Self-stabilizing Localization of the Middle Point of a Line Segment by an Oblivious Robot with Limited Visibility
This paper poses a question about a simple localization problem, which is arisen from self-stabilizing location problems by oblivious mobile autonomous robots with limited visibility. The question is if an oblivious mobile robot on a line-segment can localize the middle point of the line-segment in finite steps observing the direction (i.e., Left or Right) and distance to the nearest end point. This problem is also akin to (a continuous version of) binary search, and could be closely related to computable real functions. Contrary to appearances, it is far from trivial if this simple problem is solvable or not, and unsettled yet. This paper is concerned with three variants of the original problem, minimally relaxing, and presents self-stabilizing algorithms for them. We also show an easy impossibility theorem for bilaterally symmetric algorithms.
KeywordsSelf-stabilization Oblivious mobile autonomous robot with limited visibility Computable real functions Continuous binary search
This work is partly supported by JSPS KAKENHI Grant Numbers 15K15938 and 17K19982.
- 2.Ando, H., Suzuki, I., Yamashita, M.: Formation and agreement problems for synchronous mobile robots with limited visibility. In: IEEE Symposium of Intelligent Control, pp. 453–460 (1995)Google Scholar
- 7.Defago, X., Konagaya, A.: Circle formation for oblivious anonymous mobile robots with no common sense of orientation. In: Proceedings of Workshop on Principles of Mobile Computing, pp. 97–104 (2002)Google Scholar
- 8.Euler, L.: Variae observationes circa series infinitas. Commentarii Academiae Scientiarum Petropolitanae 9, 160–188 (1737)Google Scholar
- 15.Fujisaki, G.: Field and Galois Theory. Iwanami, Tokyo (1991). (in Japanese)Google Scholar
- 16.Kleinberg, J.M.: The localization problem for mobile robots. In: Proceedings of FOCS, pp. 521–531 (1994)Google Scholar
- 18.Shibata, M., Mega, T., Ooshita, F., Kakugawa, H., Masuzawa, T.: Uniform deployment of mobile agents in asynchronous rings. In: Proceedings of PODC, pp. 415–424 (2016)Google Scholar