### Abstract

In this paper, we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain physical constraints: each atom reaches at most constant velocity and can displace at most a constant number of other atoms. We assume that one of the atoms has access to the coordinates of atoms in the target configuration. Our algorithms involve a total of O(n^{2}) atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n^{2}) parallel steps or do not respect the constraints mentioned above. In fact, in the settings considered, our algorithms are optimal. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configuration space, and only requires local communication.

Original language | English (US) |
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Pages (from-to) | 59-71 |

Number of pages | 13 |

Journal | Robotica |

Volume | 29 |

Issue number | 1 SPEC. ISSUE |

DOIs | |

State | Published - Jan 2011 |

### All Science Journal Classification (ASJC) codes

- Software
- Control and Systems Engineering
- Mathematics(all)
- Computer Science Applications

### Keywords

- Control of robotic systems
- Mobile robots
- Modular robots
- Motion planning
- Path planning

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## Cite this

*Robotica*,

*29*(1 SPEC. ISSUE), 59-71. https://doi.org/10.1017/S026357471000072X