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- W1805728873 abstract "The Circle Formation Problem (CFP) consists in the design of a protocol insuring that starting from an initial arbitrary configuration (where no two robots are at the same position), n robots eventually form a regular n -gon in finite time. None of the deterministic solutions proposed so far works for a system made of 4 or 3 robots. This comes from the fact that it is very difficult to maintain a geometric invariant with such a few number of robots, e.g., the smallest enclosing circle, concentric cycles, properties of the convex hull, or a leader. As a matter of fact, due to the high rate of symmetric configurations, the problem was suspected to be unsolvable with 4 robots. In this paper, we disprove this conjecture. We present two non-trivial deterministic protocols that solves CFP with 4 and 3 robots, respectively. The proposed solutions do not require that each robot reaches its destination in one atomic step. Our result closes CFP for any number n ( > 0) of robots in the semi-synchronous model." @default.
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- W1805728873 date "2008-01-01" @default.
- W1805728873 modified "2023-09-23" @default.
- W1805728873 title "Squaring the Circle with Weak Mobile Robots" @default.
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- W1805728873 doi "https://doi.org/10.1007/978-3-540-92182-0_33" @default.
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