Skip to main content
Springer Nature Link
Log in

Spatial Reasoning Based on Rough Mereology: A Notion of a Robot Formation and Path Planning Problem for Formations of Mobile Autonomous Robots

  • Chapter
Transactions on Rough Sets XII

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 6190))

Abstract

We address in this work problems of path planning for autonomous robots; we extend this topic by introducing a new definition of a robot formation and we give a parallel treatment of planning and navigation problems for robot formations. In our investigations into problems of multi-robot planning and navigation, we apply rough mereological theory of spatial reasoning to problems of formations of many robots in a rigorous way and we address the planning and navigation problems for formations of many robots.

In approaching those problems, we employ rough mereology – a theory for approximate reasoning based on the notion of a part to a degree. Using the primitive predicate of a rough inclusion, we construct counterparts of classical predicates of elementary geometry as introduced by Alfred Tarski, which serve us in building a description of robot environment.

The software system Player/Stage is employed as the environment in which predicates of rough mereological geometry are implemented as SQL functions and as means of simulation and visualization of robot trajectories to chosen goals.

This work does extend the scope of the Special Session on Rough Mereology at RSKT 2008, Chengdu, Sichuan, China, May 2008.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Arkin, R.C.: Behavior–Based Robotics. MIT Press, Cambridge (1998)

    Google Scholar 

  2. Balch, T., Arkin, R.C.: Behavior–based formation control for multirobot teams. IEEE Transactions on Robotics and Automation 14(6), 926–939 (1998)

    Article  Google Scholar 

  3. van Benthem, J.: The Logic of Time. Reidel, Dordrecht (1983)

    Book  MATH  Google Scholar 

  4. Brumitt, B., Stentz, A., Hebert, M.: CMU UGV Group: Autonomous driving with concurrent goals and multiple vehicles: Mission planning and architecture. Autonomous Robots 11, 103–115 (2001)

    Article  MATH  Google Scholar 

  5. Uny Cao, Y., Fukunaga, A.S., Kahng, A.B.: Cooperative mobile robotics: Antecedents and directions. Autonomous Robots 4, 7–27 (1997)

    Article  Google Scholar 

  6. Chen, Q., Luh, J.Y.S.: Coordination and control of a group of small mobile robots. In: Proceedings of IEEE Intern. Conference on Robotics and Automation, pp. 2315–2320 (1998)

    Google Scholar 

  7. Choset, H., Lynch, K.M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L., Thrun, S.: Principles of Robot Motion. In: Theory, Algorithms, and Implementations. MIT Press, Cambridge (2005)

    Google Scholar 

  8. Clarke, B.L.: A calculus of individuals based on connection. Notre Dame Journal of Formal Logic 22(2), 204–218 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  9. Das, A., Fierro, R., Kumar, V., Ostrovski, J.P., Spletzer, J., Taylor, C.J.: A vision-based formation control framework. IEEE Transactions on Robotics and Automation 18(5), 813–825 (2002)

    Article  Google Scholar 

  10. Gotts, N.M., Gooday, J.M., Cohn, A.G.: A connection based approach to commonsense topological description and reasoning. The Monist 79(1), 51–75 (1996)

    Article  Google Scholar 

  11. Khatib, O.: Real–time obstacle avoidance for manipulators and mobile robots. In: Proceedings IEEE Intern. Conf. on Robotics and Automation, St. Louis MO, pp. 500–505 (1986); Also see: International Journal of Robotic Research 5, 90–98 (1986)

    Google Scholar 

  12. Kramer, J., Scheutz, M.: Development environments for autonomous mobile robots: A survey. Autonomous Robots 22, 101–132 (2007)

    Article  Google Scholar 

  13. Krogh, B.: A generalized potential field approach to obstacle avoidance control, SME-I Technical paper MS84–484, Society of Manufacturing Engineers, Dearborn MI (1984)

    Google Scholar 

  14. Kuipers, B.I., Byun, Y.T.: A qualitative approach to robot exploration and map learning. In: Proceedings of the IEEE Workshop on Spatial Reasoning and Multi-Sensor Fusion, pp. 390–404. Morgan Kaufmann, San Mateo (1987)

    Google Scholar 

  15. Ladanyi, H.: SQL Unleashed. Sams Publishing, USA (1997)

    Google Scholar 

  16. De Laguna, T.: Point, line, surface as sets of solids, J. Philosophy 19, 449–461 (1922)

    Google Scholar 

  17. Latombe, J.: Robot Motion Planning. Kluwer, Boston (1991)

    Book  MATH  Google Scholar 

  18. Ehrich Leonard, N., Fiorelli, E.: Virtual leaders, artificial potentials and coordinated control of groups. In: Proceedings of the 40th IEEE Conference on Decision and Control, Orlando Fla, pp. 2968–2973 (2001)

    Google Scholar 

  19. Leonard, H., Goodman, N.: The calculus of individuals and its uses. The Journal of Symbolic Logic 5, 45–55 (1940)

    Article  MathSciNet  MATH  Google Scholar 

  20. Leśniewski, S.: O Podstawach Ogolnej Teorii Mnogosci (On Foundations of General Theory of Sets. The Polish Scientific Circle in Moscow, Moscow (1916) (in Polish)

    Google Scholar 

  21. Leśniewski, S.: Grundzüge eines neuen Systems der Grundlagen der Mathematik. Fundamenta Mathematicae 24, 242–251 (1926)

    Google Scholar 

  22. Leśniewski, S.: Über die Grundlegen der Ontologie. C.R. Soc. Sci. Lettr. Varsovie III, 111–132 (1930)

    Google Scholar 

  23. Leśniewski, S.: On the Foundations of Mathematics. Przegla̧d Filozoficzny 30, 164–206 (1927) (in Polish); 31, 261–291 (1928); 32, 60–101 (1929); 33, 77–105 (1930); 34, 142–170 (1931)

    Google Scholar 

  24. Leśniewski, S.: On the foundations of mathematics. Topoi 2, 7–52 (1982)

    Google Scholar 

  25. Ośmiałowski, P.: Player and Stage at PJIIT Robotics Laboratory. Journal of Automation, Mobile Robotics and Intelligent Systems 2, 21–28 (2007)

    Google Scholar 

  26. Ośmiałowski, P.: On path planning for mobile robots: Introducing the mereological potential field method in the framework of mereological spatial reasoning. Journal of Automation, Mobile Robotics and Intelligent Systems 3(2), 24–33 (2009)

    Google Scholar 

  27. Ośmiałowski, P., Polkowski, L.: Spatial reasoning based on rough mereology: path planning problem for autonomous mobile robots. In: Transactions on Rough Sets. LNCS (in print)

    Google Scholar 

  28. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, Dordrecht (1991)

    Book  MATH  Google Scholar 

  29. Player/Stage, http://playerstage.sourceforge.net

  30. Polkowski, L.: On connection synthesis via rough mereology. Fundamenta Informaticae 46, 83–96 (2001)

    MathSciNet  MATH  Google Scholar 

  31. Polkowski, L.: A rough set paradigm for unifying rough set theory and fuzzy set theory (a plenary lecture). In: Proceedings RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 70–78. Springer, Heidelberg (2003)

    Google Scholar 

  32. Polkowski, L.: Toward rough set foundations. Mereological approach (a plenary lecture). In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 8–25. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  33. Polkowski, L.: A unified approach to granulation of knowledge and granular computing based on rough mereology: A survey. In: Pedrycz, W., Skowron, A., Kreinovich, V. (eds.) Handbook of Granular Computing, pp. 375–400. John Wiley and Sons, Chichester (2008)

    Chapter  Google Scholar 

  34. Polkowski, L., Ośmiałowski, P.: Spatial reasoning with applications to mobile robotics. In: Jing, X.-J. (ed.) Mobile Robots Motion Planning. New Challenges, pp. 43–55. I-Tech Education and Publishing KG, Vienna (2008)

    Google Scholar 

  35. Polkowski, L., Ośmiałowski, P.: A framework for multiagent mobile robotics: Spatial reasoning based on rough mereology in Player/stage system. In: Chan, C.-C., Grzymala-Busse, J.W., Ziarko, W.P. (eds.) RSCTC 2008. LNCS (LNAI), vol. 5306, pp. 142–149. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  36. Polkowski, L., Skowron, A.: Rough mereology: a new paradigm for approximate reasoning. International Journal of Approximate Reasoning 15(4), 333–365 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  37. Polkowski, L., Skowron, A.: Rough mereology in information systems with applications to qualitative spatial reasoning. Fundamenta Informaticae 43, 291–320 (2000)

    MathSciNet  MATH  Google Scholar 

  38. Ramsey, P.: PostGIS Manual, In: Postgis. pdf file downloaded from Refractions Research home page

    Google Scholar 

  39. Shao, J., Xie, G., Yu, J., Wang, L.: Leader–following formation control of multiple mobile robots. In: Proceedings of the 2005 IEEE Intern. Symposium on Intelligent Control, Limassol, Cyprus, pp. 808–813 (2005)

    Google Scholar 

  40. Skowron, A., Rauszer, C.: The discernibility matrices and functions in decision systems. In: Słowiński, R. (ed.) Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory, pp. 311–362. Kluwer, Dordrecht (1992)

    Google Scholar 

  41. sfsexp, http://sexpr.sourceforge.net

  42. Sugihara, K., Suzuki, I.: Distributed motion coordination of multiple mobile robots. In: Proceedings 5th IEEE Intern. Symposium on Intelligent Control, Philadelphia PA, pp. 138–143 (1990)

    Google Scholar 

  43. Švestka, P., Overmars, M.H.: Coordinated path planning for multiple robots. Robotics and Autonomous Systems 23, 125–152 (1998)

    Article  Google Scholar 

  44. Tarski, A.: Les fondements de la géométrie des corps. In: Supplement to Annales de la Sociéte Polonaise de Mathématique, Cracow, pp. 29–33 (1929)

    Google Scholar 

  45. Tarski, A.: What is elementary geometry? In: The Axiomatic Method with Special Reference to Geometry and Physics, pp. 16–29. North-Holland, Amsterdam (1959)

    Google Scholar 

  46. Tribelhorn, B., Dodds, Z.: Evaluating the Roomba: A low-cost, ubiquitous platform for robotics research and education. In: 2007 IEEE International Conference on Robotics and Automation, ICRA 2007, Roma, Italy, April 10-14, pp. 1393–1399 (2007)

    Google Scholar 

  47. Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics. MIT Press, Cambridge (2005)

    MATH  Google Scholar 

  48. Urdiales, C., Perez, E.J., Vasquez-Salceda, J., Sànchez-Marrè, M., Sandoval, F.: A purely reactive navigation scheme for dynamic environments using Case–Based Reasoning. Autonomous Robots 21, 65–78 (2006)

    Article  Google Scholar 

  49. Whitehead, A.N.: Process and Reality. In: An Essay in Cosmology. Macmillan, New York (1929); (corr. ed.: Griffin, D. R., Sherbourne, D. W. (eds.) (1978))

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Polish–Japanese Institute of Information Technology, Koszykowa 86, 02008, Warsaw, Poland

    Paweı O’smiaıowski & Lech Polkowski

Authors
  1. Paweı O’smiaıowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lech Polkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, Winnipeg, R3T 5V6, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Insitute of Computing Science, Laboratory of Intelligent Decision Support Systems, Poznań University of Technology, Piotrowo 2, 60-965, Poznań, Poland

    Roman Słowiński

  4. Department of Mathematics and Computing Science, Saint Mary’s University, B3H 3C3, Halifax, NS, Canada

    Pawan Lingras

  5. School of Electronics and Information Engineering, Tongji University, 201804, Shanghai, P.R. China

    Duoqian Miao

  6. Faculty of Medicine, Department of Medical Informatics, 89-1 Enya-cho, Shimane University, 693-8501, Izumo, Japan

    Shusaku Tsumoto

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

O’smiaıowski, P., Polkowski, L. (2010). Spatial Reasoning Based on Rough Mereology: A Notion of a Robot Formation and Path Planning Problem for Formations of Mobile Autonomous Robots. In: Peters, J.F., Skowron, A., Słowiński, R., Lingras, P., Miao, D., Tsumoto, S. (eds) Transactions on Rough Sets XII. Lecture Notes in Computer Science, vol 6190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14467-7_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-14467-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14466-0

  • Online ISBN: 978-3-642-14467-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics