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.
Partially supported by the EU within FP7-ICT-2007-1 under contract no. 215270 (FRONTS) and DFG-project “Smart Teams” within the SPP 1183 “Organic Computing” and International Graduate School Dynamic Intelligent Systems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
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)
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)
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)
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)
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)
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)
Dieudonné, Y., Petit, F.: Self-stabilizing deterministic gathering. In: Algorithmic Aspects of Wireless Sensor Networks, pp. 230–241 (2009)
Souissi, S., Défago, X., Yamashita, M.: Gathering asynchronous mobile robots with inaccurate compasses. In: Principles of Distributed Systems, pp. 333–349 (2006)
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)
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)
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)
Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM Journal on Computing 34(6), 1516–1528 (2005)
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)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Degener, B., Kempkes, B., Kling, P., Meyer auf der Heide, F. (2010). A Continuous, Local Strategy for Constructing a Short Chain of Mobile Robots. In: Patt-Shamir, B., Ekim, T. (eds) Structural Information and Communication Complexity. SIROCCO 2010. Lecture Notes in Computer Science, vol 6058. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13284-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-13284-1_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13283-4
Online ISBN: 978-3-642-13284-1
eBook Packages: Computer ScienceComputer Science (R0)