Abstract
A collection of n anonymous mobile robots is deployed on a unit-perimeter ring or a unit-length line segment. Every robot starts moving at constant speed, and bounces each time it meets any other robot or segment endpoint, changing its walk direction. We study the problem of position discovery, in which the task of each robot is to detect the presence and the initial positions of all other robots. The robots cannot communicate or perceive information about the environment in any way other than by bouncing. Each robot has a clock allowing it to observe the times of its bounces. The robots have no control on their walks, which are determined by their initial positions and the starting directions. Each robot executes the same position detection algorithm, which receives input data in real-time about the times of the bounces, and terminates when the robot is assured about the existence and the positions of all the robots.
Some initial configuration of robots are shown to be infeasible — no position detection algorithm exists for them. We give complete characterizations of all infeasible initial configurations for both the ring and the segment, and we design optimal position detection algorithms for all feasible configurations. For the case of the ring, we show that all robot configurations in which not all the robots have the same initial direction are feasible. We give a position detection algorithm working for all feasible configurations. The cost of our algorithm depends on the number of robots starting their movement in each direction. If the less frequently used initial direction is given to k ≤ n/2 robots, the time until completion of the algorithm by the last robot is \(\frac{1}{2}\lceil \frac{n}{k} \rceil\). We prove that this time is optimal. By contrast to the case of the ring, for the unit segment we show that the family of infeasible configurations is exactly the set of so-called symmetric configurations. We give a position detection algorithm which works for all feasible configurations on the segment in time 2, and this algorithm is also proven to be optimal.
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References
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)
Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. In: Distributed Computing, pp. 235–253 (2006)
Angluin, D., Aspnes, J., Eisenstat, D.: Stably computable predicates are semilinear. In: Proc. of PODC, pp. 292–299 (2006)
Cohen, R., Peleg, D.: Local spreading algorithms for autonomous robot systems. Theoretical Computer Science 399(1-2), 71–82 (2008)
Cohen, R., Peleg, D.: Convergence Properties of the Gravitational Algorithm in Asynchronous Robot Systems. SIAM Journal on Computing 34(6), 1516–1528 (2005)
Czyzowicz, J., Gąsieniec, L., Kosowski, A., Kranakis, E.: Boundary Patrolling by Mobile Agents with Distinct Maximal Speeds. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 701–712. Springer, Heidelberg (2011)
Das, S., Flocchini, P., Santoro, N., Yamashita, M.: On the Computational Power of Oblivious Robots: Forming a Series of Geometric Patterns. In: Proc. of PODC, pp. 267–276 (2010)
Dijkstra, E.W.: Selected Writings on Computing: Personal Perspective, pp. 34–35. Springer, New York (1982)
Efrima, A., Peleg, D.: Distributed algorithms for partitioning a swarm of autonomous mobile robots. Theoretical Computer Science 410, 1355–1368 (2009)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous oblivious robots with limited visibility. Theor. Comput. Sci. 337(1-3), 147–168 (2005)
Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theor. Comput. Sci. 407(1-3), 412–447 (2008)
Friedetzky, T., Gąsieniec, L., Gorry, T., Martin, R.: Observe and Remain Silent (Communication-Less Agent Location Discovery). In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 407–418. Springer, Heidelberg (2012)
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.: Distributed Anonymous Mobile Robots: Formation of Geometric Patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)
Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Th. Comp. Science 411(26-28), 2433–2453 (2010)
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Czyzowicz, J., Gąsieniec, L., Kosowski, A., Kranakis, E., Ponce, O.M., Pacheco, E. (2012). Position Discovery for a System of Bouncing Robots. In: Aguilera, M.K. (eds) Distributed Computing. DISC 2012. Lecture Notes in Computer Science, vol 7611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33651-5_24
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DOI: https://doi.org/10.1007/978-3-642-33651-5_24
Publisher Name: Springer, Berlin, Heidelberg
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