Skip to main content

Towards Optimal Positioning of Surveillance UGVs

  • Conference paper
Optimization and Cooperative Control Strategies

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 381))

Abstract

Unmanned Ground Vehicles (UGVs) equipped with surveillance cameras present a flexible complement to the numerous stationary sensors being used in security applications today. However, to take full advantage of the flexibility and speed offered by a group of UGV platforms, a fast way to compute desired camera locations to cover an area or a set of buildings, e.g., in response to an alarm, is needed.

Building upon earlier results in terrain guarding and sensor placement we propose a way to find candidate guard positions that satisfy a large set of view angle and range constraints simulataneously. Since the original problem is NP-complete, we do not seek to find the true optimal set of guard positions. Instead, a near optimal subset of the candidate points is chosen using a scheme with a known approximation ratio of O(log(n)). A number of examples are presented to illustrate the approach.

All three authors were funded by the Swedish defence materiel administration (FMV) and the Swedish armed forces through the Technologies for Autonomous and Intelligent Systems (TAIS) project. 297316-LB704859.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. ChvĂ¡tal, V.: A Combinatorial Theorem in Plane Geometry. Journal of Combinatorial Theory Series B 18, 39–41 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. GonzĂ¡lez-Banos, H., Latombe, J.: A Randomized Art-Gallery Algorithm for Sensor Placement. In: Proceedings of the 17th Annual Symposium on Computational Geometry, pp. 232–240 (2001)

    Google Scholar 

  3. Amit, Y., Mitchell, J.S.B., Packer, E.: Locating Guards for Visibility Coverage of Polygons. In: Proceedings of the 9th Workshop on Algorithm Engineering and Experiments. Proceedings in Applied Mathematics. SIAM, Philadelphia (2007)

    Google Scholar 

  4. Fragoudakis, C., Markou, E., Zachos, S.: How to Place Efficiently Guards and Paintings in an Art Gallery. In: Bozanis, Panayiotis, Houstis, Elias (eds.). Lecture notes in Computer Science: Advances in Informatics, pp. 145–154. Springer, Heidelberg (2005)

    Google Scholar 

  5. Ganguli, A., Cortes, J., Bullo, F.: Distributed Deployment of Asynchronous Guards in Art Galleries. In: Proceedings of the 2006 American Control Conference (2006)

    Google Scholar 

  6. Urrutia, J.: Art gallery and illumination problems. In: Sack, J.-R., Urrutia, J. (eds.) Handbook of computational geometry, pp. 973–1027. North-Holland Publishing Co., Amsterdam (2000)

    Chapter  Google Scholar 

  7. O’Rourke, J.: Art Gallery Theorems and Algorithms. Oxford University Press, New York (1987)

    MATH  Google Scholar 

  8. Efrat, A., Har-Peled, S., Mitchell, J.: Approximation Algorithms for Two Optimal Location Problems in Sensor Networks. In: Proceedings of the 14th Annual Fall Workshop on Computational Geometry. MIT, Cambridge (2004)

    Google Scholar 

  9. Gerkey, B., Thrun, S., Gordon, G.: Visibility-Based Pursuit-Evasion with Limited Field of View. The International Journal of Robotics Research 25(4), 299–315 (2006)

    Article  Google Scholar 

  10. Hoffmann, F., Kaufmann, M., Kriegel, K.: The Art Gallery Theorem for Polygons With Holes. In: Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pp. 39–48 (1991)

    Google Scholar 

  11. Hollinger, G., Kehagias, A., Singh, S.: Probabilistic Strategies for Pursuit in Cluttered Environments with Multiple Robots. In: IEEE International Conference on Robotics and Automation (2007)

    Google Scholar 

  12. Hoffmann, F.: The Art Gallery Problem for Rectilinear Polygons With Holes. B 94-22, Freie Universitat Berlin, Tech. Rep. (1994)

    Google Scholar 

  13. Eidenbenz, S.: Approximation Algorithms for Terrain Guarding. Information Processing Letters 82(2), 99–105 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Eidenbenz, S.: Optimum Inapproximability Results for Finding Minimum Hidden Guard Sets in Polygons and Terrains. In: Proceedings of the 8th Scandinavian Workshop on Algorithm Theory, pp. 60–68 (2002)

    Google Scholar 

  15. Franklin, W., Ray, C.: Higher isn’t Necessarily Better: Visibility Algorithms and Experiments. In: Proceedings of the 6th International Symposium on Spatial Data Handling, pp. 751–763 (1994)

    Google Scholar 

  16. Franklin, W.: Siting Observers on Terrain. In: Symposium on Spatial Data Handling, Ottawa, pp. 109–120 (2002)

    Google Scholar 

  17. Marengoni, M., Draper, B.: System to Place Observers on a Polyhedral Terrain in Polynomial Time. Image and Vision Computing 18(10), 773–780 (2000)

    Article  Google Scholar 

  18. Chen, S., Li, Y.: Automatic Sensor Placement for Model-Based Robot Vision. Transactions on Systems, Man and Cybernetics, Part B, IEEE 34(1), 393–408 (2004)

    Article  Google Scholar 

  19. VĂ¡zquez, P., Feixas, M., Sbert, M., Heidrich, W.: Viewpoint Selection using Viewpoint Entropy. In: Proceedings of the Vision, Modeling and Visualization Conference, pp. 273–280 (2001)

    Google Scholar 

  20. Speckmann, B., TĂ³th, C.: Allocating Vertex p-Guards in Simple Polygons via Pseudo-Triangulations. Discrete and Computational Geometry 33(2), 345–364 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lee, D., Lin, A.: Computational Complexity of Art Gallery Problems. IEEE Transactions on Information Theory 32(2), 276–282 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  22. Eidenbenz, S.: Inapproximability Results for Guarding Polygons without Holes. In: Proceedings of the 9th International Symposium on Algorithms and Computation, pp. 427–436 (1998)

    Google Scholar 

  23. Eidenbenz, S., Widmayer, P.: An Approximation Algorithm for Minimum Convex Cover with Logarithmic Performance Guarantee. SIAM Journal on Computing 32, 654 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  24. Efrat, A., Har-Peled, S.: Guarding Galleries and Terrains. In: Proceedings of the IFIP 17th World Computer Congress-TC1 Stream/2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing, pp. 181–192 (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nilsson, U., Ă–gren, P., Thunberg, J. (2009). Towards Optimal Positioning of Surveillance UGVs. In: Hirsch, M.J., Commander, C.W., Pardalos, P.M., Murphey, R. (eds) Optimization and Cooperative Control Strategies. Lecture Notes in Control and Information Sciences, vol 381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88063-9_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88063-9_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88062-2

  • Online ISBN: 978-3-540-88063-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics