Abstract
We investigate autonomous mobile robots in the Euclidean plane. A robot has a function called target function to decide the destination from the robots’ positions, and operates in Look-Compute-Move cycles, i.e., identifies the robots’ positions, computes the destination by the target function, and then moves there. Robots can have different target functions. Let \(\varPhi \) and \(\varPi \) be a set of target functions and a problem, respectively. If the robots whose target functions are chosen from \(\varPhi \) always solve \(\varPi \), we say that \(\varPhi \) is compatible with respect to \(\varPi \). Suppose that \(\varPhi \) is compatible with respect to \(\varPi \). Then two swarms controlled by (possibly different) target functions in \(\varPhi \) can merge to form a larger swarm, and a broken robot can be replaced with another robot with any target function in \(\varPhi \), keeping the correctness of solving \(\varPi \). We investigate the convergence, the gathering, and some fault tolerant convergence problems, assuming crash failures, from the view point of compatibility.
Due to the space limitation, we omit most of the proofs and some contributions. The full version of the paper [4] contains them.
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Notes
- 1.
Roughly, a target function is a function from \((R^2)^n\) to \(R^2\), where R is the set of real numbers and n is the number of robots, i.e., given a snapshot in \((R^2)^n\), it returns a destination point in \(R^2\). Later, we define a target function a bit more carefully.
- 2.
Let P, D, and \(\boldsymbol{o}\) be the multiset of robots’ positions, the axes aligned minimum box containing P, and its center, respectively. Define \(\delta * D = \{ (1 - 2 \delta ) \boldsymbol{x} + 2 \delta \boldsymbol{o} : \boldsymbol{x} \in D \}\). A function \(\phi \) is \(\delta \)-inner, if \(\phi (P)\) is included in \(\delta * D\) for any P.
- 3.
Here, we abuse term “algorithm,” since an algorithm must have a finite description. A target function may not. To compensate the abuse, we insist on giving a finite procedure when we show the existence of a target function.
- 4.
That \((0,0) \not \in P\) means an error of eye sensor, which we assume will not occur, in this paper.
- 5.
For the sake of completeness, we assume that \(\alpha (\phi ,P) = 0\) when \(\phi (P) = \bot \).
- 6.
Since \((0,0) \in Q^{(i)}_t\) by definition, \(\boldsymbol{y} \not = \bot \).
References
Agmon, N., Peleg, D.: Fault-tolerant gathering algorithms for autonomous mobile robots. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms, 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. Robot. Autom. 15, 818–828 (1999)
Asahiro, Y., Suzuki, I., Yamashita, M.: Monotonic self-stabilization and its application to robust and adaptive pattern formation. Theor. Comput. Sci. 934, 21–46 (2022)
Asahiro, Y., Yamashita, M.: Compatibility of convergence algorithms for autonomous mobile robots. arXiv:2301.10949 (2023)
Bouzid, Z., Das, S., Tixeuil, S.: Gathering of mobile robots tolerating multiple crash faults. In: Proceedings of the IEEE 33rd International Conference on Distributed Computing Systems, pp. 337–346 (2013)
Buchin, K., Flocchini, P., Kostitsyana, I., Peters, T., Santoro, N., Wada, K.: On the computational power of energy-constrained mobile robots: algorithms and cross-model analysis. In: Parter, M. (ed.) SIROCCO 2022. LNCS, vol. 13298, pp. 42–61. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-09993-9_3
Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by mobile robots: gathering. SIAM J. Comput. 41, 829–879 (2012)
Cohen, R., Peleg, D.: Convergence properties of the gravitational algorithm in asynchronous robot systems. SIAM J. Comput. 34, 1516–1528 (2005)
Cohen, R., Peleg, D.: Convergence of autonomous mobile robots with inaccurate sensors and movements. SIAM J. Comput. 38, 276–302 (2008)
Cord-Landwehr, A., et al.: A new approach for analyzing convergence algorithms for mobile robots. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6756, pp. 650–661. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22012-8_52
Das, S., Flocchini, P., Santoro, N., Yamashita, M.: Forming sequences of geometric patterns with oblivious mobile robots. Distrib. Comput. 28, 131–145 (2015). https://doi.org/10.1007/s00446-014-0220-9
Défago, X., Potop-Butucaru, M., Tixeuil, S.: Fault-tolerant mobile robots. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities. LNCS, vol. 11340, pp. 234–251. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_10
Flocchini, P.: Gathering. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities. LNCS, vol. 11340, pp. 63–82. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_4
Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by oblivious mobile robots. In: Synthesis Lectures on Distributed Computing Theory 10. Morgan & Claypool Publishers (2012)
Izumi, T., et al.: The gathering problem for two oblivious robots with unreliable compasses. SIAM J. Comput. 41, 26–46 (2012)
Katreniak, B.: Convergence with limited visibility by asynchronous mobile robots. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 125–137. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22212-2_12
Prencipe, G.: Pattern formation. In: Flocchini, P., Prencipe, G., Santoro, N. (eds.) Distributed Computing by Mobile Entities. LNTCS, vol. 11340, pp. 37–62. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-11072-7_3
Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots - formation and agreement problems. SIAM J. Comput. 28, 1347–1363 (1999)
Yamashita, M., Suzuki, I.: Characterizing geometric patterns formable by oblivious anonymous mobile robots. Theor. Comput. Sci. 411, 2433–2453 (2010)
Yamauchi, Y., Uehara, T., Kijima, S., Yamashita, M.: Plane formation by synchronous mobile robots in the three-dimensional Euclidean space. J. ACM 64, 1–43 (2017)
Acknowledgments
This work is supported in part by JSPS KAKENHI Grant Numbers JP17K00024 and JP22K11915.
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Asahiro, Y., Yamashita, M. (2023). Compatibility of Convergence Algorithms for Autonomous Mobile Robots (Extended Abstract). In: Rajsbaum, S., Balliu, A., Daymude, J.J., Olivetti, D. (eds) Structural Information and Communication Complexity. SIROCCO 2023. Lecture Notes in Computer Science, vol 13892. Springer, Cham. https://doi.org/10.1007/978-3-031-32733-9_8
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