Skip to main content
SpringerLink
Log in

Robotics

1997; (Navigation) Blum, Raghavan, Schieber 1998; (Exploration) Deng, Kameda, Papadimitriou 2001; (Localization) Fleischer, Romanik, Schuierer, Trippen

  • Reference work entry
Encyclopedia of Algorithms

  • 308 Accesses

Keywords and Synonyms

Navigation problem – Search problem Exploration problem – Mapping problem ; Gallery tour problem Localization problem – Kidnapped robot problem                    

Problem Definition

Definitions

There are three fundamental algorithmic problems in robotics: exploration, navigation, and localization. Exploration means to draw a complete map of an unknown environment. Navigation (or search) means to find a way to a predescribed location among unknown obstacles. Localization means to determine the current position on a known map. Normally, the environment is modeled as a simple polygon with or without holes. To distinguish the underlying combinatorial problems from the geometric problems, the environment may also be modeled as a graph.

Normally, a robot has a compass, i. e., it can distinguish between different directions, and it can measure travel distance. A blind (or tactile) robot can only sense its immediate surroundings (for example, it only notices an obstacle when it bumps into...

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 399.00
Price excludes VAT (USA)
  • Available as EPUB and 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

Recommended Reading

  1. Albers, S., Kursawe, K., Schuierer, S.: Exploring unknown environments with obstacles. Algorithmica 32(1), 123–143 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Baeza-Yates, R.A., Culberson, J.C., Rawlins, G.J.E.: Searching in the plane. Inf. Comput. 106(2), 234–252 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bar-Eli, E., Berman, P., Fiat, A., Yan, P.: Online navigation in a room. J. Algorithms 17(3), 319–341 (1994)

    Article  MathSciNet  Google Scholar 

  4. Berman, P., Blum, A., Fiat, A., Karloff, H., Rosén, A., Saks, M.: Randomized robot navigation algorithms. In: Proceedings of the 7th ACM-SIAM Symposium on Discrete Algorithms (SODA'96), 1996, pp. 75–84

    Google Scholar 

  5. Blum, A., Raghavan, P., Schieber, B.: Navigating in unfamiliar geometric terrain. SIAM J. Comput. 26(1), 110–137 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  6. Coffman Jr., E.G., Gilbert, E.N.: Paths through a maze of rectangles. Networks 22, 349–367 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  7. Deng, X., Kameda, T., Papadimitriou, C.H.: How to learn an unknown environment. J. ACM 45, 215–245 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dudek, G., Romanik, K., Whitesides, S.: Localizing a robot with minimum travel. SIAM J. Comput. 27(2), 583–604 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Fiat, A., Woeginger, G. (eds.) Online Algorithms – The State of the Art. Springer Lecture Notes in Computer Science, vol. 1442. Springer, Heidelberg (1998)

    Google Scholar 

  10. Fleischer, R., Kamphans, T., Klein, R., Langetepe, E., Trippen, G.: Competitive online approximation of the optimal search ratio. In: Proceedings of the 12th European Symposium on Algorithms (ESA'04). Lecture Notes in Computer Science, vol. 3221, pp. 335–346. Springer, Heidelberg (2004)

    Google Scholar 

  11. Fleischer, R., Romanik, K., Schuierer, S., Trippen, G.: Optimal robot localization in trees. Inf. Comput. 171, 224–247 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Fleischer, R., Trippen, G.: Optimal robot localization in trees. In: Proceedings of the 16th Annual Symposium on Computational Geometry (SoCG'00), 2000, pp. 373–374. A video shown at the 9th Annual Video Review of Computational Geometry

    Google Scholar 

  13. Fleischer, R., Trippen, G.: Experimental studies of graph traversal algorithms. In: Proceedings of the 2nd International Workshop on Experimental and Efficient Algorithms (WEA'03). Lecture Notes in Computer Science, vol. 2647, pp. 120–133. Springer, Heidelberg (2003)

    Google Scholar 

  14. Fleischer, R., Trippen, G.: Exploring an unknown graph efficiently. In: Proceedings of the 13th European Symposium on Algorithms (ESA'05). Lecture Notes in Computer Science, vol. 3669, pp. 11–22. Springer, Heidelberg (2005)

    Google Scholar 

  15. Hoffmann, F., Icking, C., Klein, R., Kriegel, K.: The polygon exploration problem. SIAM J. Comput. 31(2), 577–600 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Karloff, H., Rabani, Y., Ravid, Y.: Lower bounds for randomized k-server and motion-planning algorithms. SIAM J. Comput. 23(2), 293–312 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  17. Kleinberg, J.M.: The localization problem for mobile robots. In: Proceedings of the 35th Symposium on Foundations of Computer Science (FOCS'94), 1994, pp. 521–531

    Google Scholar 

  18. Koenig, S., Mudgal, A., Tovey, C.: A near-tight approximation lower bound and algorithm for the kidnapped robot problem. In: Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms (SODA'06), 2006, pp. 133–142.

    Google Scholar 

  19. Papadimitriou, C.H., Yannakakis, M.: Shortest paths without a map. Theor. Comput. Sci. 84, 127–150 (1991)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Deptartment of Computer Science and Engineering, Fudan University, Shanghai, China

    Rudolf Fleischer

Authors
  1. Rudolf Fleischer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Fleischer, R. (2008). Robotics. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_348

Download citation

Publish with us

Policies and ethics

Search

Navigation