Advertisement

A Continuous, Local Strategy for Constructing a Short Chain of Mobile Robots

  • Bastian Degener
  • Barbara Kempkes
  • Peter Kling
  • Friedhelm Meyer auf der Heide
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6058)

Abstract

We are given an arbitrarily shaped chain of n robots with fixed end points in the plane. We assume that each robot can only see its two neighbors in the chain, which have to be within its viewing range. The goal is to move the robots to the straight line between the end points. Each robot has to base the decision where to move on the relative positions of its neighbors only. Such local strategies considered until now are based on discrete rounds, where a round consists of a movement of each robot. In this paper, we initiate the study of continuous local strategies: The robots may perpetually observe the relative positions of their neighbors, and may perpetually adjust their speed and direction in response to these observations. We assume a speed limit for the robots, that we normalize to one, which corresponds to the viewing range. Our contribution is a continuous, local strategy that needs time \({\mathcal O}(min\{n, (OPT+d) \log(n)\})\). Here d is the distance between the two stationary end points, and OPT is the time needed by an optimal global strategy. Our strategy has the property that the robot which reaches its destination last always moves with maximum speed. Thus, the same bound as above also holds for the distance travelled.

Keywords

Mobile Robot Local Algorithm Local Strategy Optimal Global Algorithm Continuous Time Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Nguyen, H., Farrington, N., Pezeshkian, N., Gupta, A., Spector, J.M.: Autonomous communication relays for tactical robots. In: Proc. of the 11th International Conference on Advanced Robotics (ICAR), pp. 35–40 (2003)Google Scholar
  2. 2.
    Gordon, N., Wagner, I.A., Bruckstein, A.M.: Gathering multiple robotic a(ge)nts with limited sensing capabilities. In: Ant Colony, Optimization and Swarm Intelligence, pp. 142–153 (2004)Google Scholar
  3. 3.
    Dynia, M., Kutyłowski, J., Lorek, P., Meyer auf der Heide, F.: Maintaining Communication Between an Explorer and a Base Station. IFIP International Federation for Information Processing, vol. 216, pp. 137–146. Springer, Boston (2006)Google Scholar
  4. 4.
    Kutyłowski, J., Meyer auf der Heide, F.: Optimal strategies for maintaining a chain of relays between an explorer and a base camp. Theoretical Computer Science 410(36), 3391–3405 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Nguyen, H.G., Pezeshkian, N., Gupta, A., Farrington, N.: Maintaining communication link for a robot operating in a hazardous environment. In: Proc. of the 10th Int. Conf. on Robotics and Remote Systems for Hazardous Environments, American Nuclear Society (2004)Google Scholar
  6. 6.
    Meyer auf der Heide, F., Schneider, B.: Local strategies for connecting stations by small robotic networks. In: IFIP International Federation for Information Processing, Biologically- Inspired Collaborative Computing, September 2008, vol. 268, pp. 95–104. Springer, Boston (2008)Google Scholar
  7. 7.
    Mataric, M.: Designing emergent behaviors: From local interactions to collective intelligence. In: Proc. of the International Conference on Simulation of Adaptive Behavior: From Animals to Animats, vol. 2, pp. 432–441 (1992)Google Scholar
  8. 8.
    Dieudonné, Y., Petit, F.: Self-stabilizing deterministic gathering. In: Algorithmic Aspects of Wireless Sensor Networks, pp. 230–241 (2009)Google Scholar
  9. 9.
    Souissi, S., Défago, X., Yamashita, M.: Gathering asynchronous mobile robots with inaccurate compasses. In: Principles of Distributed Systems, pp. 333–349 (2006)Google Scholar
  10. 10.
    Izumi, T., Katayama, Y., Inuzuka, N., Wada, K.: Gathering autonomous mobile robots with dynamic compasses: An optimal result. In: Distributed Computing, pp. 298–312 (2007)Google Scholar
  11. 11.
    Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. In: SODA 2004: Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA. Society for Industrial and Applied Mathematics, pp. 1070–1078 (2004)Google Scholar
  12. 12.
    Czyzowicz, J., Gasieniec, L., Pelc, A.: Gathering few fat mobile robots in the plane. Theoretical Computer Science, Principles of Distributed Systems 410(6-7), 481–499 (2009)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM Journal on Computing 34(6), 1516–1528 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transactions on Robotics and Automation 15(5), 818–828 (1999)CrossRefGoogle Scholar
  15. 15.
    Ando, H., Suzuki, Y., Yamashita, M.: Formation agreement problems for synchronous mobile robotswith limited visibility. In: Proc. IEEE Syp. of Intelligent Control, pp. 453–460 (1995)Google Scholar
  16. 16.
    Degener, B., Kempkes, B., Meyer auf der Heide, F.: A local O(n 2) gathering algorithm. In: Symposium on Parallelism in Algorithms and Architectures (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bastian Degener
    • 1
  • Barbara Kempkes
    • 1
  • Peter Kling
    • 1
  • Friedhelm Meyer auf der Heide
    • 1
  1. 1.Heinz Nixdorf Institute, Computer Science DepartmentUniversity of Paderborn 

Personalised recommendations