Abstract
This paper considers the convergence problem in autonomous mobile robot systems. A natural algorithm for the problem requires the robots to move towards their center of gravity. Previously it was known that the gravitational algorithm converges in the synchronous or semi-synchronous model, and that two robots converge in the asynchronous model. The current paper completes the picture by proving the correctness of the gravitational algorithm in the fully asynchronous model for any number of robots. It also analyses its convergence rate, and establishes its convergence in the presence of crash faults.
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
Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. In: Proc. 15th ACM-SIAM Symp. on Discrete Algorithms, January 2004, pp. 1063–1071 (2004)
Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: A distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans. Robotics and Automation 15, 818–828 (1999)
Ando, H., Suzuki, I., Yamashita, M.: Formation and agreement problems for synchronous mobile robots with limited visibility. In: Proc. IEEE Symp. of Intelligent Control, August 1995, pp. 453–460 (1995)
Balch, T., Arkin, R.: Behavior-based formation control for multi-robot teams. IEEE Trans. on Robotics and Automation 14 (December 1998)
Beni, G., Hackwood, S.: Coherent swarm motion under distributed control. In: Proc. DARS 1992, pp. 39–52 (1992)
Cao, Y.U., Fukunaga, A.S., Kahng, A.B.: Cooperative mobile robotics: Antecedents and directions. Autonomous Robots 4(1), 7–23 (1997)
Cao, Y.U., Fukunaga, A.S., Kahng, A.B., Meng, F.: Cooperative mobile robots: Antecedents and directions. In: Proc. Int. Conf. of Intel. Robots and Sys., pp. 226–234 (1995)
Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the robots gathering problem. In: Proc. 30th Int. Colloq. on Automata, Languages and Programming, pp. 1181–1196 (2003)
Cieliebak, M., Prencipe, G.: Gathering autonomous mobile robots. In: Proc. 9th Int. Colloq. on Structural Information and Communication Complexity, June 2002, pp. 57–72 (2002)
Cohen, R., Peleg, D.: Robot convergence via center-of-gravity algorithms. In: Proc. 11th Colloq. on Structural Information and Communication Complexity (2004) (to appear)
Feller, W.: An introduction to Probability Theory and its Applications. Wiley, New York (1968)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Hard tasks for weak robots: The role of common knowledge in pattern formation by autonomous mobile robots. In: Proc. 10th Int. Symp. on Algorithms and Computation, pp. 93–102 (1999)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of autonomous mobile robots with limited visibility. In: Proc. 18th Symp. on Theoretical Aspects of Computer Science, February 2001, pp. 247–258 (2001)
Jung, D., Cheng, G., Zelinsky, A.: Experiments in realising cooperation between autonomous mobile robots. In: Proc. Int. Symp. on Experimental Robotics (June 1997)
Kawauchi, Y., Inaba, M., Fukuda, T.: A principle of decision making of cellular robotic system (CEBOT). In: Proc. IEEE Conf. on Robotics and Automation, pp. 833–838 (1993)
Mataric, M.J.: Interaction and Intelligent Behavior. PhD thesis, MIT (1994)
Murata, S., Kurokawa, H., Kokaji, S.: Self-assembling machine. In: Proc. IEEE Conf. on Robotics and Automation, pp. 441–448 (1994)
Parker, L.E.: Designing control laws for cooperative agent teams. In: Proc. IEEE Conf. on Robotics and Automation, pp. 582–587 (1993)
Parker, L.E.: On the design of behavior-based multi-robot teams. J. of Advanced Robotics 10 (1996)
Parker, L.E., Touzet, C.: Multi-robot learning in a cooperative observation task. Distributed Autonomous Robotic Systems 4, 391–401 (2000)
Parker, L.E., Touzet, C., Fernandez, F.: Techniques for learning in multi-robot teams. In: Balch, T., Parker, L.E. (eds.) Robot Teams: From Diversity to Polymorphism, A. K. Peters, Wellesley (2001)
Prencipe, G.: CORDA: Distributed coordination of a set of atonomous mobile robots. In: Proc. 4th European Research Seminar on Advances in Distributed Systems, May 2001, pp. 185–190 (2001)
Prencipe, G.: Distributed Coordination of a Set of Atonomous Mobile Robots. PhD thesis, Universita Degli Studi Di Pisa (2002)
Sugihara, K., Suzuki, I.: Distributed algorithms for formation of geometric patterns with many mobile robots. Journal of Robotic Systems 13(3), 127–139 (1996)
Suzuki, I., Yamashita, M.: Agreement on a common x-y coordinate system by a group of mobile robots. In: Proc. Dagstuhl Seminar on Modeling and Planning for Sensor-Based Intelligent Robots (September 1996)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots - formation and agreement problems. In: Proc. 3rd Colloq. on Structural Information and Communication Complexity, pp. 313–330 (1996)
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM J. on Computing 28, 1347–1363 (1999)
Wagner, I.A., Bruckstein, A.M.: From ants to a(ge)nts. Annals of Mathematics and Artificial Intelligence 31, 1–5 (1996), special issue on ant-robotics
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cohen, R., Peleg, D. (2004). Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-30140-0_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23025-0
Online ISBN: 978-3-540-30140-0
eBook Packages: Springer Book Archive