Skip to main content

Optimal Strategy for Walking in Streets with Minimum Number of Turns for a Simple Robot

  • Conference paper
  • First Online:
Book cover Combinatorial Optimization and Applications (COCOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8881))

Abstract

We consider the problem of walking a simple robot in an unknown street. The robot that cannot infer any geometric properties of the street traverses the environment to reach a target \(t\), starting from a point \(s\). The robot has a minimal sensing capability that can only report the discontinuities in the depth information (gaps), and location of the target point once it enters in its visibility region. Also, the robot can only move towards the gaps while moving along straight lines is cheap, but rotation is expensive for the robot. We maintain the location of some gaps in a tree data structure of constant size. The tree is dynamically updated during the movement. Using the data structure, we present an online strategy that generates a search path for the robot with optimal number of turns.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Disser, Y., Ghosh, S.K., Mihalk, M., Widmayer, P.: Mapping a polygon with holes using a compass. Theor. Comput. Sci. (in press, corrected proof) (Available online 18 December 2013)

    Google Scholar 

  2. Fekete, S.P., Mitchell, J.S.B., Schmidt, C.: Minimum covering with travel cost. J. Comb. Optim. 24, 32–51 (2003)

    Article  MathSciNet  Google Scholar 

  3. Ghannadpour, S.F., Noori, S., Tavakkoli-Moghaddam, R.: A multi-objective vehicle routing and scheduling problem with uncertainty in customers request and priority. J. Comb. Optim. 28, 414–446 (2012)

    Article  MathSciNet  Google Scholar 

  4. Guilamo, L., Tovar, B., LaValle, S.M.: Pursuit-evasion in an unknown environment using gap navigation trees. In: Proceedings of the 2004 IEEE/RSJ International Conference on Intelligent Robot’s and Systems, (IROS 2004), vol. 4, pp. 3456–3462. IEEE, September 2004

    Google Scholar 

  5. Hammar, M., Nilsson, B.J., Persson, M.: Competitive exploration of rectilinear polygons. Theor. Comput. Sci. 354(3), 367–378 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Icking, C., Klein, R., Langetepe, E.: An optimal competitive strategy for walking in streets. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 110–120. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  7. Katsev, M., et al.: Mapping and pursuit-evasion strategies for a simple wall-following robot. IEEE Trans. Robot. 27(1), 113–128 (2011)

    Article  MathSciNet  Google Scholar 

  8. Klein, R.: Walking an unknown street with bounded detour. Comput. Geom. 1(6), 325–351 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kumar Ghosh, S., Saluja, S.: Optimal on-line algorithms for walking with minimum number of turns in unknown streets. Comput. Geom. 8(5), 241–266 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kumar Ghosh, S.: Computing the visibility polygon from a convex set and related problems. J. Algorithms 12(1), 75–95 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  11. Lopez-Padilla, R., Murrieta-Cid, R., LaValle, S.M.: Optimal gap navigation for a disc robot. In: Frazzoli, E., Lozano-Perez, T., Roy, N., Rus, D. (eds.) Algorithmic Foundations of Robotics X. STAR, vol. 86, pp. 123–138. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  12. Lpez-Ortiz, A., Schuierer, S.: On-line parallel heuristics, processor scheduling and robot searching under the competitive framework. Theor. Comput. Sci. 310(1), 527–537 (2004)

    Article  Google Scholar 

  13. Mitchell, J.S., Rote, G., Woeginger, G.: Minimum-link paths among obstacles in the plane. Algorithmica 8(1–6), 431–459 (1998)

    MathSciNet  Google Scholar 

  14. Sachs, S., LaValle, S.M., Rajko, S.: Visibility-based pursuit-evasion in an unknown planar environment. Int. J. Robot. Res. 23(1), 3–26 (2004)

    Article  Google Scholar 

  15. Suri, S., Vicari, E., Widmayer, P.: Simple robots with minimal sensing: from local visibility to global geometry. Int. J. Robot. Res. 27(9), 1055–1067 (2008)

    Article  Google Scholar 

  16. Tabatabaei, A., Ghodsi, M.: Walking in streets with minimal sensing. In: Widmayer, P., Xu, Y., Zhu, B. (eds.) COCOA 2013. LNCS, vol. 8287, pp. 361–372. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  17. Tan, X., Bo, J.: Minimization of the maximum distance between the two guards patrolling a polygonal region. Theor. Comput. Sci. 532, 73–79 (2014)

    Article  MATH  Google Scholar 

  18. Tovar, B., Murrieta-Cid, R., LaValle, S.M.: Distance-optimal navigation in an unknown environment without sensing distances. IEEE Trans. Robot. 23(3), 506–518 (2007)

    Article  Google Scholar 

  19. Tovar, B., LaValle, S.M., Murrieta, R.: Optimal navigation and object finding without geometric maps or localization. In Proceedings of the IEEE International Conference on Robotics and Automation, ICRA’03, vol. 1, pp. 464–470. IEEE, September 2003

    Google Scholar 

  20. Xu, Y., et al.: The canadian traveller problem and its competitive analysis. J. Comb. Optim. 18(2), 195–205 (2009)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Azadeh Tabatabaei .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Tabatabaei, A., Ghodsi, M. (2014). Optimal Strategy for Walking in Streets with Minimum Number of Turns for a Simple Robot. In: Zhang, Z., Wu, L., Xu, W., Du, DZ. (eds) Combinatorial Optimization and Applications. COCOA 2014. Lecture Notes in Computer Science(), vol 8881. Springer, Cham. https://doi.org/10.1007/978-3-319-12691-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-12691-3_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12690-6

  • Online ISBN: 978-3-319-12691-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics