### Abstract

We investigate the team assembling problem for a swarm of heterogeneous mobile robots which requires the robots to autonomously partition themselves into teams satisfying a given specification A=(a_{1},a_{2},…,a_{k}), where a_{i} is the number of robots with color (i.e., robot type) i in one team. A robot, which is represented by a point in the two-dimensional Euclidean space, is asynchronous, oblivious, and anonymous in the sense that robots with the same color are indistinguishable and all robots execute the same algorithm to determine their moves. It has neither any access to the global coordinate system nor any explicit communication medium. We show that GCD(a_{1},a_{2},…,a_{k})=1 is a necessary and sufficient condition for the robots to have an algorithm to solve the team assembling problem in a self-stabilizing manner, i.e., starting from any arbitrary initial configuration, the robots form teams according to the specification.

Original language | English |
---|---|

Pages (from-to) | 27-41 |

Number of pages | 15 |

Journal | Theoretical Computer Science |

Volume | 721 |

DOIs | |

Publication status | Published - Apr 18 2018 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*721*, 27-41. https://doi.org/10.1016/j.tcs.2018.01.009

**Team assembling problem for asynchronous heterogeneous mobile robots.** / Liu, Zhiqiang; Yamauchi, Yukiko; Kijima, Shuji; Yamashita, Masafumi.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 721, pp. 27-41. https://doi.org/10.1016/j.tcs.2018.01.009

}

TY - JOUR

T1 - Team assembling problem for asynchronous heterogeneous mobile robots

AU - Liu, Zhiqiang

AU - Yamauchi, Yukiko

AU - Kijima, Shuji

AU - Yamashita, Masafumi

PY - 2018/4/18

Y1 - 2018/4/18

N2 - We investigate the team assembling problem for a swarm of heterogeneous mobile robots which requires the robots to autonomously partition themselves into teams satisfying a given specification A=(a1,a2,…,ak), where ai is the number of robots with color (i.e., robot type) i in one team. A robot, which is represented by a point in the two-dimensional Euclidean space, is asynchronous, oblivious, and anonymous in the sense that robots with the same color are indistinguishable and all robots execute the same algorithm to determine their moves. It has neither any access to the global coordinate system nor any explicit communication medium. We show that GCD(a1,a2,…,ak)=1 is a necessary and sufficient condition for the robots to have an algorithm to solve the team assembling problem in a self-stabilizing manner, i.e., starting from any arbitrary initial configuration, the robots form teams according to the specification.

AB - We investigate the team assembling problem for a swarm of heterogeneous mobile robots which requires the robots to autonomously partition themselves into teams satisfying a given specification A=(a1,a2,…,ak), where ai is the number of robots with color (i.e., robot type) i in one team. A robot, which is represented by a point in the two-dimensional Euclidean space, is asynchronous, oblivious, and anonymous in the sense that robots with the same color are indistinguishable and all robots execute the same algorithm to determine their moves. It has neither any access to the global coordinate system nor any explicit communication medium. We show that GCD(a1,a2,…,ak)=1 is a necessary and sufficient condition for the robots to have an algorithm to solve the team assembling problem in a self-stabilizing manner, i.e., starting from any arbitrary initial configuration, the robots form teams according to the specification.

UR - http://www.scopus.com/inward/record.url?scp=85043520791&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043520791&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2018.01.009

DO - 10.1016/j.tcs.2018.01.009

M3 - Article

AN - SCOPUS:85043520791

VL - 721

SP - 27

EP - 41

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -