. Robot. Autom., 17(6), 905-908.
  12. Erdmann, M. and Lozano-Perez, T. (1986), "On multiple moving objects", Proceedings of the IEEE ICRA.
  13. Florea, A.G. and Buiu, C. (2017), Membrane Computing for Distributed Control of Robotic Swarms: Emerging Research and Opportunities, IGI Global, Hershey, Pennsylvania, U.S.A.
  14. Gnys, P. (2017), Mereogeometry Based Approach for Behavioral Robotics, Rough Sets, IJCRS 2017, Lecture Notes in Computer Science, Springer, Cham, 10314.
  15. Grossman, D.D. (1988), "Traffic control of multiple robot vehicles", IEEE J. Robot. Automat., 4(5), 491-497.
  16. Hajek, P. (1998), Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, the Netherlands.
  17. Hopcroft, J., Schwartz, J.T. and Sharir, M. (1984), "On the complexity of motion planning for multiple independent objects: P-space hardness of the warehouseman's problem", Int. J. Robot. Res., 3(4), 76-88.
  18. Hwang, Y. and Ahuja, N. (1992), "Gross motion planning-a survey", ACM Comput. Surv., 24(3), 219-291.
  19. Kube, C.R. and Zhang, H. (1996), "The use of perceptual cues in multi-robot box-pushing", Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, U.S.A., April.
  20. Latombe, J.C. (1991), Robot Motion Planning, Kluwer Acad. Publ., Boston, U.S.A.
  21. Lawton, J.R.T., Beard, R.W. and Young, B.J. (2003), "A decentralized approach to formation maneuvers", IEEE Trans. Robot. Autom., 19(6), 933-941.
  22. La Valle, S.M. and Hutchinson, S.A. (1999), "Multiple robot motion planning under independent objectives", IEEE Trans. Robot. Autom.
  23. Lesniewski, S. (1916), Foundations of General Set Theory (in Polish), Moscow, Russia, (1982), See Also: On the Foundations of Mathematics, Topoi 2, 7-5.
  24. Lewis, M.A. and Tan, K.H. (1997), "High precision formation control of mobile robots using virtual structures", Autonom. Robot., 4(4), 387-403.
  25. Liu, Y.H., Kuroda, S., Naniwa, T., Noborio, H. and Arimoto, S. (1989), "A practical algorithm for planning collision-free coordinated motion of multiple mobile robots", Proceedings of the IEEE ICRA, Scottdale, U.S.A., May.
  26. Mataric, M. (1994), "Interaction and intelligent behavior", Ph.D. Dissertation, MIT, U.S.A.
  27. McFarland, D. (1994), "Towards robot cooperation", Proceedings of the Simulation of Adaptive Behavior.
  28. Mitchell, T. (1998), Machine Intelligence, Prentice-Hall, Englewood Cliffs, New Jersey, U.S.A.
  29. O'Donnell, P.A. and Lozano-Perez, T. (1989), "Deadlock-free and collision-free coordination of two robotic manipulators", Proceedings of the IEEE ICRA, Scottsdale, Arizona, U.S.A., May.
  30. Oikawa, R., Tahimoto, M. and Kambayashi, Y. (2015), "Distributed formation control for swarm robots using mobile agents", Proceedings of the 10th IEEE Jubilee International Symposium on Applied Machine Intelligence and Informatics, Timisoara, Romania, May.
  31. Orozco-Rosas, U., Montiel, O. and Sepulveda, R. (2015), "Pseudo-bacterial potential field based path planner for autonomous mobile robot navigation", Int. J. Adv. Robot. Syst., 12(7), 81.
  32. O'smialowski, P. (2009), "On path planning for mobile robots: Introducing the mereological potential field method in the framework of mereological spatial reasoning", J. Automat. Mob. Robot. Intellig. Syst., 3(2), 24-33.
  33. Osmialowski, P. (2010), "Spatial reasoning based on rough mereology in planning and navigation problems of mobile autonomous robots", Ph.D. Dissertation, Polish-Japanese Institute of IT, Warszawa, Poland.
  34. Paun, G. (2010), "A quick introduction to membrane computing", J. Log. Algebr. Program., 79(6), 291-294.
  35. Polkowski, L. (2011), Approximate Reasoning by Parts. An Introduction to Rough Mereology, IRSL Vol. 20, Springer-Verlag Berlin-Heidelberg.
  36. Polkowski, L. and Osmialowski, P. (2008), Spatial Reasoning with Applications to Mobile Robotics, Mobile Robots Motion Planning, New Challenges, I-Tech Vienna, 433-453.
  37. Polkowski, L. and Osmialowski, P. (2010), Navigation for Mobile Autonomous Robots and Their Formations: An Application of Spatial Reasoning Induced from Rough Mereological Geometry, Mobile Robots Navigation, In Tech Zagreb, 329-354.
  38. Polkowski L. and Skowron, A. (1996), "Rough mereology: A new paradigm for approximate reasoning", Int. J. Approx. Reason., 15(4), 333-365.
  39. Polkowski, L. and Skowron, A. (1994), "Rough mereology", Proceedings of the ISMIS 1994, LNCS, Springer-Verlag, Berlin, Germany.
  40. Polkowski, L. (2017), Rough Sets, Rough Mereology and Uncertainty, Thriving Rough Sets, Stusdies in Computational Intelligence, Springer, Cham.
  41. Polkowski, L., Zmudzinski, L. and Artiemjew, P. (2018), "Robot navigation and path planning by means of rough mereology", Proceedings of the IEEE International Conference on Robotic Computing, Laguna Hills, California, U.S.A., January-February.
  42. PyGame Project .
  43. Revesz, P. (1990), Random Walk in Random and Non Random Environments, World Scientific, Singapore.
  44. Reynolds, C. (1992), "An evolved, vision-based behavioral model of coordinated group motion", Proceedings of the Simulation of Adaptive Behavior, 2, 384-392.
  45. Reynolds, C. (1987), "Flocks, herds and schools. A distributed behavioral model", Comput. Graph., 21(4), 25-34.
  46. RoboSim Project .
  47. Schwartz, J.T. and Sharir, M. (1983), "On the "piano movers" problem: III. Coordinating the motion of several independent bodies: The special case of circular bodies moving amidst polygonal obstacles", Int. J. Robot. Res., 2(3), 46-75.
  48. Svestka, P. and Overmars, M.H. (1998), "Coordinated path planning for multiple robots", Robot. Autonom. Syst., 23(3), 125-152.
  49. Tarski, A. (1959), What is Elementary Geometry?, The Axiomatic Method with Special Reference to Geometry and Physics, Studies in Logic and Foundations of Mathematics, North-Holland, Amsterdam, the Netherlands.
  50. Toibero, J.M., Roberti, F., Carelli, R. and Fiorini, P. (2008), Formation Control for Non-Holonomic Mobile Robots: A Hybrid Approach, In: Lazinica, A., Recent Advances in Multi-Robot Systems, I-Tech Education and Publishing, Vienna, Austria.
  51. Van Benthem, J. (1983), The Logic of Time, Reidel, Dordrecht, the Netherlands.
  52. Vidal, T., Ghallab, M. and Alami, R. (1996), "Incremental mission allocation to a large team of robots", Proceedings IEEE International Conference on Robotics and Automation, Minneapolis, U.S.A., April.
  53. Wei, G., Xiaolu, W. and Xiaoping, Z. (2015), "Lane formation in pedestrian counterflows driven by a potential field considering following and avoidance behaviours", Phys. A: Statis. Mech. Its Appl., 432, 87-101.
  54. Werner, G. and Dyer, M. (1992), "Evolution of herding behavior in artificial animals", Proceedings of the 2nd International Conference on Simulation of Adaptive Behavior, 2, 393.
  55. Xu, D., Zhang, X., Zhu, Z., Chen, C. and Yang, P. (2014), "Behavior-based formation control of swarm robots", Math. Prob. Eng., 2014, 13.
  56. Zmudzinski, L. and Artiemjew, P. (2017), "Path planning based on potential fields from rough mereology", Proceedings of the International Joint Conference on Rough Sets, Olsztyn, Poland, Lecture Notes in Computer Science (LNCS), 10314, 158-168, Springer, Heidelberg, Germany.